相关论文: Finite-size Topology

This monograph offers an overview on the topological invariants in fermionic topological insulators from the complex classes. Tools from K-theory and non-commutative geometry are used to define bulk and boundary invariants, to establish the…

The identification, description, and classification of topological features is an engine of discovery and innovation in several fields of physics. This research encompasses a broad variety of systems, from the integer and fractional Chern…

We study the zero-temperature phase diagram of a two dimensional square lattice loaded by spinless fermions, with nearest neighbor hopping and algebraically decaying pairing. We find that for sufficiently long-range pairing, new phases, not…

Boltzmann's principle S(E,N,V...)=ln W(E,N,V...) allows the interpretation of Statistical Mechanics of a closed system as Pseudo-Riemannian geometry in the space of the conserved parameters E,N,V... (the conserved mechanical parameters in…

We derive a series of quantitative bulk-boundary correspondences for 3D bosonic and fermionic symmetry-protected topological (SPT) phases under the assumption that the surface is gapped, symmetric and topologically ordered, i.e., a…

The notion of topological phases extended to dynamical systems stimulates extensive studies, of which the characterization of non-equilibrium topological invariants is a central issue and usually necessitates the information of quantum…

We focus on a scenario of non-Hermitian bulk--boundary correspondence that uses a topological invariant defined in a bulk geometry under a modified periodic boundary condition. Although this has succeeded in describing the topological…

The Floquet Hamiltonian has often been used to describe a time-periodic system. Nevertheless, because the Floquet Hamiltonian depends on a micro-motion parameter, the Floquet Hamiltonian with a fixed micro-motion parameter cannot faithfully…

A definition of topological phases of density matrices is presented. The topological invariants in case of both noninteracting and interacting systems are extended to nonzero temperatures. Influence of electron interactions on topological…

We describe a one-dimensional self-gravitating system derived from the problem of large-scale structure formation in cosmology. Considering small times so that the expansion can be neglected we present a thermodynamical analysis of this…

Recently, several authors have investigated topological phenomena in periodically-driven systems of non-interacting particles. These phenomena are identified through analogies between the Floquet spectra of driven systems and the band…

Higher-order topological insulators in two spatial dimensions display fractional corner charges. While fractional charges in one dimension are known to be captured by a many-body bulk invariant, computed by the Resta formula, a many-body…

Topological phases in non-Hermitian systems have become fascinating subjects recently. In this paper, we attempt to classify topological phases in 1D interacting non-Hermitian systems. We begin with the non-Hermitian generalization of the…

We show that fully-localized, three-dimensional, time-reversal-symmetry-broken insulators do not belong to a single phase of matter but can realize topologically distinct phases that are labelled by integers. The phase transition occurs…

We introduce $\mathbb Z_2$-valued bulk invariants for symmetry-protected topological phases in $2+1$ dimensional driven quantum systems. These invariants adapt the $W_3$-invariant, expressed as a sum over degeneracy points of the…

Two-dimensional topological phases are characterized by TKNN integers, which classify Bloch energy bands or groups of Bloch bands. However, quantization does not survive thermal averaging or dephasing to mixed states. We show that using…

In this paper we study a class of physical systems that combine a finite number of mechanical and thermodynamic observables. We call them finite dimensional thermo-mechanical systems. We introduce these systems by means of simple examples.…

We present theoretical and experimental results probing the rich topological structure of arbitrarily disordered finite tight binding Hamiltonians with chiral symmetry. We extend the known classification by considering the topological…

This paper demonstrates the existence of topological models with gapped edge states but protected extended bulk states against disorder. Such systems will be labeled as trivial by the current classification of topological insulators. Our…

We study topological insulators under dephasing noise. With examples of both a $2d$ Chern insulator and a $3d$ topological insulator protected by time-reversal symmetry, we demonstrate that there is a phase transition at finite dephasing…