# Publications by Dmitry Kovrizhin

## Dynamical localization in Z2 lattice gauge theories

American Physical Society **97** (2018)

We study quantum quenches in two-dimensional lattice gauge theories with fermions coupled to dynamical Z 2 gauge fields. Through the identification of an extensive set of conserved quantities, we propose a generic mechanism of charge localization in the absence of quenched disorder both in the Hamiltonian and in the initial states. We provide diagnostics of this localization through a set of experimentally relevant dynamical measures, entanglement measures, as well as spectral properties of the model. One of the defining features of the models that we study is a binary nature of emergent disorder, related to Z 2 degrees of freedom. This results in a qualitatively different behavior in the strong disorder limit compared to typically studied models of localization. For example, it gives rise to a possibility of a delocalization transition via a mechanism of quantum percolation in dimensions higher than 1D. We highlight the importance of our general phenomenology to questions related to dynamics of defects in Kitaev's toric code, and to quantum quenches in Hubbard models. While the simplest models we consider are effectively noninteracting, we also include interactions leading to many-body localizationlike logarithmic entanglement growth. Finally, we consider effects of interactions that generate dynamics for conserved charges, which gives rise to only transient localization behavior, or quasi-many-body localization.

## Zero point fluctuations for magnetic spirals and Skyrmions, and the fate of the Casimir energy in the continuum limit

Annals of Physics Elsevier **399** (2018) 239-257

We study the role of zero-point quantum fluctuations in a range of magnetic states which on the classical level are close to spin-aligned ferromagnets. These include Skyrmion textures characterized by non-zero topological charge, and topologically-trivial spirals arising from the competition of the Heisenberg and Dzyaloshin-skii–Moriya interactions. For the former, we extend our previous results on quantum exactness of classical Bogomolny–Prasad–Sommerfield (BPS) ground-state degeneracies to the general case of Kähler manifolds, with a specific example of Grassmann manifolds . These are relevant to quantum Hall ferromagnets with internal states and integer filling factor . A promising candidate for their experimental implementation is monolayer graphene with corresponding to spin and valley degrees of freedom at the charge neutrality point with filled Landau levels. We find that the vanishing of the zero-point fluctuations in taking the continuum limit occurs differently in the case of BPS states compared to the case of more general smooth textures, with the latter exhibiting more pronounced lattice effects. This motivates us to consider the vanishing of zero-point fluctuations in such near-ferromagnets more generally. We present a family of lattice spin models for which the vanishing of zero-point fluctuations is evident, and show that some spirals can be thought of as having nonzero but weak zero-point fluctuations on account of their closeness to this family. Between them, these instances provide concrete illustrations of how the Casimir energy, dependent on the full UV-structure of the theory, evolves as the continuum limit is taken.

## Disorder-Free Localization.

Physical review letters **118** (2017) 266601-266601

The venerable phenomena of Anderson localization, along with the much more recent many-body localization, both depend crucially on the presence of disorder. The latter enters either in the form of quenched disorder in the parameters of the Hamiltonian, or through a special choice of a disordered initial state. Here, we present a model with localization arising in a very simple, completely translationally invariant quantum model, with only local interactions between spins and fermions. By identifying an extensive set of conserved quantities, we show that the system generates purely dynamically its own disorder, which gives rise to localization of fermionic degrees of freedom. Our work gives an answer to a decades old question whether quenched disorder is a necessary condition for localization. It also offers new insights into the physics of many-body localization, lattice gauge theories, and quantum disentangled liquids.

## Quantized gravitational responses, the sign problem, and quantum complexity.

Science advances **3** (2017) e1701758-e1701758

It is believed that not all quantum systems can be simulated efficiently using classical computational resources. This notion is supported by the fact that it is not known how to express the partition function in a sign-free manner in quantum Monte Carlo (QMC) simulations for a large number of important problems. The answer to the question-whether there is a fundamental obstruction to such a sign-free representation in generic quantum systems-remains unclear. Focusing on systems with bosonic degrees of freedom, we show that quantized gravitational responses appear as obstructions to local sign-free QMC. In condensed matter physics settings, these responses, such as thermal Hall conductance, are associated with fractional quantum Hall effects. We show that similar arguments also hold in the case of spontaneously broken time-reversal (TR) symmetry such as in the chiral phase of a perturbed quantum Kagome antiferromagnet. The connection between quantized gravitational responses and the sign problem is also manifested in certain vertex models, where TR symmetry is preserved.

## Nonlinear Luttinger liquid: Exact result for the Green function in terms of the fourth Painlevé transcendent

SciPost Physics **2** (2017)

## Absence of Ergodicity without Quenched Disorder: From Quantum Disentangled Liquids to Many-Body Localization.

Physical review letters **119** (2017) 176601-176601

We study the time evolution after a quantum quench in a family of models whose degrees of freedom are fermions coupled to spins, where quenched disorder appears neither in the Hamiltonian parameters nor in the initial state. Focusing on the behavior of entanglement, both spatial and between subsystems, we show that the model supports a state exhibiting combined area and volume-law entanglement, being characteristic of the quantum disentangled liquid. This behavior appears for one set of variables, which is related via a duality mapping to another set, where this structure is absent. Upon adding density interactions between the fermions, we identify an exact mapping to an XXZ spin chain in a random binary magnetic field, thereby establishing the existence of many-body localization with its logarithmic entanglement growth in a fully disorder-free system.

## Majorana spectroscopy of three-dimensional Kitaev spin liquids

Physical Review B American Physical Society **93** (2016) 235146

We analyze the dynamical response of a range of three-dimensional Kitaev quantum spin liquids, using lattice models chosen to explore the different possible low-energy spectra for gapless Majorana fermions, with either Fermi surfaces, nodal lines, or Weyl points. We find that the behavior of the dynamical structure factor is distinct in all three cases, reflecting the quasiparticle density of states in two fundamentally different ways. First, the low-energy response is either straightforwardly related to the power with which the low-energy density of states vanishes; or for a nonvanishing density of states, to the phase shifts encountered in the corresponding x-ray edge problem, whose phenomenology we extend to the case of Majorana fermions. Second, at higher energies, there is a rich fine structure, determined by microscopic features of the Majorana spectrum. Our theoretical results test the usefulness of inelastic neutron scattering as a probe of these quantum spin liquids: we find that although spin flips fractionalize, the main features of the dynamical spin response nevertheless admit straightforward interpretations in terms of Majorana and flux loop excitations.

## Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet.

Nature materials **15** (2016) 733-740

Quantum spin liquids (QSLs) are topological states of matter exhibiting remarkable properties such as the capacity to protect quantum information from decoherence. Whereas their featureless ground states have precluded their straightforward experimental identification, excited states are more revealing and particularly interesting owing to the emergence of fundamentally new excitations such as Majorana fermions. Ideal probes of these excitations are inelastic neutron scattering experiments. These we report here for a ruthenium-based material, α-RuCl3, continuing a major search (so far concentrated on iridium materials) for realizations of the celebrated Kitaev honeycomb topological QSL. Our measurements confirm the requisite strong spin-orbit coupling and low-temperature magnetic order matching predictions proximate to the QSL. We find stacking faults, inherent to the highly two-dimensional nature of the material, resolve an outstanding puzzle. Crucially, dynamical response measurements above interlayer energy scales are naturally accounted for in terms of deconfinement physics expected for QSLs. Comparing these with recent dynamical calculations involving gauge flux excitations and Majorana fermions of the pure Kitaev model, we propose the excitation spectrum of α-RuCl3 as a prime candidate for fractionalized Kitaev physics.

## Fermionic response from fractionalization in an insulating two-dimensional magnet

NATURE PHYSICS **12** (2016) 912-915

## Large and exact quantum degeneracy in a skyrmion magnet

Physical Review B American Physical Society **93** (2016) ARTN 094426-

We identify a large family of ground states of a topological C P N − 1 skyrmion magnet whose classical degeneracy persists to all orders in a semiclassical expansion. This goes along with an exceptional robustness of the concomitant ground-state configurations, which are not at all dressed by quantum fluctuations. We trace these twin observations back to a common root: this class of topological ground states saturates a Bogomolny inequality. A similar phenomenology occurs in high-energy physics for some field theories exhibiting supersymmetry. We propose quantum Hall ferromagnets, where these skyrmions configurations arise naturally as ground states away from integer filling, as the best available laboratory realisations.

## Dynamics of fractionalization in quantum spin liquids

Physical review B: Condensed matter and materials physics American Physical Society **92** (2015) ARTN 115127-

We present the theory of dynamical spin response for the Kitaev honeycomb model, obtaining exact results for the structure factor (SF) in gapped and gapless, Abelian and non-Abelian quantum spin-liquid (QSL) phases. We also describe the advances in methodology necessary to compute these results. The structure factor shows signatures of spin fractionalization into emergent quasiparticles: Majorana fermions and fluxes of Z2 gauge field. In addition to a broad continuum from spin fractionalization, we find sharp (δ-function) features in the response. These arise in two distinct ways: from excited states containing only (static) fluxes and no (mobile) fermions, and from excited states in which fermions are bound to fluxes. The SF is markedly different in Abelian and non-Abelian QSLs, and bound fermion-flux composites appear only in the non-Abelian phase.

## Neutron scattering signatures of the 3D hyperhoneycomb Kitaev quantum spin liquid

Physical review B: Condensed matter and materials physics American Physical Society **92** (2015) ARTN 180408-

Motivated by recent synthesis of the hyperhoneycomb material β−Li2IrO3, we study the dynamical structure factor (DSF) of the corresponding 3D Kitaev quantum spin-liquid (QSL), whose fractionalized degrees of freedom are Majorana fermions and emergent flux loops. The properties of this 3D model are known to differ in important ways from those of its 2D counterpart—it has a finite-temperature phase transition, as well as distinct features in the Raman response. We show, however, that the qualitative behavior of the DSF is broadly dimension-independent. Characteristics of the 3D DSF include a response gap even in the gapless QSL phase and an energy dependence deriving from the Majorana fermion density of states. Since the majority of the response is from states containing a single Majorana excitation, our results suggest inelastic neutron scattering as the spectroscopy of choice to illuminate the physics of Majorana fermions in Kitaev QSLs.

## Raman scattering signatures of Kitaev spin liquids in A2IrO3 iridates with A=Na or Li

Physical Review Letters American Physical Society **113** (2014) ARTN 187201-

We show how Raman spectroscopy can serve as a valuable tool for diagnosing quantum spin liquids (QSL). We find that the Raman response of the gapless QSL of the Kitaev-Heisenberg model exhibits signatures of spin fractionalization into Majorana fermions, which give rise to a broad signal reflecting their density of states, and Z2 gauge fluxes, which also contribute a sharp feature. We discuss the current experimental situation and explore more generally the effect of breaking the integrability on response functions of Kitaev spin liquids.

## Dynamics of a two-dimensional quantum spin liquid: signatures of emergent Majorana fermions and fluxes

Phys. Rev. Lett. American Physical Society **112** (2013) 207203-

Topological states of matter present a wide variety of striking new phenomena. Prominent among these is the fractionalisation of electrons into unusual particles: Majorana fermions [1], Laughlin quasiparticles [2] or magnetic monopoles [3]. Their detection, however, is fundamentally complicated by the lack of any local order, such as, for example, the magnetisation in a ferromagnet. While there are now several instances of candidate topological spin liquids [4], their identification remains challenging [5]. Here, we provide a complete and exact theoretical study of the dynamical structure factor of a two-dimensional quantum spin liquid in gapless and gapped phases. We show that there are direct signatures - qualitative and quantitative - of the Majorana fermions and gauge fluxes emerging in Kitaev's honeycomb model. These include counterintuitive manifestations of quantum number fractionalisation, such as a neutron scattering response with a gap even in the presence of gapless excitations, and a sharp component despite the fractionalisation of electron spin. Our analysis identifies new varieties of the venerable X-ray edge problem and explores connections to the physics of quantum quenches.

## Bulk-edge correspondence in fractional Chern insulators

Physical review B: Condensed matter and materials physics American Physical Society **88** (2013) ARTN 081106-

It has been recently realized that strong interactions in topological Bloch bands give rise to the appearance of novel states of matter. Here we study connections between these systems—fractional Chern insulators and the fractional quantum Hall states—via generalization of a gauge-fixed Wannier-Qi construction in the cylinder geometry. Our setup offers a number of important advantages compared to the earlier exact diagonalization studies on a torus. Most notably, it gives access to edge states and to a single-cut orbital entanglement spectrum, hence to the physics of bulk-edge correspondence. It is also readily implemented in the state-of-the-art density matrix renormalization group method that allows for numerical simulations of significantly larger systems. We demonstrate our general approach on examples of flat-band models on ruby and kagome lattices at bosonic filling fractions ν = 1/2 and ν = 1, which show the signatures of (non)-Abelian phases, and establish the correspondence between the physics of edge states and the entanglement in the bulk. Notably, we find that the non-Abelian ν = 1 phase can be stabilized by purely on-site interactions in the presence of a confining potential.

## Solution of a model for the two-channel electronic Mach-Zehnder interferometer

Phys. Rev. B **87** (2012) 045120-

We develop the theory of electronic Mach-Zehnder interferometers built from quantum Hall edge states at Landau level filling factor \nu = 2, which have been investigated in a series of recent experiments and theoretical studies. We show that a detailed treatment of dephasing and non-equlibrium transport is made possible by using bosonization combined with refermionization to study a model in which interactions between electrons are short-range. In particular, this approach allows a non-perturbative treatment of electron tunneling at the quantum point contacts that act as beam-splitters. We find an exact analytic expression at arbitrary tunneling strength for the differential conductance of an interferometer with arms of equal length, and obtain numerically exact results for an interferometer with unequal arms. We compare these results with previous perturbative and approximate ones, and with observations.

## Multicomponent Skyrmion lattices and their excitations

Physical Review Letters American Physical Society **110** (2013) ARTN 186802-

We study quantum Hall ferromagnets with a finite density of topologically charged spin textures in the presence of internal degrees of freedom such as spin, valley, or layer indices, so that the system is parametrized by a d -component spinor field. In the absence of anisotropies we find a hexagonal Skyrmion lattice that completely breaks the underlying SU(d) symmetry with the low-lying excitation spectrum separating into d2−1 gapless acoustic magnetic modes and a magnetophonon. The ground state charge density modulations, which inevitably exist in these lattices, vanish exponentially in d. We discuss the role of effective mass anisotropy for SU(3)-valley Skyrmions relevant to experiments with AlAs quantum wells. Here we find a transition which breaks a sixfold rotational symmetry of the triangular lattice, followed by the formation of a square lattice at large values of anisotropy strength.

## Relaxation in driven integer quantum Hall edge states.

Physical Review Letters **109** (2012) 106403-

A highly nonthermal electron distribution is generated when quantum Hall edge states originating from sources at different potentials meet at a quantum point contact. The relaxation of this distribution to a stationary form as a function of distance downstream from the contact has been observed in recent experiments [C. Altimiras et al., Phys. Rev. Lett. 105, 056803 (2010)]. Here we present an exact treatment of a minimal model for the system at filling factor ν=2, with results that account well for the observations.

## Equilibration of integer quantum Hall edge states

Phys. Rev. B **84** (2010) 085105-

We study equilibration of quantum Hall edge states at integer filling factors, motivated by experiments involving point contacts at finite bias. Idealising the experimental situation and extending the notion of a quantum quench, we consider time evolution from an initial non-equilibrium state in a translationally invariant system. We show that electron interactions bring the system into a steady state at long times. Strikingly, this state is not a thermal one: its properties depend on the full functional form of the initial electron distribution, and not simply on the initial energy density. Further, we demonstrate that measurements of the tunneling density of states at long times can yield either an over-estimate or an under-estimate of the energy density, depending on details of the analysis, and discuss this finding in connection with an apparent energy loss observed experimentally. More specifically, we treat several separate cases: for filling factor \nu=1 we discuss relaxation due to finite-range or Coulomb interactions between electrons in the same channel, and for filling factor \nu=2 we examine relaxation due to contact interactions between electrons in different channels. In both instances we calculate analytically the long-time asymptotics of the single-particle correlation function. These results are supported by an exact solution at arbitrary time for the problem of relaxation at \nu=2 from an initial state in which the two channels have electron distributions that are both thermal but with unequal temperatures, for which we also examine the tunneling density of states.

## Density matrix renormalization group for bosonic quantum Hall effect

Physical Review B American Physical Society **81** (2010)

<p style="text-align:justify;"> We developed a density matrix renormalization group technique to study quantum Hall fractions of fast rotating bosons. In this paper, we present a discussion of the method together with the results which we obtain in three distinct cases of the narrow-channel, cylinder, and spherical geometries. In the narrow-channel case, which is relevant to anisotropic confining traps in the limit of extremely fast rotation, we find a series of zero-temperature phase transitions in the strongly interacting regime as a function of the interaction strength between bosons. We compute energies and density profiles for different filling fractions on a cylinder and compare the convergence rates of the method in the cylinder and a sphere geometries. </p>