Matrix product states for $su(2)$ invariant quantum spin chains

TL;DR

This paper develops a systematic approach using matrix product states to analyze $su(2)$ invariant quantum spin chains, enabling high-precision calculations of physical properties and revealing crossover phenomena in correlations.

Contribution

It introduces a comprehensive MPS framework for $su(2)$ invariant spin-$s$ chains, utilizing Wigner calculus for algebraic calculations and providing explicit results for complex quantum models.

Findings

High-accuracy ground-state energy calculations

Explicit entanglement entropy and correlation functions

Observation of crossover phenomena in correlation lengths

Abstract

A systematic and compact treatment of arbitrary $su(2)$ invariant spin-$s$ quantum chains with nearest-neighbour interactions is presented. The ground-state is derived in terms of matrix product states (MPS). The fundamental MPS calculations consist of taking products of basic tensors of rank 3 and contractions thereof. The algebraic $su(2)$ calculations are carried out completely by making use of Wigner calculus. As an example of application, the spin-1 bilinear-biquadratic quantum chain is investigated. Various physical quantities are calculated with high numerical accuracy of up to 7 digits. We obtain explicit results for the ground-state energy, entanglement entropy, singlet operator correlations and the string order parameter. We find interesting crossover phenomena in the correlation lengths.