Abstract
In an earlier work [1] we developed a holographic theory for the phase transition between bosonic symmetry-protected topological (SPT) states. This paper is a continuation of it. Here we present the holographic theory for fermionic SPT phase transitions. We show that in any dimension d, the critical states of fermionic SPT phase transitions has an emergent Z2T symmetry and can be realized on the boundary of a d+1-dimensional bulk SPT with an extra Z2T symmetry.
Highlights
Symmetry protected topological states (SPTs) are new quantum phases of matter
We consider a specific interacting version of the holographic bulk SPT under the proviso that the interaction term does not collapse the bulk gap. We show that such interacting bulk SPT can be viewed as containing condensed Z2T domain walls
In Appendix A we present the rules for regularizing a continuum field theories of SPTs on a hyper-cubic lattice
Summary
Symmetry protected topological states (SPTs) are new quantum phases of matter. They are characterized by a fully gapped bulk but gapless boundary. This higher dimensional SPT can be interpreted as a state whose Z2T domain walls are “decorated” [2] with the lower dimensional non-trivial SPT The implication of this theory are (1) The excitations of the critical theory are the fluctuating boundaries between the two SPT phases. In this paper we emphasize another implication of the holographic correspondence, namely, (3) in the presence of (emergent) Lorentz symmetry, the conformal spectrum of the critical theory at the SPT phase transition is the same as the ground state entanglement spectrum of the holographic bulk SPT. In Appendix D we relate the interface gapless modes in Appendix C to the boundary gapless modes of regularized lattice theory of non-trivial SPTs. In Appendix E we summarize the topological classification for free fermion SPTs protected by the T Q C symmetries. Appendix J, we discuss the space-time rotation necessary to establish the correspondence between the ground state wavefunction of the holographic bulk and the Boltzmann weight of the conformal field theory at the SPT critical point
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