We present a family of electronbased coupledwire models of bosonic orbifold topological phases, referred to as twist liquids, in two spatial dimensions. All local fermion degrees of freedom are gapped and removed from the topological order by manybody interactions. Bosonic chiral spin liquids and anyonic superconductors are constructed on an array of interacting wires, each supports emergent massless Majorana fermions that are nonlocal (fractional) and constitute the S O ( N ) KacMoody WessZuminoWitten algebra at level 1. We focus on the dihedral D k symmetry of S O ( 2 n ) 1 , and its promotion to a gauge symmetry by manipulating the locality of fermion pairs. Gauging the symmetry (sub)group generates the C / G twist liquids, where G = Z 2 for C = U ( 1 ) l , S U ( n ) 1 , and G = Z 2 , Z k , D k for C = S O ( 2 n ) 1 . We construct exactly solvable models for all of these topological states. We prove the presence of a bulk excitation energy gap and demonstrate the appearance of edge orbifold conformal field theories corresponding to the twist liquid topological orders. We analyze the statistical properties of the anyon excitations, including the nonAbelian metaplectic anyons and a new class of quasiparticles referred to as Isingfluxons. We show an eightfold periodic gauging pattern in S O ( 2 n ) 1 / G by identifying the nonchiral components of the twist liquids with discrete gauge theories.
more »
« less
Gauging U(1) symmetry in (2+1)d topological phases
We study the gauging of a global U(1) symmetry in a gapped system in(2+1)d. The gauging procedure has been wellunderstood for a finiteglobal symmetry group, which leads to a new gapped phase with emergentgauge structure and can be described algebraically using themathematical framework of modular tensor category (MTC). We develop acategorical description of U(1) gauging in a MTC, taking into accountthe dynamics of U(1) gauge field absent in the finite group case. Whenthe ungauged system has a nonzero Hall conductance, the gauged theoryremains gapped and we determine the complete set of anyon data for thegauged theory. On the other hand, when the Hall conductance vanishes, weargue that gauging has the same effect of condensing a special Abeliananyon nucleated by inserting 2\pi 2 π U(1) flux. We apply our procedure to theSU(2) _k k MTCs and derive the full MTC data for the \mathbb{Z}_k ℤ k parafermion MTCs. We also discuss a dual U(1) symmetry that emergesafter the original U(1) symmetry of an MTC is gauged.
more »
« less
 Award ID(s):
 1846109
 NSFPAR ID:
 10400892
 Date Published:
 Journal Name:
 SciPost Physics
 Volume:
 12
 Issue:
 6
 ISSN:
 25424653
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
More Like this


Based on several previous examples, we summarize explicitly thegeneral procedure to gauge models with subsystem symmetries, which aresymmetries with generators that have support within a submanifold ofthe system. The gauging process can be applied to any local quantummodel on a lattice that is invariant under the subsystem symmetry. Wefocus primarily on simple 3D paramagnetic states with planar symmetries.For these systems, the gauged theory may exhibit foliated fracton orderand we find that the species of symmetry charges in the paramagnetdirectly determine the resulting foliated fracton order. Moreover, wefind that gauging linear subsystem symmetries in 2D or 3D models resultsin a selfduality similar to gauging global symmetries in 1D.more » « less

null (Ed.)Strong interactions between electrons occupying bands of opposite (orlike) topological quantum numbers (Chern =\pm1 = ± 1 ),and with flat dispersion, are studied by using lowest Landau level (LLL)wavefunctions. More precisely, we determine the ground states for twoscenarios at halffilling: (i) LLL’s with opposite sign of magneticfield, and therefore opposite Chern number; and (ii) LLL’s with the samemagnetic field. In the first scenario – which we argue to be a toy modelinspired by the chirally symmetric continuum model for twisted bilayergraphene – the opposite Chern LLL’s are Kramer pairs, and thus thereexists timereversal symmetry ( \mathbb{Z}_2 ℤ 2 ).Turning on repulsive interactions drives the system to spontaneouslybreak timereversal symmetry – a quantum anomalous Hall state describedby one particle per LLL orbital, either all positive Chern {++\cdots+}\rangle  + + ⋯ + ⟩ or all negative {\cdots}\rangle  − − ⋯ − ⟩ .If instead, interactions are taken between electrons of likeChernnumber, the ground state is an SU(2) S U ( 2 ) ferromagnet, with total spin pointing along an arbitrary direction, aswith the \nu=1 ν = 1 spin \frac{1}{2} 1 2 quantum Hall ferromagnet. The ground states and some of theirexcitations for both of these scenarios are argued analytically, andfurther complimented by density matrix renormalization group (DMRG) andexact diagonalization.more » « less

A bstract We study solvable deformations of twodimensional quantum field theories driven by a bilinear operator constructed from a pair of conserved U(1) currents J a . We propose a quantum formulation of these deformations, based on the gauging of the corresponding symmetries in a path integral. This formalism leads to an exact dressing of the S matrix of the system, similarly as what happens in the case of a $$ \textrm{T}\overline{\textrm{T}} $$ T T ¯ deformation. For conformal theories the deformations under study are expected to be exactly marginal. Still, a peculiar situation might arise when the conserved currents J a are not welldefined local operators in the original theory. A simple example of this kind of system is provided by rotation currents in a theory of multiple free, massless, noncompact bosons. We verify that, somewhat unexpectedly, such a theory is indeed still conformal after deformation and that it coincides with a TsT transformation of the original system. We then extend our formalism to the case in which the conserved currents are nonAbelian and point out its connection with Deformed Tdual Models and homogeneous YangBaxter deformations. In this case as well the deformation is based on a gauging of the symmetries involved and it turns out to be nontrivial only if the symmetry group admits a nontrivial central extension. Finally we apply what we learned by relating the $$ \textrm{T}\overline{\textrm{T}} $$ T T ¯ deformation to the central extension of the twodimensional Poincaré algebra.more » « less

(3+1)D topological phases of matter can host a broad class of nontrivial topological defects of codimension1, 2, and 3, of which the wellknown point charges and flux loops are special cases. The complete algebraic structure of these defects defines a higher category, and can be viewed as an emergent higher symmetry. This plays a crucial role both in the classification of phases of matter and the possible faulttolerant logical operations in topological quantum errorcorrecting codes. In this paper, we study several examples of such higher codimension defects from distinct perspectives. We mainly study a class of invertible codimension2 topological defects, which we refer to as twist strings. We provide a number of general constructions for twist strings, in terms of gauging lower dimensional invertible phases, layer constructions, and condensation defects. We study some special examples in the context of \mathbb{Z}_2 ℤ 2 gauge theory with fermionic charges, in \mathbb{Z}_2 \times \mathbb{Z}_2 ℤ 2 × ℤ 2 gauge theory with bosonic charges, and also in nonAbelian discrete gauge theories based on dihedral ( D_n D n ) and alternating ( A_6 A 6 ) groups. The intersection between twist strings and Abelian flux loops sources Abelian point charges, which defines an H^4 H 4 cohomology class that characterizes part of an underlying 3group symmetry of the topological order. The equations involving background gauge fields for the 3group symmetry have been explicitly written down for various cases. We also study examples of twist strings interacting with nonAbelian flux loops (defining part of a noninvertible higher symmetry), examples of noninvertible codimension2 defects, and examples of the interplay of codimension2 defects with codimension1 defects. We also find an example of geometric, not fully topological, twist strings in (3+1)D A_6 A 6 gauge theory.more » « less