Characterizing Real-space Topology in Rice-Mele Model by Thermodynamics

TL;DR

This paper uses thermodynamic quantities related to energy-level statistics to characterize the real-space topology of the Rice-Mele model, revealing how boundary conditions influence topological phase transitions and edge states.

Contribution

It introduces a thermodynamic approach to analyze the Rice-Mele model's topology, linking boundary conditions to critical points and edge state emergence.

Findings

Critical point equals inverse domain length for symmetric boundary conditions.

Edge states are associated with non-normalizable wave functions in infinite domains.

Thermodynamic properties reflect topological phase transitions and boundary effects.

Abstract

The thermodynamic quantities which are related to energy-level statistics are used to characterize the real-space topology of the Rice-Mele model. Through studying the energy spectrum of the model under different boundary conditions, we found that the non-normalizable wave function for the infinite domain is reduced to the edge state adhered to the boundary. For the finite domain with symmetric boundary condition, the critical point for the topological phase transition is equal to the inverse of the domain length. In contrast, the critical point is zero for the semi-infinite domain. Additionally, the symmetry of the energy spectrum is found to be sensitive to the boundary conditions of the Rice-Mele model, and the emergence of the edge states as well as the topological phase transition can be reflected in the thermodynamic properties. A potentially practical scheme is proposed for simulating the Rice-Mele model and detecting the relevant thermodynamic quantities in the context of Bose-Einstein condensate.