Publications
2023

(2023) Physical Review B. 108, 24, L241102. Abstract
NonAbelian 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 alreadydemonstrated 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 yesno outcomes that fingerprint the possible nonAbelian 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 nonAbelian candidates at halffilling in graphene and semiconductor heterostructures.

(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 faulttolerant quantum computation. We show that the anomalous edge modes of onedimensional (1D) clusterstatelike symmetryprotected 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 nearestneighbor 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 twospin interactions supplemented by a Zeeman field. Our approach may provide a pathway toward realizing Kitaev honeycomb spin liquids in spinorbitcoupled Mott insulators.

(2023) Physical Review B. 107, 11, 115113. Abstract
Symmetryresolved entanglement is a useful tool for characterizing symmetryprotected 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 tensornetwork methods that can access much larger systems and determine universal and nonuniversal features in their entanglement. Specifically, we construct onedimensional matrix product operators that encapsulate all the entanglement data of twodimensional symmetryprotected topological states. We first demonstrate our approach for the LevinGu model. Next, we use the cohomology formalism to deform the phase away from the finetuned 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 manybody AharonovBohm flux.
2022

(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 longwavelength structure of vortices when the microscopic particles  electrons or spinful bosons  are near halffilling. These conditions lead to a compact gauge theory of spinons and chargons, which arise as the fundamental topological defects of the lowenergy 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 coupledwire array. Finally, we demonstrate how the latter can be exploited to construct parent Hamiltonians for fractional phases and their transitions.

(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 twodimensional models exhibiting this exotic behavior as they transition from superconducting or topological phases into fully chargelocalized insulators. We study these Mott transitions and the confinement of neutral fermions at a second transition into a symmetrybroken phase. In the process, we also derive coupledwire parent Hamiltonians for a nonAbelian QSL and a Z_{4} QSL.

(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 twodimensional models exhibiting this exotic behavior as they transition from superconducting or topological phases into fully chargelocalized insulators. We study these Mott transitions and the confinement of neutral fermions at a second transition into a symmetrybroken phase. In the process, we also derive coupledwire parent Hamiltonians for a nonAbelian QSL and a Z4 QSL.

(2022) Science. 375, 6577, p. 193197 Abstract
Quantum Hall states can harbor exotic quantum phases. The nature of these states is reflected in the gapless edge modes owing to ‘bulkedge’ correspondence. The moststudied putative nonabelian state is the spinpolarized filling factor ν = 5/2, which permits different topological orders that can be abelian or nonabelian. 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 halfplanes, 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 counterpropagating chirality of the Majorana mode, probed by measuring partition noise, is consistent with the particlehole Pfaffian (PHPf) topological order and rules out the antiPfaffian order.

(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 particlehole symmetric Pfaffian topological order, which is supported by recent thermal measurements. Additionally, it distinguishes between the MooreRead and antiPfaffian topological orders, which are favored by numerical calculations.
2020

(2020) Physical Review Research. 2, 043437. Abstract
The fractionalization of microscopic degrees of freedom is a remarkable manifestation of strong interactions in quantum manybody 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 onedimensional quantum wires. We unify these approaches for twodimensional 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 gaugefield 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.

(2020) Physical Review Letters. 125, 236802. Abstract
The quest for nonAbelian 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 halfinteger 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 quantumHall system and a magnetic insulator. We show that nontopological "thermal metal"phases that form due to quenched disorder may disguise as nonAbelian 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.

(2020) Physical Review B. 102, 195153. Abstract
We introduce a family of pairedcompositefermion trial wave functions for any odd Cooperpair angular momentum. These wave functions are parameterfree and can be efficiently projected into the lowest Landau level. We use largescale Monte Carlo simulations to study three cases: Firstly, the MooreRead phase, which serves us as a benchmark. Secondly, we explore the pairing associated with the antiPfaffian and the particleholesymmetric Pfaffian. Specifically, we assess whether their trial states feature exponentially decaying correlations and thus represent gapped phases of matter. For MooreRead and antiPfaffian we find decay lengths of ζMooreRead=1.30(5) and ζantiPfaffian=1.38(14), in units of the magnetic length. By contrast, for the case of PHPfaffian, we find no evidence of a finite length scale for up to 56 particles.

(2020) Physical Review Letters. 124, 096802. Abstract
Time crystals form when arbitrary physical states of a periodically driven system spontaneously break discrete timetranslation symmetry. We introduce onedimensional timecrystalline topological superconductors, for which timetranslation symmetry breaking and topological physics intertwineyielding anomalous Floquet Majorana modes that are not possible in freefermion 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

(2018) Physical Review B. 98, 201111. Abstract
We introduce (3+1)dimensional models of shortrangeinteracting electrons that form a strongly correlated manybody state whose lowenergy 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.

(2018) Physical Review B. 98, 085143. Abstract
Parafermion zero modes are generalizations of Majorana modes that underlie comparatively rich nonAbeliananyon properties. We introduce exact mappings that connect parafermion chains, which can emerge in twodimensional fractionalized media, to strictly onedimensional fermionic systems. In particular, we show that parafermion zero modes in the former setting translate into symmetryenriched Majorana modes that intertwine with a bulk order parameteryielding braiding and fusion properties that are impossible in standard Majorana platforms. Fusion characteristics of symmetryenriched 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 timereversal symmetry. In this case, one of our pumping protocols entails fairly minimal experimental requirements: Cycling a weakly correlated wire between a trivial phase and timereversalinvariant topological superconducting state produces an edge magnetization with quadrupled periodicity. Our work highlights new avenues for exploring beyondMajorana physics in experimentally relevant onedimensional electronic platforms, including proximitized ferromagnetic chains.

(2018) Physical Review B. 98, 081107. Abstract
We numerically assess model wave functions for the recently proposed particleholesymmetric Pfaffian ("PHPfaffian") 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 MooreReadinspired trial state for the PHPfaffian, 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 PHPfaffian trial state performs reasonably well energetically in the halffilled lowest Landau level, but is likely not a good starting point for understanding the v = 5/2 ground state. Our results suggest that the PHPfaffian model wave function either encodes anomalously weak pwave pairing of composite fermions or fails to represent a gapped, incompressible phase altogether.

(2018) Physical Review Letters. 121, 026801. Abstract
The thermal Hall conductance in the halffilled 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 nonAbelian 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 disorderinduced 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 nonAbelian 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

(2017) Physical Review X. 7, 041016. Abstract
Recent work on a family of bosonfermion mappings has emphasized the interplay of symmetry and duality: Phases related by a particlevortex duality of bosons (fermions) are related by timereversal 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 oneand twodimensional 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 longrange interactions and discover a continuous family of dualities embedding the previously studied cases.
2016

(2016) Physical Review Letters. 117, 136802. Abstract
We introduce a particleholesymmetric metallic state of bosons in a magnetic field at oddinteger filling. This state hosts composite fermions whose energy dispersion features a quadratic band touching and corresponding 2π Berry flux protected by particlehole and discrete rotation symmetries. We also construct an alternative particlehole 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 particlehole symmetry recovers the familiar ChernSimons theory. We discuss realizations of this phase both in 2D and on bosonic topological insulator surfaces, as well as signatures in experiments and simulations.

(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 longrange interactions encoded by an emergent gauge field. This mapping allows us to construct parent Hamiltonians for exotic topologicalinsulator surface phases, derive the particleholesymmetric field theory of a halffilled Landau level, and nontrivially constrain QED3 scaling dimensions. We similarly establish duality between bosonic topological insulator surfaces and N=2 QED3.

(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 nonAbelian defects that trap Z4 parafermion zero modes.
2015

(2015) Physical Review X. 5, Abstract
Spontaneous breaking of translational symmetry, known as densitywave 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 spindensity wave (SDW) with spatially modulated magnetic order. Related phenomena occur in pairdensitywave (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 (symmetrybreaking) and spinglass (EdwardsAnderson) 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 La_{2−x}Ba_{x}Cu_{2}O_{4}.

(2015) Physical Review B. 91, 115111. Abstract
States of matter with a sharp Fermi surface but no welldefined 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 Fermisurface [U(1) spinliquid] state of a Mott insulator; (iii) HalperinLeeRead composite fermion charge liquid state of a halffilled Landau level. In this work, we use renormalization group techniques to investigate possible instabilities of such nonFermi liquids in two spatial dimensions to Cooper pairing. We consider the Isingnematic quantum critical point as an example of an ordering phase transition in a metal, and demonstrate that the attractive interaction mediated by the orderparameter 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 HalperinLeeRead states are stable against Cooper pairing for a sufficiently weak attractive shortrange 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 spinliquid states; (ii) HalperinLeeRead and MooreRead states.

(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 threedimensional 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 nonAbelian 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 twodimensional electron gases. To controllably access these states we exploit a quasi1D 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

(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.

(2012) Physical Review Letters. 108, 267001 . Abstract
We construct a theory of continuous stripe melting quantum phase transitions in twodimensional 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 nonLandau 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 nonLandau quantum criticality in an experiment.
2011

(2011) Physical Review B. 84, 165126, Abstract
We present a theoretical approach to describing the Mott transition of electrons on a twodimensional lattice that begins with the lowenergy 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 lowenergy 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 coarsegrained 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 spingapped charge metal previously also discussed in terms of slave particle constructions.

(2011) Modern Physics Letters B. 25, p. 1083 Abstract
Motivated by proposals to employ RKKYcoupled spins as building blocks in a solidstate quantum computer, we analyze how the RKKY interaction in a 2D electron gas is influenced by spinorbit interactions. Using a twoimpurity Kondo model with added Dresselhaus and Rashba spinorbit interactions we find that spinrotational invariance of the RKKY interaction — essential for a wellcontrollable twoqubit 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 twoimpurity Kondo model in the presence of spinorbit interactions, and extract the leading correction to the block entanglement scaling due to these interactions.
2010

(2010) Physical Review B. 82, 045121. Abstract
The destruction of Fermiliquid 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 manybody physics. Examples include fermions coupled to a fluctuating transverse gauge field pertinent to quantum spinliquid Mott insulators, and quantum critical metals near a Pomeranchuk transition. We develop a controlled theoretical approach to determine the lowenergy physics. Our approach relies on combining an expansion in the inverse number (N) of fermion species with a further expansion in the parameter ϵ=z_{b}−2, where z_{b} is the dynamical critical exponent of the boson field. We show how this limit allows a systematic calculation of the universal lowenergy physics of these problems. The method is illustrated by studying spinon Fermisurface spin liquids, and a quantum critical metal at a secondorder electronic nematic phase transition. We calculate the lowenergy singleparticle spectra, and various interesting twoparticle correlation functions. In some cases, deviations from the popular randomphase approximation results are found. Some of the same universal singularities are also calculated to leading nonvanishing order using a perturbative renormalizationgroup 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 powerlaw suppression at low energies.
2009

(2009) Physical Review B. 80, 155302. Abstract
We study the twoimpurity Kondo model (TIKM) in two dimensions with spinorbit coupled conduction electrons. In the first part of the paper we analyze how spinorbit interactions of Rashba as well as Dresselhaus type influence the Kondo and RudermanKittelKasuyaYoshida (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 spinorbit interactions on the nonFermiliquid quantum critical transition between the RKKYsinglet and Kondoscreened RKKYtriplet states. We argue that spinorbit 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 spinorbit interactions affect the entanglement between two localized RKKYcoupled 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 gatecontrolled spinorbit 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

(2008) Physical Review B. 78, 035449. Abstract
We propose a realization of the twoimpurity Anderson model in a double quantumdot device. When charge transfer between the dots is suppressed, the system exhibits a quantum phase transition, which is controlled by a surface of nonFermiliquid 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 nonFermiliquid state after the system is suddenly shifted into the critical region, e.g., by a change of a nearby gate voltage.