Ground state of the random-bond spin-1 Heisenberg chain

TL;DR

This study uses quantum Monte Carlo simulations to analyze the ground state of a disordered spin-1 Heisenberg chain, confirming predictions of the random-singlet phase and improving simulation efficiency.

Contribution

It provides numerical evidence for the decay of correlations in the disordered spin-1 chain and introduces a directed loop algorithm to enhance simulation performance.

Findings

Average string-correlation decays algebraically with exponent ~-0.378

Average spin-correlation decays with exponent ~-1

Directed loop implementation reduces autocorrelation times by up to two orders of magnitude

Abstract

Stochastic series expansion quantum Monte Carlo is used to study the ground state of the antiferromagnetic spin-1 Heisenberg chain with bond disorder. Typical spin- and string-correlations functions behave in accordance with real-space renormalization group predictions for the random-singlet phase. The average string-correlation function decays algebraically with an exponent of -0.378(6), in very good agreement with the prediction of $-(3-\sqrt{5})/2\simeq -0.382$, while the average spin-correlation function is found to decay with an exponent of about -1, quite different from the expected value of -2. By implementing the concept of directed loops for the spin-1 chain we show that autocorrelation times can be reduced by up to two orders of magnitude.