arXiv subjects

Polina Matveeva

Publications and source records attributed to Polina Matveeva.

7 recordsLinked to original sources

arXiv2026

Topological properties of gapless phases in an interacting spinful wire

We study topology in gapless phases of an interacting spinful model with spin-charge separation. We focus on the gapless boundaries between $\mathbb{Z}_2$ symmetry-breaking phases. We find two topologically non-trivial gapless states that occur at the boundary between a non-trivial and a trivial insulator. They correspond to topological Luther-Emery liquid and topological Mott insulator. The Luther-Emery liquid is characterized by gapless charge excitations and features topological edge modes that carry fractional spin, while the topological Mott insulator has gapless spin sector and features edge states that carry fractional charge. Surprisingly, even though there is no mean-field description of the interacting gapless phases, as there is no local order parameter, we show that they can be adiabatically connected to a non-interacting topological metal. This non-interacting state is a phase boundary between decoupled Su-Schrieffer-Heeger chains with the winding number $\nu=2$ and chains with $\nu=1$.

cond-mat.str-el↗

arXiv2025

Topological phases and spontaneous symmetry breaking: the revenge of the original Su-Schrieffer-Heeger model

We study the interplay of spontaneous symmetry breaking and topological properties in interacting one-dimensional models. We solve these models using bozonization and identify topologically non-trivial phases by counting the additional degeneracy (affiliated with the edge modes) of a finite-size system relative to the infinite one. We find even if the mean-field solution is topological, this may not be true when it arises from spontaneous symmetry breaking, including in the Su-Schrieffer-Heeger (SSH) model. This implies that the original SSH model, as presented by Su, Schrieffer, and Heeger, is topologically trivial, as opposed to its mean-field version. A spinful version, on the other hand, does exhibit a topologically non-trivial phase. In that state, both mean-field solutions are topologically non-trivial and correspond to non-interacting SSH chains in the opposite phases with the winding number $ν=1$. We show that this phase is protected by a chiral symmetry, similar to the non-interacting phases.

cond-mat.mes-hall↗

arXiv2024

Weakly interacting one-dimensional topological insulators: a bosonization approach

We investigate the topological properties of one-dimensional weakly interacting topological insulators using bosonization. To do that we study the topological edge states that emerge at the edges of a model realized by a strong impurity or at the boundary between topologically distinct phases. In the bosonic model, the edge states are manifested as degenerate bosonic kinks at the boundaries. We first illustrate this idea on the example of the interacting Su-Schrieffer-Heeger (SSH) chain. We compute the localization length of the edge states as the width of an edge soliton that occurs in the SSH model in the presence of a strong impurity. Next, we examine models of two capacitively coupled SSH chains that can be either identical or in distinct topological phases. We find that weak Hubbard interaction reduces the ground state degeneracy in the topological phase of identical chains. We then prove that similarly to the non-interacting model, the degeneracy of the edge states in the interacting case is protected by chiral symmetry. We then study topological insulators built from two SSH chains with inter-chain hopping, that represent models of different chiral symmetric universality classes. We demonstrate in bosonic language that the topological index of a weakly coupled model is determined by the type of inter-chain coupling, invariant under one of two possible chiral symmetry operators. Finally, we show that a general one-dimensional model in a phase with topological index $\nu$ is equivalent at low energies to a theory of at least $\nu$ SSH chains. We illustrate this idea on the example of an SSH model with longer-range hopping.

cond-mat.mes-hall↗

arXiv2023

Elementary models of 3D topological insulators with chiral symmetry

We construct a set of lattice models of non-interacting topological insulators with chiral symmetry in three dimensions. We build a model of the topological insulators in the class AIII by coupling lower dimensional models of $\mathbb{Z}$ classes. By coupling the two AIII models related by time-reversal symmetry we construct other chiral symmetric topological insulators that may also possess additional symmetries (the time-reversal and/or particle-hole). There are two different chiral symmetry operators for the coupled model, that correspond to two distinct ways of defining the sublattices. The integer topological invariant (the winding number) in case of weak coupling can be either the sum or difference of indices of the basic building blocks, dependent on the preserved chiral symmetry operator. The value of the topological index in case of weak coupling is determined by the chiral symmetry only and does not depend on the presence of other symmetries. For $\mathbb{Z}$ topological classes AIII, DIII, and CI with chiral symmetry are topologically equivalent, it implies that a smooth transition between the classes can be achieved if it connects the topological sectors with the same winding number. We demonstrate this explicitly by proving that the gapless surface states remain robust in $\mathbb{Z}$ classes as long as the chiral symmetry is preserved, and the coupling does not close the gap in the bulk. By studying the surface states in $\mathbb{Z}_2$ topological classes, we show that class CII and AII are distinct, and can not be adiabatically connected.

cond-mat.mes-hall↗

arXiv2022

Boundary logarithmic corrections to the dynamical correlation functions of one-dimensional spin-1/2 chains

The asymptotic dynamical correlation functions in one-dimensional spin chains are described by power-laws. The corresponding exponents characterize different bulk and boundary critical behavior. We present novel results for the logarithmic contribution to the boundary correlations of an isotropic Heisenberg chain. The exponent of the logarithm, $λ=1$, is derived using a renormalization group technique. We confirm our analytical results by comparing with numerical quantum Monte Carlo data.

cond-mat.str-el↗

arXiv2022

One-dimensional non-interacting topological insulators with chiral symmetry

We construct microscopical models of one-dimensional non-interacting topological insulators in all of the chiral universality classes. Specifically, we start with a deformation of the Su-Schrieffer-Heeger (SSH) model that breaks time-reversal symmetry, which is in the AIII class. We then couple this model to its time-reversal counterpart in order to build models in the classes BDI, CII, DIII and CI. We find that the $\mathbb{Z}$ topological index (the winding number) in individual chains is defined only up to a sign. This comes from noticing that changing the sign of the chiral symmetry operator changes the sign of the winding number. The freedom to choose the sign of the chiral symmetry operator on each chain independently allows us to construct two distinct possible chiral symmetry operators when the chains are weakly coupled -- in one case, the total winding number is given by the sum of the winding number of individual chains while in the second case, the difference is taken. We find that the chiral models that belong to $\mathbb{Z}$ classes, AIII, BDI and CII are topologically equivalent, so they can be adiabatically deformed into one another so long as the chiral symmetry is preserved. We study the properties of the edge states in the constructed models and prove that topologically protected edge states must all be localised on the same sublattice (on any given edge). We also discuss the role of particle-hole symmetry on the protection of edge states and explain how it manages to protect edge states in $\mathbb{Z}_2$ classes, where the integer invariant vanishes and chiral symmetry alone does not protect the edge states anymore. We discuss applications of our results to the case of an arbitrary number of coupled chains, construct possible chiral symmetry operators for the multiple chain case, and briefly discuss the generalisation to any odd number of dimensions.

cond-mat.mes-hall↗

arXiv2019

Construction and universal application of entanglement erasing partner states

We investigate the subadditivity of the bipartite entanglement entropy (EE) of many-particle states, represented by Slater determinants, with respect to single particle excitations. In this setting, subadditivity can be phrased as erasure of EE, i.e. as a relative decrease in EE when adding excitations to the quantum state. We identify sets of single particle states that yield zero EE if jointly excited. Such states we dub entanglement erasing partner states (EEPS). These EEPS reveal a mechanism that describes how to disentangle two subspaces of a Hilbert space by exciting additional states. We demonstrate this general finding in Anderson and many-body localized models. The studied concept of entanglement erasure further enables us to derive the EE of Slater determinants in the free tight binding model. Here, our analytical findings show surprisingly good agreement with numerical results of the interacting XXX chain. The described EEPS further impose a universal, i.e. model independent, erasure of EE for randomly excited Slater determinants. This feature allows to compute many-particle EE by means of the associated single particle states and the filling ratio. This novel finding can be employed to drastically reduce the computational effort in free models.

quant-ph↗