Symmetry breaking and criticality in tensor-product states

Author(s): C. Liu, L. Wang, A. W. Sandvik, Y.-C. Su, Y.-J. Kao

Journal: Phys. Rev. B

Volume: 82

Page(s): 060410

Year: 2010

DOI Number: 10.1103/PhysRevB.82.060410

Link: Link to publication


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→∞. The asymptotic critical behavior is then always of mean-field type (the magnetization exponent β=1/2) but a window of field strengths where true Ising scaling holds (β=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. The behaviors should be generic at symmetry-breaking transitions.


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