Multiscale entanglement renormalization ansatz for spin chains with continuously varying criticality

作者：Bridgeman Jacob C^*; O'Brien Aroon; Bartlett Stephen D; Doherty Andrew C

来源：Physical Review B, 2015, 91(16): 165129.

DOI：10.1103/PhysRevB.91.165129

We use the multiscale entanglement renormalization ansatz (MERA) to numerically investigate three critical quantum spin chains with Z(2) x Z(2) on-site symmetry: a staggered XXZ model, a transverse field cluster model, and the quantum Ashkin-Teller model. All three models possess a continuous one-parameter family of critical points. Along this critical line, the thermodynamic limit of these models is expected to be described by classes of c = 1 conformal field theories (CFTs) of two possible types: the S-1 free boson and its Z(2)-orbifold. Our numerics using MERA with explicitly enforced Z(2) x Z(2) symmetry allow us to extract conformal data for each model, with strong evidence supporting the identification of the staggered XXZ model and critical transverse field cluster model with the S-1 boson CFT, and the Ashkin-Teller model with the Z(2)-orbifold boson CFT. Our first two models describe the phase transitions between symmetry-protected topologically ordered phases and trivial phases, which lie outside the usual Landau-Ginsburg-Wilson paradigm of symmetry breaking. Our results show that a range of critical theories can arise at the boundary of a single symmetry protected phase.

• 出版日期2015-4-24