MERA for Spin Chains with Continuously Varying Criticality

TL;DR

This paper employs MERA to numerically analyze three critical quantum spin chains with Z_2 x Z_2 symmetry, identifying their conformal field theory descriptions and revealing diverse critical behaviors at phase boundaries.

Contribution

The study applies MERA with symmetry enforcement to identify the conformal field theories of models with continuously varying critical points, linking them to S^1 and Z_2-orbifold boson CFTs.

Findings

Models correspond to S^1 and Z_2-orbifold boson CFTs.

Phase transitions occur outside traditional symmetry-breaking paradigms.

Critical theories vary within a single symmetry protected phase.

Abstract

We use the multiscale entanglement renormalisation 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.