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Symmetry Breaking and Criticality in Tensor-product States by Liu, Chen; Wang, Ling; Sandvik, Anders W.; Su, Yu-Cheng; Kao, Ying-Jer is a scholarly article available to read on EtoBox.

What is Symmetry Breaking and Criticality in Tensor-product States about?

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.

Author

Liu, Chen; Wang, Ling; Sandvik, Anders W.; Su, Yu-Cheng; Kao, Ying-Jer

Published

2010

Language

EN