Decoding quantum criticalities from fermionic/parafermionic topological 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 $c\le 1$, characterizing the quantum critical theories separating the fermionic/parafermionic topological phases from the trivial phases with the same symmetry.

arXiv comment14 pages, 10 figures. The manuscript has been substantially expanded and revised

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Cited by in corpus (3)

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• Thermodynamics of a Higher-Order Topological Insulator
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