A discriminating string order parameter for topological phases of gapped SU(N) spin chains

TL;DR

This paper introduces a non-local string order parameter that uniquely characterizes the N topological phases in one-dimensional gapped SU(N) spin chains, enabling detection of phase transitions.

Contribution

The authors propose a new string order parameter for SU(N) spin chains that unambiguously identifies each topological phase and detects quantum phase transitions.

Findings

Order parameter extracts quantized topological invariants

Numerical results confirm the order parameter's effectiveness

Discontinuous jumps indicate phase transitions

Abstract

One-dimensional gapped spin chains with symmetry PSU(N) = SU(N)/Z_N are known to possess N different topological phases. In this paper, we introduce a non-local string order parameter which characterizes each of these N phases unambiguously. Numerics confirm that our order parameter allows to extract a quantized topological invariant from a given non-degenerate gapped ground state wave function. Discontinuous jumps in the discrete topological order that arise when varying physical couplings in the Hamiltonian may be used to detect quantum phase transitions between different topological phases.