Variational Tensor Wavefunctions for the Interacting Quantum Spin Hall Phase

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.

6+15 pages,12 figures. Numerical calculations are added

References in corpus (12)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge
• Fermionic Matrix Product States and One-Dimensional Topological Phases
• Anyon condensation and a generic tensor-network construction for symmetry protected topological phases
• Fermionic projected entangled-pair states and topological phases
• Symmetries and boundary theories for chiral Projected Entangled Pair States
• Microscopic Realization of 2-Dimensional Bosonic Topological Insulators
• Exactly solvable lattice models for interacting electronic insulators in two dimensions

Cited by in corpus (2)

• Boundary anomaly detection in two-dimensional subsystem symmetry-protected topological phases
• Frustration-free free fermions