Decoding quantum criticalities from fermionic/parafermionic topological states

TL;DR

This paper develops a method to decode quantum critical points in one-dimensional topological phases with fermions and parafermions using matrix product states, revealing conformal field theories with central charge up to 1.

Contribution

It generalizes matrix product state techniques to systems with finite correlation length and applies them to identify quantum critical spectra in fermionic and parafermionic topological phases.

Findings

Critical spectra described by conformal field theories with c ≤ 1

Decoding quantum criticality from interacting Majorana/parafermion states

Extension of MPS framework to finite correlation length states

Abstract

Under an appropriate symmetric bulk bipartition in a one-dimensional symmetry protected topological phase with the Affleck-Kennedy-Lieb-Tasaki matrix product state wave function for the odd integer spin chains, a bulk critical entanglement spectrum can be obtained, describing the excitation spectrum of the critical point separating the topological phase from the trivial phase with the same symmetry. Such a critical point is beyond the standard Landau-Ginzburg-Wilson paradigm for symmetry breaking phase transitions. Recently, the framework of matrix product states for topological phases with Majorana fermions/parafermions has been established. Here we first generalize these fixed-point matrix product states with the zero correlation length to the more generic ground-state wave functions with a finite correlation length for the general one-dimensional interacting Majorana fermion/parafermion systems. Then we employ the previous method to decode quantum criticality from the interacting Majorana fermion/parafermion matrix product states. The obtained quantum critical spectra are described by the conformal field theories with central charge $c\leq 1$, characterizing the quantum critical theories separating the fermionic/parafermionic topological phases from the trivial phases with the same symmetry.