Topological Phase Transitions for Interacting Finite Systems

TL;DR

This paper identifies a robust signature of topological phase transitions in interacting finite systems, emphasizing the role of level crossings and spatial symmetries, with practical implications for experiments and simulations.

Contribution

It introduces the concept of topologically protected level crossings as a signature of phase transitions in finite interacting systems, highlighting the importance of spatial symmetries.

Findings

Level crossings serve as robust indicators of topological transitions.

Spatial symmetries influence boundary conditions for detecting transitions.

Demonstrated in the Haldane-Fermi-Hubbard model using exact diagonalization.

Abstract

In this paper, we investigate signatures of topological phase transitions in interacting systems. We show that the key signature is the existence of a topologically protected level crossing, which is robust and sharply defines the topological transition, even in finite-size systems. Spatial symmetries are argued to play a fundamental role in the selection of the boundary conditions to be used to locate topological transitions in finite systems. We discuss the theoretical implications of this result, and utilize exact diagonalization to demonstrate its manifestations in the Haldane-Fermi-Hubbard model. Our findings provide an efficient way to detect topological transitions in experiments and in numerical calculations that cannot access the ground-state wave function.