Numerical study of critical properties and hidden orders in dimerized spin ladders

TL;DR

This study uses exact diagonalization to analyze quantum phase transitions and hidden order parameters in dimerized spin ladders, revealing critical properties and non-local order distinctions in these quantum systems.

Contribution

It provides a detailed numerical analysis of critical properties and hidden string order parameters in dimerized spin ladders, including estimates of critical exponents.

Findings

Identification of quantum critical points in dimerized ladders

Detection of non-local string order parameters distinguishing phases

Estimation of critical exponents nu and beta

Abstract

Dimerized antiferromagnetic spin-1/2 ladders are known to exhibit a quantum critical phase transition in the ground state, the existence or absence of which is dependent on the dimerization pattern of the ladder. The gapped phases cannot be distinguished by the conventional Landau long-range order parameter. However, they possess a non-local (hidden) string order parameter, which is non-zero in one phase and vanishes in the other. We use an exact diagonalization technique to calculate ground state energies, energy gaps and string order parameters of dimerized two- and three-leg Heisenberg ladders, as well as a critical scaling analysis to yield estimates of the critical exponents nu and beta.