Matrix product states for $su(2)$ invariant quantum spin chains
Abstract
A systematic and compact treatment of arbitrary invariant spin- 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 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.
Cite
@article{arxiv.1603.07769,
title = {Matrix product states for $su(2)$ invariant quantum spin chains},
author = {Rubina Zadourian and Andreas Fledderjohann and Andreas Klümper},
journal= {arXiv preprint arXiv:1603.07769},
year = {2016}
}
Comments
15 pages, 10 figures