Tensor network renormalization group study of spin-1 random Heisenberg chains

TL;DR

This paper employs tensor network strong-disorder renormalization group techniques to analyze phase transitions and critical properties in disordered spin-1 Heisenberg chains, revealing new insights into the critical behavior and phase boundaries.

Contribution

It introduces an efficient tensor network SDRG method for studying disordered quantum chains and accurately characterizes the quantum critical point and phases in spin-1 chains.

Findings

Identified the quantum critical point between Haldane and random-singlet phases.

Determined critical exponents for string order and correlation functions.

Found improved agreement with theoretical predictions over previous studies.

Abstract

We use a tensor network strong-disorder renormalization group (tSDRG) method to study spin-1 random Heisenberg antiferromagnetic chains. The ground state of the clean spin-1 Heisenberg chain with uniform nearest-neighbor couplings is a gapped phase known as the Haldane phase. Here we consider disordered chains with random couplings, in which the Haldane gap closes in the strong disorder regime. As the randomness strength is increased further and exceeds a certain threshold, the random chain undergoes a phase transition to a critical random-singlet phase. The strong-disorder renormalization group method formulated in terms of a tree tensor network provides an efficient tool for exploring ground-state properties of disordered quantum many-body systems. Using this method we detect the quantum critical point between the gapless Haldane phase and the random-singlet phase via the disorder-averaged string order parameter. We determine the critical exponents related to the average string order parameter, the average end-to-end correlation function and the average bulk spin-spin correlation function, both at the critical point and in the random-singlet phase. Furthermore, we study energy-length scaling properties through the distribution of energy gaps for a finite chain. Our results are in closer agreement with the theoretical predictions than what was found in previous numerical studies. As a benchmark, a comparison between tSDRG results for the average spin correlations of the spin-1/2 random Heisenberg chain with those obtained by using unbiased zero-temperature QMC method is also provided.