Properties of the random-singlet phase: from the disordered Heisenberg chain to an amorphous valence-bond solid

TL;DR

This paper investigates the properties of the random-singlet phase in disordered spin chains using SDRG and QMC methods, revealing logarithmic corrections and the formation of an amorphous valence-bond solid.

Contribution

It demonstrates the presence of logarithmic corrections in correlation functions and characterizes the amorphous valence-bond solid as a variant of the random-singlet phase.

Findings

Logarithmic corrections to correlation functions.

Formation of amorphous valence-bond solid.

Differences in short-distance properties from standard random-singlet states.

Abstract

We use a strong-disorder renormalization group (SDRG) method and ground-state quantum Monte Carlo (QMC) simulations to study S=1/2 spin chains with random couplings, calculating disorder-averaged spin and dimer correlations. The QMC simulations demonstrate logarithmic corrections to the power-law decaying correlations obtained with the SDRG scheme. The same asymptotic forms apply both for systems with standard Heisenberg exchange and for certain multi-spin couplings leading to spontaneous dimerization in the clean system. We show that the logarithmic corrections arise in the valence-bond (singlet pair) basis from a contribution that can not be generated by the SDRG scheme. In the model with multi-spin couplings, where the clean system dimerizes spontaneously, random singlets form between spinons localized at domain walls in the presence of disorder. This amorphous valence-bond solid is asymptotically a random-singlet state and only differs from the random-exchange Heisenberg chain in its short-distance properties.