637 research outputs found

### Gauge choices and Entanglement Entropy of two dimensional lattice gauge fields

In this paper, we explore the question of how different gauge choices in a
gauge theory affect the tensor product structure of the Hilbert space in
configuration space. In particular, we study the Coulomb gauge and observe that
the naive gauge potential degrees of freedom cease to be local operators as
soon as we impose the Dirac brackets. We construct new local set of operators
and compute the entanglement entropy according to this algebra in $2+1$
dimensions. We find that our proposal would lead to an entanglement entropy
that behave very similar to a single scalar degree of freedom if we do not
include further centers, but approaches that of a gauge field if we include
non-trivial centers. We explore also the situation where the gauge field is
Higgsed, and construct a local operator algebra that again requires some
deformation. This should give us some insight into interpreting the
entanglement entropy in generic gauge theories and perhaps also in
gravitational theories.Comment: 38 pages,25 figure

### Revisiting Entanglement Entropy of Lattice Gauge Theories

Casini et al raise the issue that the entanglement entropy in gauge theories
is ambiguous because its definition depends on the choice of the boundary
between two regions.; even a small change in the boundary could annihilate the
otherwise finite topological entanglement entropy between two regions. In this
article, we first show that the topological entanglement entropy in the Kitaev
model which is not a true gauge theory, is free of ambiguity. Then, we give a
physical interpretation, from the perspectives of what can be measured in an
experiement, to the purported ambiguity of true gauge theories, where the
topological entanglement arises as redundancy in counting the degrees of
freedom along the boundary separating two regions. We generalize these
discussions to non-Abelian gauge theories.Comment: 15 pages, 3 figure

### Universal symmetry-protected topological invariants for symmetry-protected topological states

Symmetry-protected topological (SPT) states are short-range entangled states
with a symmetry G. They belong to a new class of quantum states of matter which
are classified by the group cohomology $H^{d+1}(G,\mathbb{R}/\mathbb{Z})$ in
d-dimensional space. In this paper, we propose a class of symmetry- protected
topological invariants that may allow us to fully characterize SPT states with
a symmetry group G (ie allow us to measure the cocycles in
$H^{d+1}(G,\mathbb{R}/\mathbb{Z})$ that characterize the SPT states). We give
an explicit and detailed construction of symmetry-protected topological
invariants for 2+1D SPT states. Such a construction can be directly generalized
to other dimensions.Comment: 12 pages, 11 figures. Added reference

### Quantized topological terms in weak-coupling gauge theories with symmetry and their connection to symmetry enriched topological phases

We study the quantized topological terms in a weak-coupling gauge theory with
gauge group $G_g$ and a global symmetry $G_s$ in $d$ space-time dimensions. We
show that the quantized topological terms are classified by a pair $(G,\nu_d)$,
where $G$ is an extension of $G_s$ by $G_g$ and $\nu_d$ an element in group
cohomology \cH^d(G,\R/\Z). When $d=3$ and/or when $G_g$ is finite, the
weak-coupling gauge theories with quantized topological terms describe gapped
symmetry enriched topological (SET) phases (i.e. gapped long-range entangled
phases with symmetry). Thus, those SET phases are classified by
\cH^d(G,\R/\Z), where $G/G_g=G_s$. We also apply our theory to a simple case
$G_s=G_g=Z_2$, which leads to 12 different SET phases in 2+1D, where
quasiparticles have different patterns of fractional $G_s=Z_2$ quantum numbers
and fractional statistics. If the weak-coupling gauge theories are gapless,
then the different quantized topological terms may describe different gapless
phases of the gauge theories with a symmetry $G_s$, which may lead to different
fractionalizations of $G_s$ quantum numbers and different fractional statistics
(if in 2+1D).Comment: 13 pages, 2 figures, PRB accepted version with added clarification on
obtaining G_s charge for a given PSG with non-trivial topological terms.
arXiv admin note: text overlap with arXiv:1301.767

- β¦