arXiv subjects

Victor Galitski

Publications and source records attributed to Victor Galitski.

At least 55 records · Page 3Linked to original sources

arXiv2023

Monopole Josephson Effects in a Dirac Spin Liquid

Dirac Spin liquids (DSLs) are gapless featureless states, yet interesting by virtue of the effective field theory describing them -- (2+1)-dimensional quantum electrodynamics (QED$_3$). Further, a DSL is known to be a "parent state" of various seemingly unrelated ordered states, such as antiferromagnets and valence bond solids in the sense that one can obtain ordered states by condensing magnetic monopoles of the emergent gauge field. Can operators in the effective field theory, such as the emergent electric field, be externally induced and measured? In this work, we exploit the parent state picture to argue that the answer is yes. We propose a range of "monopole Josephson effects" that arise when two ordered states are separated by a region of the parent DSL. In particular, we show that one can induce an AC monopole Josephson effect, which manifests itself as an AC emergent electric field in the spin liquid, accompanied by a measurable spin current. Further, we show that this AC emergent electric field can be measured as a sharp tunable peak in Raman scattering. This work provides a theoretical proof of principle that emergent gauge fields in spin liquids can be externally induced, manipulated, and probed using more conventional states, which offers a generic platform for studying the exotic spin phases.

cond-mat.str-el↗

arXiv2023

On the path integral approach to quantum anomalies in interacting models

The prediction and subsequent discovery of topological semimetal phases of matter in solid state systems has instigated a surge of activity investigating the exotic properties of these unusual materials. Amongst these are transport signatures which can be attributed to the chiral anomaly; the breaking of classical chiral symmetry in a quantum theory. This remarkable quantum phenomenon, first discovered in the context of particle physics has now found new life in condensed matter physics, connecting topological quantum matter and band theory with effective field theoretic models. In this paper we investigate the interplay between interactions and the chiral anomaly in field theories inspired by semimetals using Fujikawa's path integral method. Starting from models in one spatial dimension we discuss how the presence of interactions can affect the consequences of the chiral anomaly leading to renormalization of excitations and their transport properties. This is then generalised to the three dimensional case where we show that the anomalous response of the system, namely the chiral magnetic and quantum hall effects, are modified by the presence of interactions. These properties are investigated further through the identification of anomalous modes which exist within interacting Weyl semimetals. These massive excitations are nonperturbative in nature and are a direct consequence of the chiral anomaly. The effects of interactions on mixed axial-gravitational anomalies are then investigated and the conditions required for interactions effects to be observed are discussed.

cond-mat.str-el↗

arXiv2022

Classical vertex model dualities in a family of 2D frustrated quantum antiferromagnets

We study a general class of easy-axis spin models on a lattice of corner sharing even-sided polygons with all-to-all interactions within a plaquette. The low energy description corresponds to a quantum dimer model on a dual lattice of even coordination number with a multi dimer constraint. At an appropriately constructed frustration-free Rokhsar-Kivelson (RK) point, the ground state wavefunction can be exactly mapped onto a classical vertex model on the dual lattice. When the dual lattice is bipartite, the vertex models are bonded and are self dual under Wegner's duality, with the self dual point corresponding to the RK point of the original multi-dimer model. We argue that the self dual point is a critical point based on known exact solutions to some of the vertex models. When the dual lattice is non-bipartite, the vertex model is arrowed, and we use numerical methods to argue that there is no phase transition as a function of the vertex weights. Motivated by these wavefunction dualities, we construct two other distinct families of frustration-free Hamiltonians whose ground states can be mapped onto these vertex models. Many of these RK Hamiltonians provably host $\mathbb{Z}_2$ topologically ordered phases.

cond-mat.str-el↗

arXiv2022

Field theory approach to eigenstate thermalization in random quantum circuits

We use field-theoretic methods to explore the statistics of eigenfunctions of the Floquet operator for a large family of Floquet random quantum circuits. The correlation function of the quasienergy eigenstates is calculated and shown to exhibit random matrix circular unitary ensemble statistics, which is consistent with the analogue of Berry's conjecture for quantum circuits. This quantity determines all key metrics of quantum chaos, such as the spectral form factor and thermalizing time-dependence of the expectation value of an arbitrary observable. It also allows us to explicitly show that the matrix elements of local operators satisfy the eigenstate thermalization hypothesis (ETH); i.e., the variance of the off-diagonal matrix elements of such operators is exponentially small in the system size. These results represent a proof of ETH for the family of Floquet random quantum circuits at a physical level of rigor. An outstanding open question for this and most of other sigma-model calculations is a mathematically rigorous proof of the validity of the saddle-point approximation in the large-N limit.

quant-ph↗

arXiv2022

Moiré Gravity and Cosmology

The vacuum catastrophe is a fundamental puzzle, where the observed scales of the cosmological constant are many orders of magnitude smaller than the natural scales expected in the theory. This work proposes a new "bi-world" construction that may offer an insight into the cosmological constant problem. The model generally includes a $(3+1)$-dimensional manifold with two different geometries and matter fields residing on them. In contrast to bimetric or massive theories of gravity, classically, and in the vacuum limit, the model reduces to two massless gravity theories, thereby living ghost-free. The diffeomorphism invariance and causality highly constrain the two metrics to be conformally related, $η_{μν} = ϕ^2 g_{μν}$. This reduces the theory to a standard single-world description, but introduces a new inherently geometrical "moiré field," $ϕ$. Interestingly, the moiré field has the character of both a dilaton and Higgs field familiar in the conventional theory. Integrating out the moiré field naturally gives rise to the Starobinsky action and inflationary dynamics. In the framework of the Friedmann-Lemaitre-Robertson-Walker solution, we reduce an effective action for the moiré field to that of a particle moving in a Mexican hat potential. The equations of motion are then solved numerically and the moiré field is shown to approach a Mexican-hat minimum in an oscillatory fashion, which is accompanied by the decay of the Hubble parameter. Under additional reasonable assumptions, the vacuum energy asymptotically approaches zero in the end of inflationary evolution. The physics presented here shares similarities with the moiré phenomena in condensed matter and elsewhere, where two similar structures superimposed upon give rise to a superstructure with low emergent energy scales compared to the native theories.

hep-th↗

arXiv2022

Spectral Form Factor of a Quantum Spin Glass

It is widely expected that systems which fully thermalize are chaotic in the sense of exhibiting random-matrix statistics of their energy level spacings, whereas integrable systems exhibit Poissonian statistics. In this paper, we investigate a third class: spin glasses. These systems are partially chaotic but do not achieve full thermalization due to large free energy barriers. We examine the level spacing statistics of a canonical infinite-range quantum spin glass, the quantum $p$-spherical model, using an analytic path integral approach. We find statistics consistent with a direct sum of independent random matrices, and show that the number of such matrices is equal to the number of distinct metastable configurations -- the exponential of the spin glass "complexity" as obtained from the quantum Thouless-Anderson-Palmer equations. We also consider the statistical properties of the complexity itself and identify a set of contributions to the path integral which suggest a Poissonian distribution for the number of metastable configurations. Our results show that level spacing statistics can probe the ergodicity-breaking in quantum spin glasses and provide a way to generalize the notion of spin glass complexity beyond models with a semi-classical limit.

cond-mat.stat-mech↗

arXiv2022

Effective field theory of random quantum circuits

Quantum circuits have been widely used as a platform to simulate generic quantum many-body systems. In particular, random quantum circuits provide a means to probe universal features of many-body quantum chaos and ergodicity. Some such features have already been experimentally demonstrated in the noisy intermediate-scale quantum (NISQ) devices. On the theory side, properties of random quantum circuits have been studied on a case-by-case basis and for certain specific systems, a hallmark of quantum chaos - universal Wigner-Dyson level statistics - has been derived. This work develops an effective field theory for a large class of random quantum circuits. The theory has the form of a replica sigma model and is similar to the low-energy approach to diffusion in disordered systems. The method is used to explicitly derive universal random matrix behavior of a large family of random circuits. In particular, we rederive Wigner-Dyson spectral statistics of the brickwork circuit model by Chan, De Luca, and Chalker [Phys. Rev. X 8, 041019 (2018)] and show within the same calculation that its various permutations and higher-dimensional generalizations preserve the universal level statistics. Finally, we use the replica sigma model framework to rederive the Weingarten calculus, which is a method to evaluate integrals of polynomials of matrix elements with respect to the Haar measure over compact groups and has many applications in the studies of quantum circuits. The effective field theory, derived here, provides both a method to quantitatively characterize quantum dynamics of random Floquet systems (e.g., calculating operator and entanglement spreading) and also path to understanding the general fundamental mechanism behind quantum chaos and thermalization in these systems.

quant-ph↗

arXiv2022

Non-Abelian bosonization in a (3+1)-d Kondo semimetal via quantum anomalies

Kondo lattice models have established themselves as an ideal platform for studying the interplay between topology and strong correlations such as in topological Kondo insulators or Weyl-Kondo semimetals. The nature of these systems requires the use of non-perturbative techniques which are few in number, especially in high dimensions. Motivated by this we study a model of Dirac fermions in $3+1$ dimensions coupled to an arbitrary array of spins via a generalization of functional non-Abelian bosonization. We show that there exists an exact transformation of the fermions which allows us to write the system as decoupled free fermions and interacting spins. This decoupling transformation consists of a local chiral, Weyl and Lorentz transformation parameterized by solutions to a set of nonlinear differential equations which order by order takes the form of Maxwell's equations with the spins acting as sources. Owing to its chiral and Weyl components this transformation is anomalous and generates a contribution to the action. From this we obtain the effective action for the spins and expressions for the anomalous transport in the system. In the former we find that the coupling to the fermions generates kinetic terms for the spins, a long ranged interaction and a Wess-Zumino like term. In the latter we find generalizations of the chiral magnetic and Hall effects.

cond-mat.str-el↗

arXiv2022

Strained Bilayer Graphene, Emergent Energy Scales, and Moire Gravity

Twisted bilayer graphene is a rich condensed matter system, which allows one to tune energy scales and electronic correlations. The low-energy physics of the resulting moiré structure can be mathematically described in terms of a diffeomorphism in a continuum formulation. We point out that twisting is just one example of moiré diffeomorphisms. Another particularly simple and experimentally relevant transformation is a homogeneous isomorphic strain of one of the layers, which gives rise to a nearly identical moiré pattern (rotated by $90^\circ $ relative to the twisted structure) and potentially flat bands. We further observe that low-energy physics of the strained bilayer graphene takes the form of a theory of fermions tunneling between two curved space-times. Conformal transformation of the metrics results in emergent "moiré energy scales," which can be tuned to be much lower than those in the native theory. This observation generalizes to an arbitrary space-time dimension with or without an underlying lattice or periodicity and suggests a family of toy models of "moiré gravity" with low emergent energy scales. Motivated by these analogies, we present an explicit toy construction of moiré gravity, where the effective cosmological constant can be made arbitrarily small. We speculate about possible relevance of this scenario to the fundamental vacuum catastrophe in cosmology.

cond-mat.mes-hall↗

arXiv2022

Emergence of many-body quantum chaos via spontaneous breaking of unitarity

It is suggested that many-body quantum chaos appears as the spontaneous symmetry breaking of unitarity in interacting quantum many-body systems. It has been shown that many-body level statistics, probed by the spectral form factor (SFF) defined as $K(η,t)=\langle|{\rm Tr}\, \exp(-ηH + itH)|^2\rangle$, is dominated by a diffuson-type mode in a field theory analysis. The key finding of this Letter is that the "unitary" $η=0$ case is different from the $η\to 0^{\pm}$ limit, with the latter leading to a finite mass of these modes due to interactions. This mass suppresses a rapid exponential ramp in the SFF, which is responsible for the fast emergence of Poisson statistics in the non-interacting case, and gives rise to a non-trivial random matrix structure of many-body levels. The interaction-induced mass in the SFF shares similarities with the dephasing rate in the theory of weak localization and the Lyapunov exponent of the out-of-time-ordered correlators.

cond-mat.stat-mech↗

arXiv2022

Dark Andreev States in Superconductors

The conventional Bardeen-Cooper-Schrieffer (BCS) model of superconductivity assumes a frequency-independent order parameter, which allows a relatively simple description of the superconducting state. In particular, its excitation spectrum readily follows from the Bogoliubov-de-Gennes (BdG) equations. A more realistic description of a superconductor is the Migdal-Eliashberg theory, where the pairing interaction, the order parameter, and electronic self-energy are strongly frequency dependent. This work combines these ingredients of phonon-mediated superconductivity with the standard BdG approach. Surprisingly, we find qualitatively new features such as the emergence of a shadow superconducting gap in the quasiparticle spectrum at energies close to the Debye energy. We show how these features reveal themselves in standard tunneling experiments. Finally, we also predict the existence of additional high-energy bound states, which we dub "dark Andreev states."

cond-mat.supr-con↗

arXiv2022

Universal Dephasing Mechanism of Many-Body Quantum Chaos

Ergodicity is a fundamental principle of statistical mechanics underlying the behavior of generic quantum many-body systems. However, how this universal many-body quantum chaotic regime emerges due to interactions remains largely a puzzle. This paper demonstrates using both heuristic arguments and a microscopic calculation that a dephasing mechanism, similar to Altshuler-Aronov-Khmelnitskii dephasing in the theory of localization, underlies this transition to chaos. We focus on the behavior of the spectral form factor (SFF) as a function of "time", t, which characterizes level correlations in the many-body spectrum. The SFF can be expressed as a sum over periodic classical orbits and its behavior hinges on the interference of trajectories related to each other by a time translation. In the absence of interactions, time-translation symmetry is present for each individual particle, which leads to a fast exponential growth of the SFF and correspondingly loss of correlations between many-body levels. Interactions lead to dephasing, which disrupts interference, and breaks the massive time-translation symmetry down to a global time-translation/energy conservation. This in turn gives rise to the hallmark linear-in-$t$ ramp in the SFF reflecting Wigner-Dyson level repulsion. This general picture is supported by a microscopic analysis of an interacting many-body model. Specifically, we study the complex $\mbox{SYK}_2+\mbox{SYK}_2^2$ model, which allows to tune between an integrable and chaotic regime. It is shown that the dephasing mass vanishes in the former case, which maps to the non-interacting $\mbox{SYK}_2$ model via a time reparameterization. In contrast, the chaotic regime gives rise to dephasing, which suppresses the exponential ramp of the non-interacting theory and induces correlations between many-body levels.

cond-mat.stat-mech↗

arXiv2022

Probing many-body quantum chaos with quantum simulators

The spectral form factor (SFF), characterizing statistics of energy eigenvalues, is a key diagnostic of many-body quantum chaos. In addition, partial spectral form factors (PSFFs) can be defined which refer to subsystems of the many-body system. They provide unique insights into energy eigenstate statistics of many-body systems, as we show in an analysis on the basis of random matrix theory and of the eigenstate thermalization hypothesis. We propose a protocol that allows the measurement of the SFF and PSFFs in quantum many-body spin models, within the framework of randomized measurements. Aimed to probe dynamical properties of quantum many-body systems, our scheme employs statistical correlations of local random operations which are applied at different times in a single experiment. Our protocol provides a unified testbed to probe many-body quantum chaotic behavior, thermalization and many-body localization in closed quantum systems which we illustrate with numerical simulations for Hamiltonian and Floquet many-body spin-systems.

quant-ph↗

arXiv2022

Interplay of hyperbolic plasmons and superconductivity

Hyperbolic plasmons are collective electron excitations in layered conductors. They are of relevance to a number of superconducting materials, including the cuprates and layered hyperbolic metamaterials [V. N. Smolyaninova, et al. Scientific Reports 6, 34140 (2016)]. This work studies how the unusual dispersion of hyperbolic plasmons affects Cooped pairing. We use the Migdal-Eliashberg equations, which are solved both numerically and analytically using the Grabowski-Sham approximation, with consistent results. We do not find evidence for plasmon-mediated pairing within a reasonable parameter range. However, it is shown that the hyperbolic plasmons can significantly reduce the effects of Coulomb repulsion in the Cooper channel leading to an enhancement of the transition temperature originating from other pairing mechanisms. In the model of a hyperbolic material composed of identical layers, we find this enhancement to be the strongest in the $d$-wave channel. We also discuss strategies for engineering an optimal hyperbolic plasmon background for a further enhancement of superconductivity in both $s$-wave and $d$-wave channels.

cond-mat.supr-con↗

arXiv2021

Interaction-driven breakdown of dynamical localization in a kicked quantum gas

Quantum interference can terminate energy growth in a continually kicked system, via a single-particle ergodicity-breaking mechanism known as dynamical localization. The effect of many-body interactions on dynamically localized states, while important to a fundamental understanding of quantum decoherence, has remained unexplored despite a quarter-century of experimental studies. We report the experimental realization of a tunably-interacting kicked quantum rotor ensemble using a Bose-Einstein condensate in a pulsed optical lattice. We observe signatures of a prethermal localized plateau, followed for interacting samples by interaction-induced anomalous diffusion with an exponent near one half. Echo-type time reversal experiments establish the role of interactions in destroying reversibility. These results quantitatively elucidate the dynamical transition to many-body quantum chaos, advance our understanding of quantum anomalous diffusion, and delimit some possibilities for protecting quantum information in interacting driven systems.

cond-mat.quant-gas↗

arXiv2021

Dynamical Quantum Phase transitions and Recurrences in the Non-Equilibrium BCS model

Non-equilibrium aspects of the BCS model have fascinated physicists for decades, from the seminal works of Eliashberg to modern realizations in cold atom experiments. The latter scenarios have lead to a great deal of interest in the quench dynamics of fermions with pairing interactions. The recently introduced notion of a dynamical quantum phase transition is an attempt to classify the myriad of possible phenomena which can result in such far from equilibrium systems. These are defined as non-analytic points of the logarithm of the Loschmidt echo and are linked to oscillations in the dynamics a systems order parameter. In this work we analytically investigate the relation between DQPTs and oscillation of the superconducting order parameter in quenches of the BCS model. We find that each oscillation of the order parameter is accompanied by a DQPT which is first order in nature. We show this for a variety of initial states and furthermore find that when the order parameter attains a constant steady state then no DQPTS occur.

cond-mat.supr-con↗

arXiv2021

Loschmidt Echo of Far-From-Equilibrium Fermionic Superfluids

Non-analyticities in the logarithm of the Loschmidt echo, known as dynamical quantum phase transitions [DQPTs], are a recently introduced attempt to classify the myriad of possible phenomena which can occur in far from equilibrium closed quantum systems. In this work, we analytically investigate the Loschmidt echo in nonequilibrium $s$-wave and topological $p_x+ip_y$ fermionic superfluids. We find that the presence of non-analyticities in the echo is not invariant under global rotations of the superfluid phase. We remedy this deficiency by introducing a more general notion of a grand canonical Loschmidt echo. Overall, our study shows that DQPTs are not a good indicator for the long time dynamics of an interacting system. In particular, there are no DQPTs to tell apart distinct dynamical phases of quenched BCS superconductors. Nevertheless, they can signal a quench induced change in the topology and also keep track of solitons emerging from unstable stationary states of a BCS superconductor.

cond-mat.quant-gas↗

arXiv2021

Solitons in lattice field theories via tight-binding supersymmetry

Reflectionless potentials play an important role in constructing exact solutions to classical dynamical systems, non-perturbative solutions of various large-N field theories, and closely related solitonic solutions to the Bogoliubov-de Gennes equations in the theory of superconductivity. These solutions rely on the inverse scattering method, which reduces these seemingly unrelated problems to identifying reflectionless potentials of an auxiliary one-dimensional quantum scattering problem. There are several ways of constructing these potentials, one of which is quantum mechanical supersymmetry (SUSY). In this paper, motivated by recent experimental platforms, we generalize this framework to develop a theory of solitons in lattice versions of interacting field theories. Our analysis hinges on the use of trace identities, which are relations connecting the potential of an equation of motion to the scattering data. For a discrete Schrödinger operator, such trace identities are well known, and we derive a new set of identities for the discrete Dirac operator. We then use these in a lattice Gross-Neveu and chiral Gross-Neveu (Nambu-Jona-Lasinio) model to show that lattice solitons correspond to reflectionless potentials associated with the discrete scattering problem. These models are of significance as they are equivalent to a mean-field theory of a lattice superconductor. To explicitly construct these solitons, we generalize supersymmetric quantum mechanics to tight-binding models. We show that a matrix transformation exists that maps a tight-binding model to an isospectral one which shares the same structure and scattering properties. The corresponding soliton solutions have both modulated hopping and onsite potential; we explicitly compute both topological and non-topological soliton solutions as well as bound state spectra in the aforementioned models.

cond-mat.str-el↗