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Lev Spodyneiko

Publications and source records attributed to Lev Spodyneiko.

16 recordsLinked to original sources
arXiv2025

Higher symmetries, anomalies, and crossed squares in lattice gauge theory

We examine higher-form symmetries of quantum lattice gauge theories through the lens of homotopy theory and operator algebras. We show that in the operator-algebraic approach both higher-form symmetries and 't Hooft anomalies arise from considering restrictions of symmetry transformations to spatial regions. The data of these restrictions are naturally packaged into a higher group. For example, for gauge theories in two spatial dimensions, this information is encoded in a crossed square of groups, which is an algebraic model of a 3-group. In general, we propose that higher groups appear in lattice models and QFT as crossed n-cubes of groups via a nonabelian version of the Cech construction.

hep-th↗
arXiv2023

Hall conductivity pump

The Thouless charge pump represents a transfer of electric charge through a gapped one-dimensional system between its zero-dimensional boundaries under a periodic change of a parameter. The value of the passed charged during a single cycle is known to be a topological invariant. We construct an analogous topological invariant that measures a pump of Hall conductance inside of three-dimensional material between its two-dimensional boundaries.

cond-mat.mes-hall↗
arXiv2023

A note on GMP algebra, dipole symmetry, and Hohenberg-Mermin-Wagner theorem in the lowest Landau level

After projection to the lowest Landau level translational invariance and particle conservation combine into dipole symmetry. We show that the new symmetry forbids spontaneous $U(1)$ symmetry breaking at zero temperature. In the case of the spatially inhomogeneous magnetic field, where the translational invariance is absent, we show that the dipole symmetry disappears and the constraint on the symmetry breaking is lifted. We pay special attention to the fate of the Girvin-Macdonald-Platzman algebra in the inhomogeneous magnetic field and show that a natural generalization of it is still present even though the dipole symmetry is not.

cond-mat.str-el↗
arXiv2022

Hohenberg-Mermin-Wagner-type theorems and dipole symmetry

We study the possibility of spontaneous symmetry breaking in systems with both charge and dipole symmetries. For $d$-dimensional systems at a positive temperature, we show that charge symmetry cannot be spontaneously broken for $d\leq 4$, while dipole symmetry cannot be spontaneously broken for $d\leq 2$. For $T=0$, we show that charge symmetry cannot be spontaneously broken for $d\leq 2$ if the compressibility is finite. We also show that continuum systems with a dipole symmetry have infinite inertial mass density.

cond-mat.str-el↗
arXiv2022

Microscopic formulas for thermoelectric transport coefficients in lattice systems

A macroscopic description of thermoelectric phenomena involves several tensorial transport coefficients. Textbook microscopic Kubo formulas for them are plagued with ambiguities in the definitions of the current operators and the magnetization. We derive a version of these formulas for lattice systems which is free from ambiguities but contains additional terms compared to the textbook results. For symmetric components of thermoelectric tensors, we identify a large class of lattice systems for which the additional terms vanish with a natural choice of the energy current. To eliminate ambiguities in the skew-symmetric components, one needs to interpret them as relative quantities: only their differences for pairs of materials are well-defined.

cond-mat.str-el↗
arXiv2021

Nernst and Ettingshausen effects in gapped quantum materials

We investigate whether there could exist topological invariants of gapped 2D materials related to dissipationless thermoelectric transport at low temperatures. We give both macroscopic and microscopic arguments showing that thermoelectric transport coefficients vanish in the limit of zero temperature and thus topological invariants arise only from the electric Hall conductance and the thermal Hall conductance. Our arguments apply to systems with arbitrarily strong interactions. We also show that there is no analog of the Thouless pump for entropy.

cond-mat.str-el↗
arXiv2020

Higher-dimensional generalizations of the Thouless charge pump

We define and study analogs of the Thouless charge pump for many-body gapped systems in dimension $D$. We show how to attach a topological invariant to a $D$-dimensional family of such systems, provided all of them have an on-site $U(1)$ symmetry. For a large class of families we argue that this topological invariant is an integer. In the case of gapped systems of free fermions in two dimensions, the invariant can be expressed in terms of the curvature of the Bloch-Berry connection. We also obtain a new formula for the Thouless charge pump in 1d which involves only static linear response and is analogous to the Streda formula for Hall conductivity.

cond-mat.str-el↗
arXiv2020

Higher-dimensional generalizations of the Berry curvature

A family of finite-dimensional quantum systems with a non-degenerate ground state gives rise to a closed 2-form on the parameter space: the curvature of the Berry connection. Its cohomology class is a topological invariant of the family. We seek generalizations of the Berry curvature to families of gapped many-body systems in D spatial dimensions. Field theory predicts that in spatial dimension D the analog of the Berry curvature is a closed (D+2)-form on the parameter space (the Wess-Zumino-Witten form). We construct such closed forms for arbitrary families of interacting lattice systems in all dimensions. In the special case of systems of free fermions in one dimension, we show that these forms can be expressed in terms of the Bloch-Berry connection on the product of the Brillouin zone and the parameter space. In the case of families of Short-Range Entangled systems, we argue that integrals of our forms over spherical cycles are quantized.

cond-mat.str-el↗
arXiv2019

Thermal Hall conductance and a relative topological invariant of gapped two-dimensional systems

We derive a Kubo-like formula for the thermal Hall conductance of a 2d lattice systems which is free from ambiguities associated with the definition of energy magnetization. We use it to define a relative topological invariant of gapped 2d lattice systems at zero temperature. Up to a numerical factor, it can be identified with the difference of chiral central charges for the corresponding edge modes. This establishes the bulk-boundary correspondence for the chiral central charge. We also show that for any Local Commuting Projector Hamiltonian the relative chiral central charge vanishes, while for free fermionic systems it is related to the zero-temperature electric Hall conductance via the Wiedemann-Franz law.

cond-mat.str-el↗
arXiv2019

Absence of energy currents in an equilibrium state and chiral anomalies

A long time ago F. Bloch showed that in a system of interacting non-relativistic particles the net particle-number current must vanish in any equilibrium state. Bloch's argument does not generalize easily to the energy current. We devise an alternative argument which proves the vanishing of the net energy currents in equilibrium states of lattice systems as well as systems of non-relativistic particles with finite-range potential interactions. We discuss some applications of these results. In particular, we show that neither a 1d lattice system nor a 1d system of non-relativistic particles with finite-range potential interactions can flow to a Conformal Field Theory with unequal left-moving and right-moving central charges.

cond-mat.stat-mech↗
arXiv2018

De Sitter Space and the Swampland

It has been notoriously difficult to construct a meta-stable de Sitter (dS) vacuum in string theory in a controlled approximation. This suggests the possibility that meta-stable dS belongs to the swampland. In this paper, we propose a swampland criterion in the form of $|\nabla V|\geq\ c \cdot V$ for a scalar potential $V$ of any consistent theory of quantum gravity, for a positive constant $c$. In particular, this bound forbids dS vacua. The existence of this bound is motivated by the abundance of string theory constructions and no-go theorems which exhibit this behavior. We also extend some of the well-known no-go theorems for the existence of dS vacua in string theory to more general accelerating universes and reinterpret the results in terms of restrictions on allowed scalar potentials.

hep-th↗
arXiv2017

New Kaluza-Klein Instantons and Decay of AdS Vacua

We construct a generalization of Witten's Kaluza-Klein instanton, where a higher-dimensional sphere (rather than a circle as in Witten's instanton) collapses to zero size and the geometry terminates at a bubble of nothing, in a low energy effective theory of M theory. We use the solution to exhibit instability of non-supersymmetric AdS_5 vacua in M Theory compactified on positive Kaehler-Einstein spaces, providing a further evidence for the recent conjecture that any non-supersymmetric anti-de Sitter vacuum supported by fluxes must be unstable.

hep-th↗
arXiv2016

On W algebras commuting with a set of screenings

We consider the problem of classification of all W algebras which commute with a set of exponential screening operators. Assuming that the W algebra has a nontrivial current of spin 3, we find equations satisfied by the screening operators and classify their solutions.

hep-th↗
arXiv2014

AGT correspondence, Ding-Iohara algebra at roots of unity and Lepowsky-Wilson construction

It was recently conjectured that the AGT correspondence between the $U(r)$-instanton counting on $\mathbb R^4/\mathbb Z_p$ and the two-dimensional field theories with the conformal symmetry algebra $\mathcal A(r,p)$ can be considered as a root of unity limit of its K-theoretic analogue. From this point of view, the algebra $\mathcal A(r,p)$ and a special basis in its representation are limits of the Ding-Iohara algebra and the Macdonald polynomials respectively. In this paper we confirm this conjecture for the special case $r=1$. We uncover the implicit $\mathcal A(1,p)$ symmetry in this limit. We also found that the vertex operators in the special basis have factorized AFLT form.

hep-th↗
arXiv2014

Minimal Liouville Gravity on the Torus via Matrix Models

In this paper we use recent results on resonance relations between the matrix models and the minimal Liouville gravity to compute the torus correlation numbers in (3,p) minimal Liouville gravity. Namely, we calculate the torus generating partition function of the (3,p) matrix models and use it to obtain the one- and two-point correlation numbers in the minimal Liouville gravity.

hep-th↗