Publications
2024
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(2024) Physical Review B. 110, 16, 165402. Abstract
Recent quantum Hall experiments have observed "daughter states"next to several plateaus at half-integer filling factors in various platforms. These states were first proposed based on model wave functions for the Moore-Read state by Levin and Halperin. We show that these daughters and their parents belong to an extensive family tree that encompasses all pairing channels and permits a unified description in terms of weakly interacting composite fermions. Each daughter represents a bosonic integer quantum Hall state formed by composite-fermion pairs. The pairing of the parent dictates an additional number of filled composite-fermion Landau levels. We support our field-theoretic composite-fermion treatment by using the K-matrix formalism, analysis of trial wave functions, and a coupled-wire construction. Our analysis yields the topological orders, quantum numbers, and experimental signatures of all daughters of paired states at half-filling and "next-generation"even denominators. Crucially, no two daughters share the same two parents. The unique parentage implies that Hall conductance measurements alone could pinpoint the topological order of even-denominator plateaus. Additionally, we propose a numerically suitable trial wave function for one daughter of the SU(2)2 topological order, which arises at filling factor ν=611. Finally, our insights explain experimentally observed features of transitions in wide-quantum wells, such as suppression of the Jain states with the simultaneous development of half-filled and daughter states.
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(2024) arXiv.org. Abstract
Bilayer graphene has emerged as a key platform for studying non-Abelian fractional quantum Hall (FQH) states. Its multiple half-filled plateaus with large energy gaps combined with its tunability offer an opportunity to distill the principles that determine their topological order. Here, we report four additional plateaus at ν=12 for different spin and valley, revealing a systematic pattern of non-Abelian states according to their Levin--Halperin daughter states. Whenever a pair of N=1 Landau levels cross, anti-Pfaffian and Pfaffian develop at half filling of the lower and higher levels, respectively. In the N=0 levels, where half-filled plateaus are absent, we instead observe four unexpected incompressible quarter-filled states along with daughters. The mutual exclusion of half- and quarter-filled states indicates a robust competition between the interactions favoring either paired states of two-flux or four-flux composite fermions. Finally, we observe several FQH states that require strong interactions between composite fermions. Our combined findings herald a new generation of quantum Hall physics in graphene-based heterostructures.
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(2024) Physical Review Research. 6, 2, 023047. Abstract
We study the entanglement spectra of surface states of symmetry-protected topological phases. The topological bulk imprints the surface with an anomaly that does not permit it to form a trivial "vacuum"state that is gapped, unfractionalized, and symmetry preserving. Any surface wave function encodes the topology of the underlying bulk in addition to a specific surface phase. We show that the real-space entanglement spectrum of such surface wave functions are dominated by the bulk topology and do not readily permit identifying the surface phase. We thus use a modified form of entanglement spectra that incorporates the anomaly and argue that they correspond to physical edge states between different surface states. We support these arguments by explicit analytical and numerical calculations for free and interacting surfaces of three-dimensional topological insulators of electrons.
2023
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(2023) Physical Review B. 108, 24, L241102. Abstract
Non-Abelian phases are among the most highly sought states of matter, with those whose anyons permit universal quantum gates constituting the ultimate prize. The most promising candidate of such a phase is the fractional quantum Hall plateau at filling factors ν=125, which putatively facilitates Fibonacci anyons. Experimental validation of this assertion poses a major challenge and remains elusive. We present a measurement protocol that could achieve this goal with already-demonstrated experimental techniques. Interfacing the ν=125 state with any readily available Abelian state yields a binary outcome of upstream noise or no noise. Judicious choices of the Abelian states can produce a sequence of yes-no outcomes that fingerprint the possible non-Abelian phase by ruling out its competitors. Crucially, this identification is insensitive to the precise value of the measured noise and can uniquely identify the anyon type at filling factors ν=125. In addition, it can distinguish any non-Abelian candidates at half-filling in graphene and semiconductor heterostructures.
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(2023) Physical Review B. 108, 18, 184406. Abstract
The Kitaev honeycomb model, which is exactly solvable by virtue of an extensive number of conserved quantities, supports a gapless quantum spin liquid phase as well as gapped descendants relevant for fault-tolerant quantum computation. We show that the anomalous edge modes of one-dimensional (1D) cluster-state-like symmetry-protected topological (SPT) phases provide natural building blocks for a variant of the Kitaev model that enjoys only a subextensive number of conserved quantities. The symmetry of our variant allows a single additional nearest-neighbor perturbation, corresponding to an anisotropic version of the Γ term studied in the context of Kitaev materials. We determine the phase diagram of the model using exact diagonalization. Additionally, we use the density matrix renormalization group to show that the underlying 1D SPT building blocks can emerge from a ladder Hamiltonian exhibiting only two-spin interactions supplemented by a Zeeman field. Our approach may provide a pathway toward realizing Kitaev honeycomb spin liquids in spin-orbit-coupled Mott insulators.
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(2023) Physical Review B. 107, 11, 115113. Abstract
Symmetry-resolved entanglement is a useful tool for characterizing symmetry-protected topological states. In two dimensions, their entanglement spectra are described by conformal field theories but the symmetry resolution is largely unexplored. However, addressing this problem numerically requires system sizes beyond the reach of exact diagonalization. Here, we develop tensor-network methods that can access much larger systems and determine universal and nonuniversal features in their entanglement. Specifically, we construct one-dimensional matrix product operators that encapsulate all the entanglement data of two-dimensional symmetry-protected topological states. We first demonstrate our approach for the Levin-Gu model. Next, we use the cohomology formalism to deform the phase away from the fine-tuned point and track the evolution of its entanglement features and their symmetry resolution. The entanglement spectra are always described by the same conformal field theory. However, the levels undergo a spectral flow in accordance with an insertion of a many-body Aharonov-Bohm flux.
2022
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(2022) Physical Review B. 106, 16, 165114. Abstract
Strong interactions between electrons in two dimensions can realize phases where their spins and charges separate. We capture this phenomenon within a dual formulation. Focusing on square lattices, we analyze the long-wavelength structure of vortices when the microscopic particles - electrons or spinful bosons - are near half-filling. These conditions lead to a compact gauge theory of spinons and chargons, which arise as the fundamental topological defects of the low-energy vortices. The gauge theory formulation is particularly suitable for studying numerous exotic phases and transitions. We support the general analysis by an exact implementation of the duality on a coupled-wire array. Finally, we demonstrate how the latter can be exploited to construct parent Hamiltonians for fractional phases and their transitions.
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(2022) Physical Review B. 105, 20, L201110. Abstract
Electrons undergoing a Mott transition may shed their charge but persist as neutral excitations of a quantum spin liquid (QSL). We introduce concrete two-dimensional models exhibiting this exotic behavior as they transition from superconducting or topological phases into fully charge-localized insulators. We study these Mott transitions and the confinement of neutral fermions at a second transition into a symmetry-broken phase. In the process, we also derive coupled-wire parent Hamiltonians for a non-Abelian QSL and a Z4 QSL.
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(2022) Physical Review B. 105, L201110. Abstract
Electrons undergoing a Mott transition may shed their charge but persist as neutral excitations of a quantum spin liquid (QSL). We introduce concrete two-dimensional models exhibiting this exotic behavior as they transition from superconducting or topological phases into fully charge-localized insulators. We study these Mott transitions and the confinement of neutral fermions at a second transition into a symmetry-broken phase. In the process, we also derive coupled-wire parent Hamiltonians for a non-Abelian QSL and a Z4 QSL.
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(2022) Physical Review Letters. 128, 1, 016401. Abstract
We propose an experiment to identify the topological order of the nu = 5/2 state through a measurement of the electric conductance of a mesoscopic device. Our setup is based on interfacing nu = 2, 5/2, and 3 in the same device. Its conductance can unambiguously establish or rule out the particle-hole symmetric Pfaffian topological order, which is supported by recent thermal measurements. Additionally, it distinguishes between the Moore-Read and anti-Pfaffian topological orders, which are favored by numerical calculations.
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(2022) Science. 375, 6577, p. 193-197 Abstract
Quantum Hall states can harbor exotic quantum phases. The nature of these states is reflected in the gapless edge modes owing to bulk-edge correspondence. The most-studied putative non-abelian state is the spin-polarized filling factor ν = 5/2, which permits different topological orders that can be abelian or non-abelian. We develop a method that interfaces the studied quantum state with another state, and employ it to identify the topological order of the ν = 5/2 state. The interface between two half-planes, one hosting the ν = 5/2 state and the other an integer ν = 3 state, supports a fractional ν = 1/2 charge mode and a neutral Majorana mode. The counter-propagating chirality of the Majorana mode, probed by measuring partition noise, is consistent with the particle-hole Pfaffian (PH-Pf) topological order and rules out the anti-Pfaffian order.
2020
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(2020) Physical Review Research. 2, 043437. Abstract
The fractionalization of microscopic degrees of freedom is a remarkable manifestation of strong interactions in quantum many-body systems. Analytical studies of this phenomenon are primarily based on two distinct frameworks: field theories of partons and emergent gauge fields, or coupled arrays of one-dimensional quantum wires. We unify these approaches for two-dimensional spin systems. Via exact manipulations, we demonstrate how parton gauge theories arise in microscopic wire arrays and explicitly relate spin operators to emergent quasiparticles and gauge-field monopoles. This correspondence allows us to compute physical correlation functions within both formulations and leads to a straightforward algorithm for constructing parent Hamiltonians for a wide range of exotic phases. We exemplify this technique for several chiral and nonchiral quantum spin liquids.
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(2020) Physical Review Letters. 125, 236802. Abstract
The quest for non-Abelian quasiparticles has inspired decades of experimental and theoretical efforts, where the scarcity of direct probes poses a key challenge. Among their clearest signatures is a thermal Hall conductance with quantized half-integer value in units of κ0=π2kB2T/3h (T is temperature, h the Planck constant, kB the Boltzmann constant). Such values were recently observed in a quantum-Hall system and a magnetic insulator. We show that nontopological "thermal metal"phases that form due to quenched disorder may disguise as non-Abelian phases by well approximating the trademark quantized thermal Hall response. Remarkably, the quantization here improves with temperature, in contrast to fully gapped systems. We provide numerical evidence for this effect and discuss its possible implications for the aforementioned experiments.
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(2020) Physical Review B. 102, 195153. Abstract
We introduce a family of paired-composite-fermion trial wave functions for any odd Cooper-pair angular momentum. These wave functions are parameter-free and can be efficiently projected into the lowest Landau level. We use large-scale Monte Carlo simulations to study three cases: Firstly, the Moore-Read phase, which serves us as a benchmark. Secondly, we explore the pairing associated with the anti-Pfaffian and the particle-hole-symmetric Pfaffian. Specifically, we assess whether their trial states feature exponentially decaying correlations and thus represent gapped phases of matter. For Moore-Read and anti-Pfaffian we find decay lengths of ζMoore-Read=1.30(5) and ζanti-Pfaffian=1.38(14), in units of the magnetic length. By contrast, for the case of PH-Pfaffian, we find no evidence of a finite length scale for up to 56 particles.
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(2020) Physical Review Letters. 124, 096802. Abstract
Time crystals form when arbitrary physical states of a periodically driven system spontaneously break discrete time-translation symmetry. We introduce one-dimensional time-crystalline topological superconductors, for which time-translation symmetry breaking and topological physics intertwine-yielding anomalous Floquet Majorana modes that are not possible in free-fermion systems. Such a phase exhibits a bulk magnetization that returns to its original form after two drive periods, together with Majorana end modes that recover their initial form only after four drive periods. We propose experimental implementations and detection schemes for this new state.
2018
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(2018) Physical Review B. 98, 201111. Abstract
We introduce (3+1)-dimensional models of short-range-interacting electrons that form a strongly correlated many-body state whose low-energy excitations are relativistic neutral fermions coupled to an emergent gauge field, QED4. We discuss the properties of this critical state and its instabilities towards exotic phases such as a gapless "composite" Weyl semimetal and fully gapped topologically ordered phases that feature anyonic pointlike as well as linelike excitations. These fractionalized phases describe electronic insulators. They may be further enriched by symmetries which result in the formation of nontrivial surface states.
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(2018) Physical Review B. 98, 081107. Abstract
We numerically assess model wave functions for the recently proposed particle-hole-symmetric Pfaffian ("PHP-faffian") topological order, a phase consistent with the recently reported thermal Hall conductance [M. Banerjee et al., Nature 559, 205 (2018)] at the ever enigmatic v = 5/2 quantum Hall plateau. We find that the most natural Moore-Read-inspired trial state for the PH-Pfaffian, when projected into the lowest Landau level, exhibits a remarkable numerical similarity on accessible system sizes with the corresponding (compressible) composite Fermi liquid. Consequently, this PH-Pfaffian trial state performs reasonably well energetically in the half-filled lowest Landau level, but is likely not a good starting point for understanding the v = 5/2 ground state. Our results suggest that the PH-Pfaffian model wave function either encodes anomalously weak p-wave pairing of composite fermions or fails to represent a gapped, incompressible phase altogether.
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(2018) Physical Review B. 98, 085143. Abstract
Parafermion zero modes are generalizations of Majorana modes that underlie comparatively rich non-Abeliananyon properties. We introduce exact mappings that connect parafermion chains, which can emerge in two-dimensional fractionalized media, to strictly one-dimensional fermionic systems. In particular, we show that parafermion zero modes in the former setting translate into symmetry-enriched Majorana modes that intertwine with a bulk order parameter-yielding braiding and fusion properties that are impossible in standard Majorana platforms. Fusion characteristics of symmetry-enriched Majorana modes are directly inherited from the associated parafermion setup and can be probed via two kinds of anomalous pumping cycles that we construct. Most notably, our mappings relate Z(4) parafermions to conventional electrons with time-reversal symmetry. In this case, one of our pumping protocols entails fairly minimal experimental requirements: Cycling a weakly correlated wire between a trivial phase and time-reversal-invariant topological superconducting state produces an edge magnetization with quadrupled periodicity. Our work highlights new avenues for exploring beyond-Majorana physics in experimentally relevant one-dimensional electronic platforms, including proximitized ferromagnetic chains.
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(2018) Physical Review Letters. 121, 026801. Abstract
The thermal Hall conductance in the half-filled first Landau level was recently measured to take the quantized noninteger value κxy=5/2 (in units of temperature times π2kB2/3h), which indicates a non-Abelian phase of matter. Such exotic states have long been predicted to arise at this filling factor, but the measured value disagrees with numerical studies, which predict κxy=3/2 or 7/2. We resolve this contradiction by invoking the disorder-induced formation of mesoscopic puddles with locally κxy=3/2 or 7/2. Interactions between these puddles generate a coherent macroscopic state that exhibits a plateau with quantized κxy=5/2. The non-Abelian quasiparticles characterizing this phase are distinct from those of the microscopic puddles and, by the same mechanism, could even emerge from a system comprised of microscopic Abelian puddles.
2017
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(2017) Physical Review X. 7, 041016. Abstract
Recent work on a family of boson-fermion mappings has emphasized the interplay of symmetry and duality: Phases related by a particle-vortex duality of bosons (fermions) are related by time-reversal symmetry in their fermionic (bosonic) formulation. We present exact mappings for a number of concrete models that make this property explicit on the operator level. We illustrate the approach with one-and two-dimensional quantum Ising models and then similarly explore the duality web of complex bosons and Dirac fermions in (2 + 1) dimensions. We generalize the latter to systems with long-range interactions and discover a continuous family of dualities embedding the previously studied cases.
2016
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(2016) Physical Review Letters. 117, 136802. Abstract
We introduce a particle-hole-symmetric metallic state of bosons in a magnetic field at odd-integer filling. This state hosts composite fermions whose energy dispersion features a quadratic band touching and corresponding 2π Berry flux protected by particle-hole and discrete rotation symmetries. We also construct an alternative particle-hole symmetric state—distinct in the presence of inversion symmetry—without Berry flux. As in the Dirac composite Fermi liquid introduced by Son [Phys. Rev. X 5, 031027 (2015)], breaking particle-hole symmetry recovers the familiar Chern-Simons theory. We discuss realizations of this phase both in 2D and on bosonic topological insulator surfaces, as well as signatures in experiments and simulations.
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(2016) Physical Review Letters. 117, 016802. Abstract
We explicitly derive the duality between a free electronic Dirac cone and quantum electrodynamics in (2+1) dimensions (QED3) with N=1 fermion flavors. The duality proceeds via an exact, nonlocal mapping from electrons to dual fermions with long-range interactions encoded by an emergent gauge field. This mapping allows us to construct parent Hamiltonians for exotic topological-insulator surface phases, derive the particle-hole-symmetric field theory of a half-filled Landau level, and nontrivially constrain QED3 scaling dimensions. We similarly establish duality between bosonic topological insulator surfaces and N=2 QED3.
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(2016) Physical Review Letters. 116, 036803. Abstract
We show that boundaries of 3D weak topological insulators can become gapped by strong interactions while preserving all symmetries, leading to Abelian surface topological order. The anomalous nature of weak topological insulator surfaces manifests itself in a nontrivial action of symmetries on the quasiparticles; most strikingly, translations change the anyon types in a manner impossible in strictly 2D systems with the same symmetry. As a further consequence, screw dislocations form non-Abelian defects that trap Z4 parafermion zero modes.
2015
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(2015) Physical Review X. 5, Abstract
Spontaneous breaking of translational symmetry, known as density-wave order, is common in nature. However, such states are strongly sensitive to impurities or other forms of frozen disorder leading to fascinating glassy phenomena. We analyze impurity effects on a particularly ubiquitous form of broken translation symmetry in solids: a spin-density wave (SDW) with spatially modulated magnetic order. Related phenomena occur in pair-density-wave (PDW) superconductors where the superconducting order is spatially modulated. For weak disorder, we find that the SDW or PDW order can generically give way to a SDW or PDW glass—new phases of matter with a number of striking properties, which we introduce and characterize here. In particular, they exhibit an interesting combination of conventional (symmetry-breaking) and spin-glass (Edwards-Anderson) order. This is reflected in the dynamic response of such a system, which—as expected for a glass—is extremely slow in certain variables, but, surprisingly, is fast in others. Our results apply to all uniaxial metallic SDW systems where the ordering vector is incommensurate with the crystalline lattice. In addition, the possibility of a PDW glass has important consequences for some recent theoretical and experimental work on La2−xBaxCu2O4.
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(2015) Physical Review B. 91, 115111. Abstract
States of matter with a sharp Fermi surface but no well-defined Landau quasiparticles arise in a number of physical systems. Examples include (i) quantum critical points associated with the onset of order in metals; (ii) spinon Fermi-surface [U(1) spin-liquid] state of a Mott insulator; (iii) Halperin-Lee-Read composite fermion charge liquid state of a half-filled Landau level. In this work, we use renormalization group techniques to investigate possible instabilities of such non-Fermi liquids in two spatial dimensions to Cooper pairing. We consider the Ising-nematic quantum critical point as an example of an ordering phase transition in a metal, and demonstrate that the attractive interaction mediated by the order-parameter fluctuations always leads to a superconducting instability. Moreover, in the regime where our calculation is controlled, superconductivity preempts the destruction of electronic quasiparticles. On the other hand, the spinon Fermi surface and the Halperin-Lee-Read states are stable against Cooper pairing for a sufficiently weak attractive short-range interaction; however, once the strength of attraction exceeds a critical value, pairing sets in. We describe the ensuing quantum phase transition between (i) U(1) and Z2 spin-liquid states; (ii) Halperin-Lee-Read and Moore-Read states.
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(2015) Physical Review X. 5, 011011. Abstract
We introduce exotic gapless states—“composite Dirac liquids”—that can appear at a strongly interacting surface of a three-dimensional electronic topological insulator. Composite Dirac liquids exhibit a gap to all charge excitations but nevertheless feature a single massless Dirac cone built from emergent electrically neutral fermions. These states thus comprise electrical insulators that, interestingly, retain thermal properties similar to those of the noninteracting topological insulator surface. A variety of novel fully gapped phases naturally descend from composite Dirac liquids. Most remarkably, we show that gapping the neutral fermions via Cooper pairing—which crucially does not violate charge conservation—yields symmetric non-Abelian topologically ordered surface phases captured in several recent works. Other (Abelian) topological orders emerge upon alternatively gapping the neutral Dirac cone with magnetism. We establish a hierarchical relationship between these descendant phases and expose an appealing connection to paired states of composite Fermi liquids arising in the half filled Landau level of two-dimensional electron gases. To controllably access these states we exploit a quasi-1D deformation of the original electronic Dirac cone that enables us to analytically address the fate of the strongly interacting surface. The algorithm we develop applies quite broadly and further allows the construction of symmetric surface topological orders for recently introduced bosonic topological insulators.
2012
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(2012) Physical Review B. 86, 115138. Abstract
We study theoretically quantum melting transitions of stripe order in a metallic environment, and the associated reconstruction of the electronic Fermi surface. We show that such quantum phase transitions can be continuous in situations where the stripe melting occurs by proliferating pairs of dislocations in the stripe order parameter without proliferating single dislocations. We develop an intuitive picture of such phases as “stripe loop metals” where the fluctuating stripes form closed loops of arbitrary size at long distances. We obtain a controlled critical theory of a few different continuous quantum melting transitions of stripes in metals. At such a (deconfined) critical point, the fluctuations of the stripe order parameter are strongly coupled, yet tractable. They also decouple dynamically from the Fermi surface. We calculate many universal properties of these quantum critical points. In particular, we find that the full Fermi surface and the associated Landau quasiparticles remain sharply defined at the critical point. We discuss the phenomenon of Fermi surface reconstruction across this transition and the effect of quantum critical stripe fluctuations on the superconducting instability. We study possible relevance of our results to several phenomena in the cuprates.
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(2012) Physical Review Letters. 108, 267001 . Abstract
We construct a theory of continuous stripe melting quantum phase transitions in two-dimensional metals and the associated Fermi surface reconstruction. Such phase transitions are strongly coupled but yet theoretically tractable in situations where the stripe ordering is destroyed by proliferating doubled dislocations of the charge stripe order. The resulting non-Landau quantum critical point has strong stripe fluctuations which we show decouple dynamically from the Fermi surface even though static stripe ordering reconstructs the Fermi surface. We discuss connections to various stripe phenomena in the cuprates. We point out several puzzling aspects of old experimental results [G. Aeppli et al., Science 278, 1432 (1997)] on singular stripe fluctuations in the cuprates, and provide a possible explanation within our theory. These results may thus have been the first observation of non-Landau quantum criticality in an experiment.
2011
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(2011) Physical Review B. 84, 165126, Abstract
We present a theoretical approach to describing the Mott transition of electrons on a two-dimensional lattice that begins with the low-energy effective theory of the Fermi liquid. The approach to the Mott transition must be characterized by the suppression of density and current fluctuations that correspond to specific shape deformations of the Fermi surface. We explore the nature of the Mott insulator and the corresponding Mott transition when these shape fluctuations of the Fermi surface are suppressed without making any a priori assumptions about other Fermi surface shape fluctuations. Building on insights from the theory of the Mott transition of bosons, we implement this suppression by identifying and condensing vortex degrees of freedom in the phase of the low-energy electron operator. We show that the resulting Mott insulator is a quantum spin liquid with a spinon Fermi surface coupled to a U(1) gauge field, which is usually described within a slave particle formulation. Our approach thus provides a coarse-grained treatment of the Mott transition and the proximate spin liquid that is nevertheless equivalent to the standard slave particle construction. This alternate point of view provides further insight into the novel physics of the Mott transition and the spin liquid state that is potentially useful. We describe a generalization that suppresses spin antisymmetric fluctuations of the Fermi surface that leads to a spin-gapped charge metal previously also discussed in terms of slave particle constructions.
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(2011) Modern Physics Letters B. 25, p. 1083 Abstract
Motivated by proposals to employ RKKY-coupled spins as building blocks in a solid-state quantum computer, we analyze how the RKKY interaction in a 2D electron gas is influenced by spin-orbit interactions. Using a two-impurity Kondo model with added Dresselhaus and Rashba spin-orbit interactions we find that spin-rotational invariance of the RKKY interaction — essential for a well-controllable two-qubit gate — is restored when tuning the Rashba coupling to have the same strength as the Dresselhaus coupling. We also discuss the critical properties of the two-impurity Kondo model in the presence of spin-orbit interactions, and extract the leading correction to the block entanglement scaling due to these interactions.
2010
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(2010) Physical Review B. 82, 045121. Abstract
The destruction of Fermi-liquid behavior when a gapless Fermi surface is coupled to a fluctuating gapless boson field is studied theoretically. This problem arises in a number of different contexts in quantum many-body physics. Examples include fermions coupled to a fluctuating transverse gauge field pertinent to quantum spin-liquid Mott insulators, and quantum critical metals near a Pomeranchuk transition. We develop a controlled theoretical approach to determine the low-energy physics. Our approach relies on combining an expansion in the inverse number (N) of fermion species with a further expansion in the parameter ϵ=zb−2, where zb is the dynamical critical exponent of the boson field. We show how this limit allows a systematic calculation of the universal low-energy physics of these problems. The method is illustrated by studying spinon Fermi-surface spin liquids, and a quantum critical metal at a second-order electronic nematic phase transition. We calculate the low-energy single-particle spectra, and various interesting two-particle correlation functions. In some cases, deviations from the popular random-phase approximation results are found. Some of the same universal singularities are also calculated to leading nonvanishing order using a perturbative renormalization-group calculation at small N extending previous results of Nayak and Wilczek. Implications for quantum spin liquids and for Pomeranchuk transitions are discussed. For quantum critical metals at a nematic transition, we show that the tunneling density of states has a power-law suppression at low energies.
2009
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(2009) Physical Review B. 80, 155302. Abstract
We study the two-impurity Kondo model (TIKM) in two dimensions with spin-orbit coupled conduction electrons. In the first part of the paper we analyze how spin-orbit interactions of Rashba as well as Dresselhaus type influence the Kondo and Ruderman-Kittel-Kasuya-Yoshida (RKKY) interactions in the TIKM, generalizing results obtained by H. Imamura et al. [Phys. Rev. B 69, 121303(R) (2004)] and J. Malecki [J. Stat. Phys. 129, 741 (2007)]. Using our findings we then explore the effect from spin-orbit interactions on the non-Fermi-liquid quantum critical transition between the RKKY-singlet and Kondo-screened RKKY-triplet states. We argue that spin-orbit interactions under certain conditions produce a line of critical points exhibiting the same leading scaling behavior as that of the ordinary TIKM. In the second part of the paper we shift focus and turn to the question of how spin-orbit interactions affect the entanglement between two localized RKKY-coupled spins in the parameter regime where the competition from the direct Kondo interaction can be neglected. Using data for a device with two spinful quantum dots patterned in a gated InAs heterostructure we show that a gate-controlled spin-orbit interaction may drive a maximally entangled state to one with vanishing entanglement or vice versa (as measured by the concurrence). This has important implications for proposals using RKKY interactions for nonlocal control of qubit entanglement in semiconductor heterostructures.
2008
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(2008) Physical Review B. 78, 035449. Abstract
We propose a realization of the two-impurity Anderson model in a double quantum-dot device. When charge transfer between the dots is suppressed, the system exhibits a quantum phase transition, which is controlled by a surface of non-Fermi-liquid fixed points parameterized by the charge valences of the dots. Employing conformal field theory techniques, we identify the scaling exponents that govern transport and thermodynamics close to criticality. We also determine the dynamical exponents that set the time scale for the buildup of the non-Fermi-liquid state after the system is suddenly shifted into the critical region, e.g., by a change of a nearby gate voltage.