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arXiv · 1002.1657

Symmetry breaking and criticality in tensor-product states

Chen Liu·Ling Wang·Anders W. Sandvik·Yu-Cheng Su·Ying-Jer Kao
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Abstract

We discuss variationally optimized matrix-product states for the transverse-field Ising chain, using D*D matrices with small D=2-10. For finite system size N there are energy minimums for symmetric as well as symmetry-broken states, which cross each other at a field value hc(N,D); thus the transition is first-order. A continuous transition develops as N->infinity. The asymptotic critical behavior is then always of mean-field type (the magnetization exponent beta=1/2), but a window of field strengths where true Ising scaling holds (beta=1/8) emerges with increasing D. We also demonstrate asymptotic mean-field behavior for infinite-size two-dimensional tensor-product (iPEPS) states with small tensors.

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Chen Liu, Ling Wang, Anders W. Sandvik, Yu-Cheng Su, Ying-Jer Kao. 2010-02-08. Symmetry breaking and criticality in tensor-product states. https://doi.org/10.1103/physrevb.82.060410

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