125 research outputs found
Symmetry-Enriched Quantum Spin Liquids in
We use the intrinsic one-form and two-form global symmetries of (3+1)
bosonic field theories to classify quantum phases enriched by ordinary
(-form) global symmetry. Different symmetry-enriched phases correspond to
different ways of coupling the theory to the background gauge field of the
ordinary symmetry. The input of the classification is the higher-form
symmetries and a permutation action of the -form symmetry on the lines and
surfaces of the theory. From these data we classify the couplings to the
background gauge field by the 0-form symmetry defects constructed from the
higher-form symmetry defects. For trivial two-form symmetry the classification
coincides with the classification for symmetry fractionalizations in .
We also provide a systematic method to obtain the symmetry protected
topological phases that can be absorbed by the coupling, and we give the
relative 't Hooft anomaly for different couplings. We discuss several examples
including the gapless pure gauge theory and the gapped Abelian finite
group gauge theory. As an application, we discover a tension with a conjectured
duality in for gauge theory with two adjoint Weyl fermions
Non-Invertible Defects in Nonlinear Sigma Models and Coupling to Topological Orders
Nonlinear sigma models appear in a wide variety of physics contexts, such as
the long-range order with spontaneously broken continuous global symmetries.
There are also large classes of quantum criticality admit sigma model
descriptions in their phase diagrams without known ultraviolet complete quantum
field theory descriptions. We investigate defects in general nonlinear sigma
models in any spacetime dimensions, which include the "electric" defects that
are characterized by topological interactions on the defects, and the
"magnetic" defects that are characterized by the isometries and homotopy
groups. We use an analogue of the charge-flux attachment to show that the
magnetic defects are in general non-invertible, and the electric and magnetic
defects form junctions that combine defects of different dimensions into
analogues of higher-group symmetry. We explore generalizations that couple
nonlinear sigma models to topological quantum field theories by defect
attachment, which modifies the non-invertible fusion and braiding of the
defects. We discuss several applications, including constraints on energy
scales and scenarios of low energy dynamics with spontaneous symmetry breaking
in gauge theories, and axion gauge theories.Comment: 39 pages, 3 figures; v2: updated references and corrected typo
Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d
We study 3d and 4d systems with a one-form global symmetry, explore their
consequences, and analyze their gauging. For simplicity, we focus on
one-form symmetries. A 3d topological quantum field theory
(TQFT) with such a symmetry has special lines that generate
it. The braiding of these lines and their spins are characterized by a single
integer modulo . Surprisingly, if the TQFT factorizes
. Here is a
decoupled TQFT, whose lines are neutral under the global symmetry and
is a minimal TQFT with the one-form symmetry
of label . The parameter labels the obstruction to gauging the
one-form symmetry; i.e.\ it characterizes the 't Hooft anomaly
of the global symmetry. When mod , the symmetry can be gauged.
Otherwise, it cannot be gauged unless we couple the system to a 4d bulk with
gauge fields extended to the bulk. This understanding allows us to consider
and 4d gauge theories. Their dynamics is gapped and it is
associated with confinement and oblique confinement -- probe quarks are
confined. In the theory the low-energy theory can include a discrete
gauge theory. We will study the behavior of the theory with a space-dependent
-parameter, which leads to interfaces. Typically, the theory on the
interface is not confining. Furthermore, the liberated probe quarks are anyons
on the interface. The theory is obtained by gauging the
one-form symmetry of the theory. Our understanding of the symmetries in
3d TQFTs allows us to describe the interface in the theory.Comment: 56 pages, 3 figures, 5 table
On Topology of the Moduli Space of Gapped Hamiltonians for Topological Phases
The moduli space of gapped Hamiltonians that are in the same topological
phase is an intrinsic object that is associated to the topological order. The
topology of these moduli spaces is used recently in the construction of Floquet
codes. We propose a systematical program to study the topology of these moduli
spaces. In particular, we use effective field theory to study the cohomology
classes of these spaces, which includes and generalizes the Berry phase. We
discuss several applications to studying phase transitions. We show that
nontrivial family of gapped systems with the same topological order can protect
isolated phase transitions in the phase diagram, and we argue that the phase
transitions are characterized by screening of topological defects. We argue
that family of gapped systems obey a version of bulk-boundary correspondence.
We show that family of gapped systems in the bulk with the same topological
order can rule out family of gapped systems on the boundary with the same
topological boundary condition, constraining phase transitions on the boundary.Comment: 37 pages, 2 figure
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