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International Conference on Strongly Correlated Electron Systems (SCES)

Topological Properties of Correlated Insulators in One Dimension

Tsuneya Yoshida, Robert Peters, Satoshi Fujimoto, Norio Kawakami

Published Jun 16, 2014• 0 citations
Publisher

Abstract

In this paper, we study a one-dimensional correlated topological insulator protected by chiral symmetry. We analyze correlation effects on gapless edge states, as well as bulk topological properties. It is found that although double occupancy gradually changes in the bulk, it shows an abrupt change at the edge sites. Correspondingly the single particle spectrum becomes gapped at the edge sites.

DOI
10.7566/jpscp.3.016010

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In this paper, we study a one-dimensional correlated topological insulator protected by chiral symmetry. We analyze correlation effects on gapless edge states, as well as bulk topological properties. It is found that although double occupancy gradually changes in the bulk, it shows an abrupt change at the edge sites. Correspondingly the single particle spectrum becomes gapped at the edge sites.
We investigate properties of a topological Mott insulator in one dimension by examining the bulk topological invariant and the entanglement spectrum of a correlated electron model. We clarify how gapless edge states in a noninteracting topological band insulator evolve into spinon edge states in a topological Mott insulator. Furthermore, we propose a topological Mott transition, which is a new type of topological phase transition which has never been observed in free fermion systems. This unconventional transition occurs in spin liquid phases in the Mott insulator and is accompanied by zeros of the single-electron Green's function and a gap closing in the spin excitation spectrum.
We consider a one-dimensional, time-reversal-invariant system with attractive interactions and spin-orbit coupling. Such a system is gapless due to the strong quantum fluctuations of the superconducting order parameter. However, we show that a sharply defined topological phase with protected, exponentially localized edge states exists. If one of the spin components is conserved, the protection of the edge modes can be understood as a consequence of the presence of a spin gap. In the more general case, the localization of the edge states arises from a gap to single-particle excitations in the bulk. We consider specific microscopic models and demonstrate both analytically and numerically (using density matrix renormalization group calculations) that they can support the topologically nontrivial phase.
Strongly correlated analogs of topological insulators have been explored in systems with purely on-site symmetries, such as time-reversal or charge conservation. Here, we use recently developed tensor network tools to study a quantum state of interacting bosons which is featureless in the bulk, but distinguished from an atomic insulator in that it exhibits entanglement which is protected by its spatial symmetries. These properties are encoded in a model many-body wave function that describes a fully symmetric insulator of bosons on the honeycomb lattice at half filling per site. While the resulting integer unit cell filling allows the state to bypass ``no-go'' theorems that trigger fractionalization at fractional filling, it nevertheless has nontrivial entanglement, protected by symmetry. We demonstrate this by computing the boundary entanglement spectra, finding a gapless entanglement edge described by a conformal field theory as well as degeneracies protected by the nontrivial action of combined charge conservation and spatial symmetries on the edge. Here, the tight-binding representation of the space group symmetries plays a particular role in allowing certain entanglement cuts that are not allowed on other lattices of the same symmetry, suggesting that the lattice representation can serve as an additional symmetry ingredient in protecting an interacting topological phase. Our results extend to a related insulating state of electrons, with short-ranged entanglement and no band insulator analog.
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We investigate correlation effects in two-dimensional topological insulators (TI). In the first part, we discuss finite size effects for interacting systems of different sizes in a ribbon geometry. For large systems, there are two pairs of well separated massless modes on both edges. For these systems, we analyze the finite size effects using a standard bosonization approach. For small systems, where the edge states are massive Dirac fermions, we use the inhomogeneous dynamical mean-field theory (DMFT) combined with iterative perturbation theory as an impurity solver to study interaction effects. We show that the finite size gap in the edge states is renormalized for weak interactions, which is consistent with a Fermi-liquid picture for small size TIs. In the second part, we investigate phase transitions in finite size TIs at zero temperature focusing on the effects of possible interedge umklapp scattering for the edge states within the inhomogeneous DMFT using the numerical renormalization group. We show that correlation effects are effectively stronger near the edge sites because the coordination number is smaller than in the bulk. Therefore the localization of the edge states around the edge sites, which is a fundamental property in TIs, is weakened for strong coupling strengths. However, we find no signs for ``edge Mott insulating states'' and the system stays in the topological insulating state, which is adiabatically connected to the noninteracting state for all interaction strengths smaller than the critical value. Increasing the interaction further, a nearly homogeneous Mott insulating state is stabilized.