TY - JOUR

T1 - Quantum phase transitions between bosonic symmetry-protected topological states without sign problem

T2 - Nonlinear sigma model with a topological term

AU - You, Yi Zhuang

AU - Bi, Zhen

AU - Mao, Dan

AU - Xu, Cenke

N1 - Publisher Copyright:
© 2016 American Physical Society.

PY - 2016/3/1

Y1 - 2016/3/1

N2 - We propose a series of simple two-dimensional (2D) lattice interacting fermion models that we demonstrate at low energy describe bosonic symmetry-protected topological (SPT) states and quantum phase transitions between them. This is because due to interaction, the fermions are gapped both at the boundary of the SPT states and at the bulk quantum phase transition, thus these models at low energy can be described completely by bosonic degrees of freedom. We show that the bulk of these models is described by a Sp(N) principal chiral model with a topological Θ term, whose boundary is described by a Sp(N) principal chiral model with a Wess-Zumino-Witten term at level 1. The quantum phase transition between SPT states in the bulk is tuned by a particular interaction term, which corresponds to tuning Θ in the field theory, and the phase transition occurs at Θ=π. The simplest version of these models with N=1 is equivalent to the familiar O(4) nonlinear sigma model (NLSM) with a topological term, whose boundary is a (1+1)D conformal field theory with central charge c=1. After breaking the O(4) symmetry to its subgroups, this model can be viewed as bosonic SPT states with U(1), or Z2 symmetries, etc. All of these fermion models, including the bulk quantum phase transitions, can be simulated with the determinant quantum Monte Carlo method without the sign problem. Recent numerical results strongly suggest that the quantum disordered phase of the O(4) NLSM with precisely Θ=π is a stable (2+1)D conformal field theory with gapless bosonic modes.

AB - We propose a series of simple two-dimensional (2D) lattice interacting fermion models that we demonstrate at low energy describe bosonic symmetry-protected topological (SPT) states and quantum phase transitions between them. This is because due to interaction, the fermions are gapped both at the boundary of the SPT states and at the bulk quantum phase transition, thus these models at low energy can be described completely by bosonic degrees of freedom. We show that the bulk of these models is described by a Sp(N) principal chiral model with a topological Θ term, whose boundary is described by a Sp(N) principal chiral model with a Wess-Zumino-Witten term at level 1. The quantum phase transition between SPT states in the bulk is tuned by a particular interaction term, which corresponds to tuning Θ in the field theory, and the phase transition occurs at Θ=π. The simplest version of these models with N=1 is equivalent to the familiar O(4) nonlinear sigma model (NLSM) with a topological term, whose boundary is a (1+1)D conformal field theory with central charge c=1. After breaking the O(4) symmetry to its subgroups, this model can be viewed as bosonic SPT states with U(1), or Z2 symmetries, etc. All of these fermion models, including the bulk quantum phase transitions, can be simulated with the determinant quantum Monte Carlo method without the sign problem. Recent numerical results strongly suggest that the quantum disordered phase of the O(4) NLSM with precisely Θ=π is a stable (2+1)D conformal field theory with gapless bosonic modes.

UR - http://www.scopus.com/inward/record.url?scp=84960855395&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84960855395&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.93.125101

DO - 10.1103/PhysRevB.93.125101

M3 - Article

AN - SCOPUS:84960855395

SN - 2469-9950

VL - 93

JO - Physical Review B

JF - Physical Review B

IS - 12

M1 - 125101

ER -