Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetry-protected topological phases in lattice gauge theories:
  topological QED$_2$   The interplay of symmetry, topology, and many-body effects in the
classification of possible phases of matter poses a formidable challenge that
is attracting great attention in condensed-matter physics. Such many-body
effects are typically induced by inter-particle interactions involving an
action at a distance, such as the Coulomb interaction between electrons in a
symmetry-protected topological (SPT) phase. In this work, we show that similar
phenomena also appear in high-energy physics, where inter-particle interactions
are mediated by gauge bosons, and constrained by a local gauge symmetry. We
introduce a variant of the so-called Schwinger model, which describes quantum
electrodynamics in (1+1) dimensions (QED$_2$), and show that it can host SPT
phases with a topological contribution to the vacuum {\theta} angle, which
leads to a new type of topological QED$_2.$ We use bosonization and
density-matrix renormalization group techniques to study its rich phase diagram
in great detail, and present a scheme for its realization in experiments of
ultra-cold atoms in optical lattices.

30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
3
The categories of this paper are: physics