Universal Finite-Size Scaling around Topological Quantum Phase Transitions

TL;DR

This paper introduces a universal finite-size scaling function for topological quantum phase transitions, applicable across multiple symmetry classes, providing a new tool to distinguish phases based on finite-size effects.

Contribution

It derives an analytic universal scaling function for finite-size corrections that differentiate topological phases in one-dimensional systems across all non-trivial symmetry classes.

Findings

The scaling function discriminates between different topological phases.

Analytic form of the scaling function matches numerical simulations.

Universal applicability across five Altland-Zirnbauer classes.

Abstract

The critical point of a topological phase transition is described by a conformal field theory, where finite-size corrections to energy are uniquely related to its central charge. We investigate the finite-size scaling away from criticality and find a scaling function, which discriminates between phases with different topological indexes. This function appears to be universal for all five Altland-Zirnbauer symmetry classes with non-trivial topology in one spatial dimension. We obtain an analytic form of the scaling function and compare it with numerical results.