Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lieb-Schultz-Mattis Theorem and its generalizations from the Perspective
  of the Symmetry Protected Topological phase   We ask whether a local Hamiltonian with a featureless (fully gapped and
nondegenerate) ground state could exist in certain quantum spin systems. We
address this question by mapping the vicinity of certain quantum critical point
(or gapless phase) of the $d-$dimensional spin system under study to the
boundary of a $(d+1)-$dimensional bulk state, and the lattice symmetry of the
spin system acts as an on-site symmetry in the field theory that describes both
the selected critical point of the spin system, and the corresponding boundary
state of the $(d+1)-$dimensional bulk. If the symmetry action of the field
theory is nonanomalous, i.e. the corresponding bulk state is a trivial state
instead of a bosonic symmetry protected topological (SPT) state, then a
featureless ground state of the spin system is allowed; if the corresponding
bulk state is indeed a nontrivial SPT state, then it likely excludes the
existence of a featureless ground state of the spin system. From this
perspective we identify the spin systems with SU($N$) and SO($N$) symmetries on
one, two and three dimensional lattices that permit a featureless ground state.
We also verify our conclusions by other methods, including an explicit
construction of these featureless spin states.

16
The categories of this paper are: stat
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
2
The categories of this paper are: math
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph