Multiscale entanglement renormalization ansatz for spin chains with continuously varying criticality

2015/01/31 by Jacob C. Bridgeman, Aroon O’Brien, Aroon O'Brien +2 · 1 citation
Physics and Astronomy · #Ansatz #Boson #Conformal field theory #Conformal map #Critical phenomena #Global symmetry #Mathematical physics #Orbifold #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum and electron transport phenomena #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Renormalization group #Spin (aerodynamics) #Spontaneous symmetry breaking #Symmetry breaking #Theoretical physics #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1103/physrevb.91.165129

published as Phys. Rev. B 91, 165129 (2015) · 13 pages, 11 figures, comments welcome; v2 published version

openalex publication_date 2015/04/24 · arxiv created 2015/04/26 · arxiv updated 2015/04/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We use the multiscale entanglement renormalization ansatz (MERA) to numerically investigate three critical quantum spin chains with Z₂\ifmmode×\else\texttimes\fiZ₂ 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 S¹ free boson and its Z₂ orbifold. Our numerics using MERA with explicitly enforced Z₂\ifmmode×\else\texttimes\fiZ₂ 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 S¹ boson CFT, and the Ashkin-Teller model with the Z₂-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.

Citations

• Quantum Multiscale Entanglement Renormalization Ansatz Channels
• Colloquium: Area laws for the entanglement entropy
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• Conformal Field Theory

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