Variational Tensor Wavefunctions for the Interacting Quantum Spin Hall Phase

TL;DR

This paper introduces a novel fermionic tensor network framework to simulate the quantum spin Hall phase in strongly-correlated systems, providing a new variational approach to study topological insulators beyond band theory.

Contribution

It develops a tensor network method based on an exactly solvable model to describe the QSH phase in correlated systems, advancing tensor algorithms for topological matter.

Findings

Derived tensor equations for symmetry transformations

Obtained variational ansatz verified numerically

Established a framework for simulating topological phases

Abstract

The quantum spin hall (QSH) phase, also known as the 2D topological insulator, is characterized by protected helical edge modes arising from time reversal symmetry. While initially proposed for band insulators, this phase can also manifest in strongly-correlated systems where conventional band theory fails. To overcome the challenge of simulating this phase in realistic correlated models, we propose a novel framework utilizing fermionic tensor network states. Our approach involves constructing a tensor representation of the fixed-point wavefunction based on an exact solvable model, enabling us to derive a set of tensor equations governing the transformation rules of local tensors under symmetry operations. These tensor equations lead to the anomalous edge theory, which provides a comprehensive description of the QSH phase. By solving these tensor equations, we obtain variational ansatz for the QSH phase, which we subsequently verify through numerical calculations. This method serves as an initial step towards employing tensor algorithms to simulate the QSH phase in strongly-correlated systems, opening new avenues for investigating and understanding topological phenomena in complex materials.