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Variational Tensor Wave Functions for the Interacting Quantum Spin Hall Phase.

Yixin Ma1, Shenghan Jiang1, Chao Xu1

  • 1Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China.

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|April 5, 2024
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Summary
This summary is machine-generated.

We introduce a new tensor network method to simulate the quantum spin Hall (QSH) phase in complex materials. This approach models topological insulators and their edge states, advancing the study of correlated systems.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Materials Science

Background:

  • The quantum spin Hall (QSH) phase, a 2D topological insulator, features protected helical edge modes due to time-reversal symmetry.
  • This phase can occur in strongly correlated systems beyond the scope of conventional band theory.

Purpose of the Study:

  • To develop a novel framework for simulating the QSH phase in realistic correlated models.
  • To overcome the limitations of current simulation techniques for topological insulators.

Main Methods:

  • Utilized fermionic tensor network states to construct a tensor representation of the fixed-point wave function.
  • Derived tensor equations from an exact solvable model to describe symmetry transformations.
  • Obtained variational ansatz for the QSH phase by solving these tensor equations.

Main Results:

  • Developed a method to derive the anomalous edge theory describing the QSH phase.
  • Successfully obtained variational ansatz for the QSH phase.
  • Verified the topological properties of the QSH phase through numerical calculations.

Conclusions:

  • The proposed tensor network approach is a viable first step for simulating the QSH phase in strongly correlated systems.
  • This work opens new avenues for investigating topological phenomena in complex materials using tensor algorithms.