Related papers: Unveiling Correlated Two-dimensional Topological I…
The standard boundary state of a topological insulator in 3+1 dimensions has gapless charged fermions. We present model systems that reproduce this standard gapless boundary state in one phase, but also have gapped phases with topological…
Higher-order topological crystalline phases in low-dimensional interacting quantum systems represent a challenging and largely unexplored research topic. Here, we derive a Hamiltonian describing fermions interacting through correlated…
Fractional topological insulators are electronic systems that carry fractionally charged excitations, conserve charge and are symmetric to reversal of time. In this review we introduce the basic essential concepts of the field, and then…
While free fermion topological crystalline insulators have been largely classified, the analogous problem in the strongly interacting case has been only partially solved. In this paper, we develop a characterization and classification of…
Trial wavefunctions that can be represented by summing over locally-coupled degrees of freedom are called tensor network states (TNSs); they have seemed difficult to construct for two-dimensional topological phases that possess protected…
We present a general framework for analyzing fractionalized, time reversal invariant electronic insulators in two dimensions. The framework applies to all insulators whose quasiparticles have abelian braiding statistics. First, we construct…
The detection of topological phases of matter becomes a central issue in recent years. Conventionally, the realization of a specific topological phase in condensed matter physics relies on probing the underlying surface band dispersion or…
We numerically verify and analytically prove a winding number invariant that correctly predicts the number of edge states in one-dimensional, nearest-neighbor (between unit cells), two-band models with any complex couplings and open…
Recent works have proved the existence of symmetry-protected edge states in certain one-dimensional topological band insulators and superconductors at the gap-closing points which define quantum phase transitions between two topologically…
Topologically protected gapless edge states are phases of quantum matter which behave as massless Dirac fermions, immunizing against disorders and continuous perturbations. Recently, a new class of topological insulators (TIs) with…
In this tutorial, we pedagogically review recent developments in the field of non-interacting fermionic phases of matter, focussing on the low energy description of higher-order topological insulators in terms of the Dirac equation. Our aim…
Topological band insulators which are dynamically generated by electron-electron interactions have been the- oretically proposed in two and three dimensional lattice models. We present evidence that the two-dimensional version can be…
A two-dimensional topological insulator may arise in a centrosymmetric commensurate N\'{e}el antiferromagnet (AF), where staggered magnetization breaks both the elementary translation and time reversal, but retains their product as a…
We develop a continuum theory to model low energy excitations of a generic four-band time reversal invariant electronic system with boundaries. We propose a variational energy functional for the wavefunctions which allows us derive natural…
Massless excitations at the surface of three-dimensional time-reversal invariant topological insulators possess both fermionic and bosonic descriptions, originating from band theory and hydrodynamic BF gauge theory, respectively. We analyze…
Tensor network states, and in particular projected entangled pair states, play an important role in the description of strongly correlated quantum lattice systems. They do not only serve as variational states in numerical simulation…
We study one-dimensional, interacting, gapped fermionic systems described by variants of the Peierls-Hubbard model and characterize their phases via a topological invariant constructed out of their Green's functions. We demonstrate that the…
Electronic topological phases of matter, characterized by robust boundary states derived from topologically nontrivial bulk states, are pivotal for next-generation electronic devices. However, understanding their complex quantum phases,…
Three dimensional topological insulator represents a class of novel quantum phases hosting robust gapless boundary excitations, which is protected by global symmetries such as time reversal, charge conservation and spin rotational symmetry.…
Two-dimensional (2D) topological electronic insulators are known to give rise to gapless edge modes, which underlie low energy dynamics, including electrical and thermal transport. This has been thoroughly investigated in the context of…