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

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.

15 pages, 10 figures

References in corpus (9)

• The density-matrix renormalization group in the age of matrix product states
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• From density-matrix renormalization group to matrix product states
• Variational quantum Monte Carlo simulations with tensor-network states
• Simulation of anyons with tensor network algorithms
• Vector chiral order in frustrated spin chains
• Variational treatment of the Shastry-Sutherland antiferromagnet using Projected Entangled Pair States (PEPS)
• Identifying Symmetry-Protected Topological Order by Entanglement Entropy
• Correlation functions of the integrable isotropic spin-1 chain: algebraic expressions for arbitrary temperature

Cited by in corpus (3)

• Combined use of translational and spin-rotational invariance for spin systems
• Bilinear-biquadratic spin-1 rings: an SU(2)-symmetric MPS algorithm for periodic boundary conditions
• Construction of Variational Matrix Product States for the Heisenberg Spin-1 Chain