Symmetry-protected topological states of interacting fermions and bosons

Abstract

We study the classification for a large class of interacting fermionic and bosonic symmetry protected topological (SPT) states, focusing on the cases where interaction reduces the classification of free fermion SPT states. We define a SPT state as whether or not it is separated from the trivial state through a bulk phase transition, which is a general definition applicable to SPT states with or without spatial symmetries. We show that in all dimensions short range interactions can reduce the classification of free fermion SPT states, and we demonstrate these results by making connection between fermionic and bosonic SPT states. We first demonstrate that our formalism gives the correct classification for several known SPT states, with or without interaction, then we will generalize our method to SPT states that involve the spatial inversion symmetry.

Decorated defect condensate: A window to unconventional quantum phases in Weyl semimetals

“…The first prominent example on deconfined quantum criticality is discovered by Senthil et al [19][20][21][22] in Mott insulator on square lattice. Deep in the Mott phase, the charge degree of freedom is frozen while the spin degree of freedom suffers from a variety of competing orders.…”

“…Each component of the rotor couples with the fermion bilinear and acts as a mass term. Once we integrating out the fermions, one obtains a Wess-Zumino-Witten theory for the fluctuating rotor 21,40,41 . The WZW term of the rotor originates from the special band structure of Weyl semimetal who contains monopole in momentum space around the Weyl points.…”

“…The common wisdom of these approach involves adding a topological term in addition to the conventional LGW theory. The topological Θ term in addition to the classical NLσM provides a new critical point which exactly describes the critical theory between SPT to trivial phase 19,21 . In addition, the transition from topological order to trivial phase can be approached by anyon condensate where the anyons, as a Lagrangian subgroup of the topological excitations, would confine any other topological quasiparticle after its proliferation 15,[24][25][26] .…”

“…In the absence of local order parameter, one cannot plainly, follow the LGW approach to described the phase transition in terms of order parameter fluctuations. The critical theory between topological order(or SPT) to trivial phase is studied by a bundle of pioneers [19][20][21][22][23] . The common wisdom of these approach involves adding a topological term in addition to the conventional LGW theory.…”

Quantum critical point of Dirac fermion mass generation without spontaneous symmetry breaking

“…This mechanism was discovered in the context of interacting topological insulators, it was found that some topological insulators/superconductors can be trivialized by interaction. Or in other words their boundary states, which without interaction are gapless Dirac fermions or Majorana fermions at one lower dimension, can be completely gapped out by interaction without topological degeneracy or condensing any fermion bilinear mass operator [7][8][9][10][11][12][13][14][15][16][17][18][19].…”