Scaling of entanglement entropy at quantum critical points in random spin chains

TL;DR

This study investigates how entanglement entropy scales near quantum critical points in disordered spin chains, revealing universal behavior consistent with infinite-randomness fixed points and highlighting differences in spin-1/2 systems.

Contribution

It provides the first unbiased numerical confirmation that the quantum critical point in disordered spin-1 chains belongs to the infinite-randomness universality class.

Findings

Entanglement entropy diverges logarithmically with system size at the QCP.

Effective central charge at the QCP is approximately 1.17.

Correlation length exponent is approximately 2.28.

Abstract

We study the scaling properties of the entanglement entropy (EE) near quantum critical points in interacting random antiferromagnetic (AF) spin chains. Using density-matrix renormalization group, we compute the half-chain EE near the topological phase transition between Haldane and Random Singlet phases in a disordered spin-1 chain. It is found to diverge logarithmically in system size with an effective central charge $c_{\rm eff} = 1.17(4)$ at the quantum critical point (QCP). Moreover, a scaling analysis of EE yields the correlation length exponent $\nu=2.28(5)$. Our unbiased calculation establishes that the QCP is in the universality class of the infinite-randomness fixed point predicted by previous studies based on strong disorder renormalization group technique. However, in the disordered spin-1/2 Majumdar-Ghosh chain, where a valence bond solid phase is unstable to disorder, the crossover length exponent obtained from a scaling analysis of EE disagrees with the expectation based on Imry-Ma argument. We provide a possible explanation.