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arXiv · 1603.07769

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

Rubina Zadourian·Andreas Fledderjohann·Andreas Klümper
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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.

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Rubina Zadourian, Andreas Fledderjohann, Andreas Klümper. 2016-03-24. Matrix product states for $su(2)$ invariant quantum spin chains. https://doi.org/10.1088/1742-5468%2F2016%2F08%2F083101

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