arXiv subjects

Alexander Avdoshkin

Publications and source records attributed to Alexander Avdoshkin.

18 recordsLinked to original sources

arXiv2026

Eigenstate thermalization in thermal first-order phase transitions

The eigenstate thermalization hypothesis (ETH) posits how isolated quantum many-body systems thermalize, assuming that individual eigenstates at the same energy density have identical expectation values of local observables in the limit of large systems. While the ETH apparently holds across a wide range of interacting quantum systems, in this work we show that it requires generalization in the presence of thermal first-order phase transitions. We introduce a class of all-to-all spin models, featuring first-order thermal phase transitions that stem from two distinct mean-field solutions (two ``branches'') that exchange dominance in the many-body density of states as the energy is varied. We argue that for energies in the vicinity of the thermal phase transition, eigenstate expectation values do not need to converge to the same thermal value. The system has a regime with coexistence of two classes of eigenstates corresponding to the two branches with distinct expectation values at the same energy density, and another regime with Schrodinger-cat-like eigenstates that are inter-branch superpositions; these two regimes are separated by an eigenstate phase transition. We support our results by semiclassical calculations and an exact diagonalization study of a microscopic spin model, and argue that the structure of eigenstates in the vicinity of thermal first-order phase transitions can be experimentally probed via non-equilibrium dynamics.

cond-mat.stat-mech↗

arXiv2025

An integrated neural wavefunction solver for spinful Fermi systems

We present an approach to solving the ground state of Fermi systems that contain spin or other discrete degrees of freedom in addition to continuous coordinates. The approach combines a Markov chain Monte Carlo sampling for energy estimation that we adapted to cover the extended configuration space with a transformer-based wavefunction to represent fermionic states. This sampling is necessary when the Hamiltonian contains explicit spin dependence and, for spin-independent Hamiltonians, we find that the inclusion of spin updates leads to faster convergence to an antiferromagnetic ground state. A transformer with both continuous position and discrete spin as inputs achieves universal approximation to spinful generalized orbitals. We validate the method on a range of two-dimensional material problems: a two-dimensional electron gas with Rashba spin-orbit coupling, a noncollinear spin texture, and a quantum antiferromagnet in a honeycomb moir\'e potential.

quant-ph↗

arXiv2024

Gauge-invariant projector calculus for quantum state geometry and applications to observables in crystals

The importance of simple geometrical invariants, such as the Berry curvature and quantum metric, constructed from the Bloch states of a crystal has become well-established over four decades of research. More complex aspects of geometry emerge in properties linking multiple bands, such as optical responses. In the companion work [arXiv:2409.16358], we identified novel multi-state geometrical invariants using an explicitly gauge-invariant formalism based on projection operators, which we used to clarify the relation between the shift current and the theory of electronic polarization among other advancements for second-order non-linear optics. Here, we provide considerably more detail on the projector formalism and the geometrical invariants arising in the vicinity of a specific value of crystal momentum. We combine the introduction to multi-state quantum geometry with broadly relevant algebraic relationships and detailed example calculations, enabling extensions toward future applications to topological and geometrical properties of insulators and metals.

cond-mat.str-el↗

arXiv2024

Geometric bound on structure factor

We show that a quadratic form of quantum geometric tensor in $k$-space sets a bound on the $q^4$ term in the static structure factor $S(q)$ at small $\vec{q}$. Bands that saturate this bound satisfy a condition similar to Laplace's equation, leading us to refer to them as $\textit{harmonic bands}$. We provide examples of harmonic bands in one- and two-dimensional systems, including (higher) Landau levels. The geometric bound further leads to a topological bound on the $q^4$ term, which is saturated only when the band geometry satisfies the trace condition and, additionally, the quantum geometric tensor is uniform in $k$-space. We speculate that these bounds taken together provide a useful guide for identifying Chern bands that favor (Abelian or non-Abelian) fractional Chern insulators.

cond-mat.mes-hall↗

arXiv2024

The multi-state geometry of shift current and polarization

The quantum metric and Berry curvature capture essential properties of non-trivial Bloch states and underpin many fascinating phenomena. However, it becomes increasingly evident that a more comprehensive understanding of quantum state geometry is necessary to explain properties involving Bloch states of multiple bands, such as optical transitions. To this end, we employ quantum state projectors to develop an explicitly gauge-invariant formalism and demonstrate its power with applications to non-linear optics and the theory of electronic polarization. We provide a simple expression for the shift current that resolves its precise relation to the moments of electronic polarization, clarifies the treatment of band degeneracies, and reveals its decomposition into the sum of the skewness of the occupied states and intrinsically multi-state geometry. The projector approach is applied to calculate non-linear optical properties of transition metal dichalcogenides (TMDs) layers, using previously calculated minimal tight-binding models, and demonstrated analytically on a three-band generalization of the Rice-Mele chain to elucidate the different contributions. We close with comments on further applications of the projector operator approach to multi-state geometry.

cond-mat.str-el↗

arXiv2024

A tale of two localizations: coexistence of flat bands and Anderson localization in a photonics-inspired amorphous system

Emerging experimental platforms use amorphousness, a constrained form of disorder, to tailor meta-material properties. We study localization under this type of disorder in a family of 2D models generalizing recent experiments on photonic systems. Models in this family reside on amorphous analogs of kagom\'{e} lattices with fixed coordination number, vary by a tunable synthetic field, and remarkabaly, permit exact results. We observe two kinds of localization that emerge in these models: Anderson localization by amorphous disorder, and the existence of compact, macroscopically degenerate localized states as in many crystalline flat bands. The flat-band-like degeneracy innate to kagom\'{e} lattices survives under amorphousness without on-site disorder. This phenomenon arises from the cooperation between the structure of the compact localized states and the geometry of the amorphous graph. More surprisingly, for particular values of the field, such states emerge in the amorphous system that were not present on the kagom\'{e} lattice in the same field. Outside the flat band, constrained amorphous graph geometry necessitates the existence of a fully delocalized state, near which we observe evidence of a localization-delocalization transition. Our platform serves as a demonstration of how the qualitative behavior of a disordered system can be tuned at fixed graph topology and lead to localization phenomena unique to amorphous systems that are not observed in their generically disordered counterparts.

cond-mat.dis-nn↗

arXiv2024

Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians

Understanding the geometric information contained in quantum states is valuable in various branches of physics, particularly in solid-state physics when Bloch states play a crucial role. While the Fubini-Study metric and Berry curvature form offer comprehensive descriptions of non-degenerate quantum states, a similar description for degenerate states did not exist. In this work, we fill this gap by showing how to reduce the geometry of degenerate states to the non-abelian (Wilczek-Zee) connection $A$ and a previously unexplored matrix-valued metric tensor $G$. Mathematically, this problem is equivalent to finding the $U(N)$ invariants of a configuration of subspaces in $\mathbb{C}^n$. For two subspaces, the configuration was known to be described by a set of $m$ principal angles that generalize the notion of quantum distance. For more subspaces, we find $3 m^2 - 3 m + 1$ additional independent invariants associated with each triple of subspaces. Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces. We also develop a procedure for calculating these invariants as integrals of $A$ and $G$ over geodesics on the Grassmannain manifold. Finally, we briefly discuss possible application of these results to quantum state preparation and $PT$-symmetric band structures.

quant-ph↗

arXiv2023

Universality of critical dynamics with finite entanglement

When a system is swept through a quantum critical point, the quantum Kibble-Zurek mechanism makes universal predictions for quantities such as the number and energy of excitations produced. This mechanism is now being used to obtain critical exponents on emerging quantum computers and emulators, which in some cases can be compared to Matrix Product State (MPS) numerical studies. However, the mechanism is modified when the divergence of entanglement entropy required for a faithful description of many quantum critical points is not fully captured by the experiment or classical calculation. In this work, we study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement, using conformally invariant critical points described approximately by an MPS as an example. We derive that the effect of finite entanglement on a Kibble-Zurek process is captured by a dimensionless scaling function of the ratio of two length scales, one determined dynamically and one by the entanglement restriction. Numerically we confirm first that dynamics at finite bond dimension $χ$ is independent of the algorithm chosen, then obtain scaling collapses for sweeps in the transverse field Ising model and the 3-state Potts model. Our result establishes the precise role played by entanglement in time-dependent critical phenomena and has direct implications for quantum state preparation and classical simulation of quantum states.

quant-ph↗

arXiv2022

Krylov complexity in quantum field theory, and beyond

We study Krylov complexity in various models of quantum field theory: free massive bosons and fermions on flat space and on spheres, holographic models, and lattice models with the UV-cutoff. In certain cases we find asymptotic behavior of Lanczos coefficients, which goes beyond previously observed universality. We confirm that in all cases the exponential growth of Krylov complexity satisfies the conjectural inequality, which generalizes the Maldacena-Shenker-Stanford bound on chaos. We discuss temperature dependence of Lanczos coefficients and note that the relation between the growth of Lanczos coefficients and chaos may only hold for the sufficiently late, truly asymptotic regime governed by the physics at the UV cutoff. Contrary to previous suggestions, we show scenarios when Krylov complexity in quantum field theory behaves qualitatively differently from the holographic complexity.

hep-th↗

arXiv2022

Disordered topological graphs enhancing nonlinear phenomena

Complex networks play a fundamental role in understanding phenomena from the collective behavior of spins, neural networks, and power grids to the spread of diseases. Topological phenomena in such networks have recently been exploited to preserve the response of systems in the presence of disorder. We propose and demonstrate topological structurally disordered systems with a modal structure that enhances nonlinear phenomena in the topological channels by inhibiting the ultrafast leakage of energy from edge modes to bulk modes. We present the construction of the graph and show that its dynamics enhances the topologically protected photon pair generation rate by an order of magnitude. Disordered nonlinear topological graphs will enable advanced quantum interconnects, efficient nonlinear sources, and light-based information processing for artificial intelligence.

physics.optics↗

arXiv2022

Direct Geometric Probe of Singularities in Band Structure

The band structure of a crystal may have points where two or more bands are degenerate in energy and where the geometry of the Bloch state manifold is singular, with consequences for material and transport properties. Ultracold atoms in optical lattices have been used to characterize such points only indirectly, e.g., by detection of an Abelian Berry phase, and only at singularities with linear dispersion (Dirac points). Here, we probe band-structure singularities through the non-Abelian transformation produced by transport directly through the singular points. We prepare atoms in one Bloch band, accelerate them along a quasi-momentum trajectory that enters, turns, and then exits the singularities at linear and quadratic touching points of a honeycomb lattice. Measurements of the band populations after transport identify the winding numbers of these singularities to be 1 and 2, respectively. Our work opens the study of quadratic band touching points in ultracold-atom quantum simulators, and also provides a novel method for probing other band geometry singularities.

cond-mat.quant-gas↗

arXiv2022

Beyond the Berry Phase: Extrinsic Geometry of Quantum States

Consider a set of quantum states $| \psi(x) \rangle$ parameterized by $x$ taken from some parameter space $M$. We demonstrate how all geometric properties of this manifold of states are fully described by a scalar gauge-invariant Bargmann invariant $P^{(3)}(x_1, x_2, x_3)=\operatorname{tr}[P(x_1) P(x_2)P(x_3)]$, where $P(x) = |\psi(x)\rangle \langle\psi(x)|$. Mathematically, $P(x)$ defines a map from $M$ to the complex projective space $\mathbb{C}P^n$ and this map is uniquely determined by $P^{(3)}(x_1,x_2,x_3)$ up to a symmetry transformation. The phase $\arg P^{(3)}(x_1,x_2,x_3)$ can be used to compute the Berry phase for any closed loop in $M$, however, as we prove, it contains other information that cannot be determined from any Berry phase. When the arguments $x_i$ of $P^{(3)}(x_1,x_2,x_3)$ are taken close to each other, to the leading order, it reduces to the familiar Berry curvature $\omega$ and quantum metric $g$. We show that higher orders in this expansion are functionally independent of $\omega$ and $g$ and are related to the extrinsic properties of the map of $M$ into $\mathbb{C}P^n$ giving rise to new local gauge-invariant objects, such as the fully symmetric 3-tensor $T$. Finally, we show how our results have immediate applications to the modern theory of polarization, calculation of electrical response to a modulated field and physics of flat bands.

quant-ph↗

arXiv2021

Intrinsic anomalous Hall conductivity in a nonuniform electric field

We study how the intrinsic anomalous Hall conductivity is modified in two-dimensional crystals with broken time-reversal symmetry due to weak inhomogeneity of the applied electric field. Focusing on a clean noninteracting two-band system without band crossings, we derive the general expression for the Hall conductivity at small finite wave vector $q$ to order $q^2$, which governs the Hall response to the second gradient of the electric field. Using the Kubo formula, we show that the answer can be expressed through the Berry curvature, Fubini-Study quantum metric, and the rank-3 symmetric tensor which is related to the quantum geometric connection and physically corresponds to the gauge-invariant part of the third cumulant of the position operator. We further compare our results with the predictions made within the semiclassical approach. By deriving the semiclassical equations of motion, we reproduce the result obtained from the Kubo formula in some limits. We also find, however, that the conventional semiclassical description in terms of the definite position and momentum of the electron is not fully consistent because of singular terms originating from the Heisenberg uncertainty principle. We thus present a clear example of a case when the semiclassical approach inherently suffers from the uncertainty principle, implying that it should be applied to systems in nonuniform fields with extra care.

cond-mat.mes-hall↗

arXiv2020

Chiral transport in curved spacetime via holography

We consider a holographic model of strongly interacting plasma with a gravitational anomaly. In this model, we compute parity-odd responses of the system at finite temperature and chemical potential to external electromagnetic and gravitational fields. Working within the linearized fluid/gravity duality, we performed the calculation up to the third order in gradient expansion. Besides reproducing the chiral magnetic(CME) and vortical (CVE) effects we also obtain gradient corrections to the CME and CVE due to the gravitational anomaly. Additionally, we find energy-momentum and current responses to the gravitational field similarly determined by the gravitational anomaly. The energy-momentum response is the first purely gravitational transport effect that has been related to quantum anomalies in holographic theories.

hep-th↗

arXiv2020

Interactions remove the quantization of the chiral photocurrent at Weyl points

The chiral photocurrent or circular photogalvanic effect (CPGE) is a photocurrent that depends on the sense of circular polarization. In a disorder-free, noninteracting chiral Weyl semimetal, the magnitude of the effect is approximately quantized with a material-independent quantum $e^3/h^2$ for reasons of band topology. We study the first-order corrections due to the Coulomb and Hubbard interactions in a continuum model of a Weyl semimetal in which known corrections from other bands are absent. We find that the inclusion of interactions generically breaks the quantization. The corrections are similar but larger in magnitude than previously studied interaction corrections to the (nontopological) linear optical conductivity of graphene, and have a potentially observable frequency dependence. We conclude that, unlike the quantum Hall effect in gapped phases or the chiral anomaly in field theories, the quantization of the CPGE in Weyl semimetals is not protected but has perturbative corrections in interaction strength.

cond-mat.str-el↗

arXiv2020

Euclidean operator growth and quantum chaos

We consider growth of local operators under Euclidean time evolution in lattice systems with local interactions. We derive rigorous bounds on the operator norm growth and then proceed to establish an analog of the Lieb-Robinson bound for the spatial growth. In contrast to the Minkowski case when ballistic spreading of operators is universal, in the Euclidean case spatial growth is system-dependent and indicates if the system is integrable or chaotic. In the integrable case, the Euclidean spatial growth is at most polynomial. In the chaotic case, it is the fastest possible: exponential in 1D, while in higher dimensions and on Bethe lattices local operators can reach spatial infinity in finite Euclidean time. We use bounds on the Euclidean growth to establish constraints on individual matrix elements and operator power spectrum. We show that one-dimensional systems are special with the power spectrum always being superexponentially suppressed at large frequencies. Finally, we relate the bound on the Euclidean growth to the bound on the growth of Lanczos coefficients. To that end, we develop a path integral formalism for the weighted Dyck paths and evaluate it using saddle point approximation. Using a conjectural connection between the growth of the Lanczos coefficients and the Lyapunov exponent controlling the growth of OTOCs, we propose an improved bound on chaos valid at all temperatures.

cond-mat.stat-mech↗

arXiv2019

Rate of cluster decomposition via Fermat-Steiner point

In quantum field theory with a mass gap correlation function between two spatially separated operators decays exponentially with the distance. This fundamental result immediately implies an exponential suppression of all higher point correlation functions, but the predicted exponent is not optimal. We argue that in a general quantum field theory the optimal suppression of a three-point function is determined by total distance from the operator locations to the Fermat-Steiner point. Similarly, for the higher point functions we conjecture the optimal exponent is determined by the solution of the Euclidean Steiner tree problem. We discuss how our results constrain operator spreading in relativistic theories.

hep-th↗

arXiv2019

A Universal Operator Growth Hypothesis

We present a hypothesis for the universal properties of operators evolving under Hamiltonian dynamics in many-body systems. The hypothesis states that successive Lanczos coefficients in the continued fraction expansion of the Green's functions grow linearly with rate $α$ in generic systems, with an extra logarithmic correction in 1d. The rate $α$ --- an experimental observable --- governs the exponential growth of operator complexity in a sense we make precise. This exponential growth even prevails beyond semiclassical or large-$N$ limits. Moreover, $α$ upper bounds a large class of operator complexity measures, including the out-of-time-order correlator. As a result, we obtain a sharp bound on Lyapunov exponents $λ_L \leq 2 α$, which complements and improves the known universal low-temperature bound $λ_L \leq 2 πT$. We illustrate our results in paradigmatic examples such as non-integrable spin chains, the Sachdev-Ye-Kitaev model, and classical models. Finally we use the hypothesis in conjunction with the recursion method to develop a technique for computing diffusion constants.

cond-mat.stat-mech↗