TY - JOUR

T1 - Composite particle theory of three-dimensional gapped fermionic phases

T2 - Fractional topological insulators and charge-loop excitation symmetry

AU - Ye, Peng

AU - Hughes, Taylor L.

AU - Maciejko, Joseph

AU - Fradkin, Eduardo

N1 - Publisher Copyright:
© 2016 American Physical Society.

PY - 2016/9/2

Y1 - 2016/9/2

N2 - Topological phases of matter are usually realized in deconfined phases of gauge theories. In this context, confined phases with strongly fluctuating gauge fields seem to be irrelevant to the physics of topological phases. For example, the low-energy theory of the two-dimensional (2D) toric code model (i.e., the deconfined phase of Z2 gauge theory) is a U(1)×U(1) Chern-Simons theory in which gauge charges (i.e., e and m particles) are deconfined and the gauge fields are gapped, while the confined phase is topologically trivial. In this paper, we point out a route to constructing exotic three-dimensional (3D) gapped fermionic phases in a confining phase of a gauge theory. Starting from a parton construction with strongly fluctuating compact U(1)×U(1) gauge fields, we construct gapped phases of interacting fermions by condensing two linearly independent bosonic composite particles consisting of partons and U(1)×U(1) magnetic monopoles. This can be regarded as a 3D generalization of the 2D Bais-Slingerland condensation mechanism. Charge fractionalization results from a Debye-Hückel-type screening cloud formed by the condensed composite particles. Within our general framework, we explore two aspects of symmetry-enriched 3D Abelian topological phases. First, we construct a new fermionic state of matter with time-reversal symmetry and Θ≠π, the fractional topological insulator. Second, we generalize the notion of anyonic symmetry of 2D Abelian topological phases to the charge-loop excitation symmetry (Charles) of 3D Abelian topological phases. We show that line twist defects, which realize Charles transformations, exhibit non-Abelian fusion properties.

AB - Topological phases of matter are usually realized in deconfined phases of gauge theories. In this context, confined phases with strongly fluctuating gauge fields seem to be irrelevant to the physics of topological phases. For example, the low-energy theory of the two-dimensional (2D) toric code model (i.e., the deconfined phase of Z2 gauge theory) is a U(1)×U(1) Chern-Simons theory in which gauge charges (i.e., e and m particles) are deconfined and the gauge fields are gapped, while the confined phase is topologically trivial. In this paper, we point out a route to constructing exotic three-dimensional (3D) gapped fermionic phases in a confining phase of a gauge theory. Starting from a parton construction with strongly fluctuating compact U(1)×U(1) gauge fields, we construct gapped phases of interacting fermions by condensing two linearly independent bosonic composite particles consisting of partons and U(1)×U(1) magnetic monopoles. This can be regarded as a 3D generalization of the 2D Bais-Slingerland condensation mechanism. Charge fractionalization results from a Debye-Hückel-type screening cloud formed by the condensed composite particles. Within our general framework, we explore two aspects of symmetry-enriched 3D Abelian topological phases. First, we construct a new fermionic state of matter with time-reversal symmetry and Θ≠π, the fractional topological insulator. Second, we generalize the notion of anyonic symmetry of 2D Abelian topological phases to the charge-loop excitation symmetry (Charles) of 3D Abelian topological phases. We show that line twist defects, which realize Charles transformations, exhibit non-Abelian fusion properties.

UR - http://www.scopus.com/inward/record.url?scp=84990892376&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84990892376&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.94.115104

DO - 10.1103/PhysRevB.94.115104

M3 - Article

AN - SCOPUS:84990892376

SN - 2469-9950

VL - 94

JO - Physical Review B

JF - Physical Review B

IS - 11

M1 - 115104

ER -