Finite Size Effects in Topological Quantum Phase Transitions

TL;DR

This paper investigates finite size effects in topological quantum phase transitions, revealing universal scaling behavior and discussing implications for real systems and potential discontinuities.

Contribution

It introduces a scaling approach to analyze finite size effects in topological transitions and explores their universality and potential discontinuities.

Findings

Finite size effects exhibit universal scaling behavior.

Topological transitions may become discontinuous due to finite size effects.

Critical exponents obey a quantum hyperscaling relation at zero temperature.

Abstract

The interest in the topological properties of materials brings into question the problem of topological phase transitions. As a control parameter is varied, one may drive a system through phases with different topological properties. What is the nature of these transitions and how can we characterize them? The usual Landau approach, with the concept of an order parameter that is finite in a symmetry broken phase is not useful in this context. Topological transitions do not imply a change of symmetry and there is no obvious order parameter. A crucial observation is that they are associated with a diverging length that allows a scaling approach and to introduce critical exponents which define their universality classes. At zero temperature the critical exponents obey a quantum hyperscaling relation. We study finite size effects at topological transitions and show they exhibit universal behavior due to scaling. We discuss the possibility that they become discontinuous as a consequence of these effects and point out the relevance of our study for real systems.