Ground state of the S = 1/2 Heisenberg spin chain with random ferro- and antiferromagnetic couplings

TL;DR

This study uses quantum Monte Carlo simulations to analyze the ground state of a disordered S=1/2 Heisenberg chain, revealing an exotic critical state with dual scaling regimes and variable exponents, challenging previous theoretical predictions.

Contribution

It provides the first unbiased quantum Monte Carlo analysis of the disordered Heisenberg chain's ground state, showing variable scaling exponents and dual correlation regimes.

Findings

Identification of an exotic critical state with dual scaling regimes.

Scaling exponents depend on the coupling distribution.

Results challenge previous spin-wave and DMRG calculations.

Abstract

We study the Heisenberg $S=1/2$ chain with random ferro- and antiferromagnetic couplings using quantum Monte Carlo simulations at ultra-low temperatures, converging to the ground state. Finite-size scaling of correlation functions and excitation gaps demonstrate an exotic critical state in qualitative agreement with previous strong-disorder renormalization group calculations but with scaling exponents depending on the coupling distribution. We find dual scaling regimes of the transverse correlations versus the distance, with an $L$ independent form $C(r)=r^{-\mu}$ for $r \ll L$ and $C(r,L)=L^{-\eta}f(r/L)$ for $r/L > 0$, where $\mu > \eta$ and the scaling function is delivered by our analysis. These results are at variance with previous spin-wave and density-matrix renormalization group calculations, thus highlighting the power of unbiased quantum Monte Carlo simulations.