Affiliation:
1. Perimeter Institute
2. University of Waterloo
3. University of Toronto
Abstract
Lieb-Schultz-Mattis (LSM) theorems provide powerful constraints on
the problem, i.e. whether a quantum phase or phase transition can emerge
in a many-body system. We derive the topological partition functions
that characterize the LSM constraints in spin systems with
G_s\times G_{int}Gs×Gint
symmetry, where G_sGs
is an arbitrary space group in one or two spatial dimensions, and
G_{int}Gint
is any internal symmetry whose projective representations are classified
by \mathbb{Z}_2^kℤ2k
with kk
an integer. We then apply these results to study the emergibility of a
class of exotic quantum critical states, including the well-known
deconfined quantum critical point (DQCP), U(1)U(1)
Dirac spin liquid (DSL), and the recently proposed non-Lagrangian
Stiefel liquid. These states can emerge as a consequence of the
competition between a magnetic state and a non-magnetic state. We
identify all possible realizations of these states on systems with
SO(3)\times \mathbb{Z}_2^TSO(3)×ℤ2T
internal symmetry and either p6mp6m
or p4mp4m
lattice symmetry. Many interesting examples are discovered, including a
DQCP adjacent to a ferromagnet, stable DSLs on square and honeycomb
lattices, and a class of quantum critical spin-quadrupolar liquids of
which the most relevant spinful fluctuations carry
spin-22.
In particular, there is a realization of spin-quadrupolar DSL that is
beyond the usual parton construction. We further use our formalism to
analyze the stability of these states under symmetry-breaking
perturbations, such as spin-orbit coupling. As a concrete example, we
find that a DSL can be stable in a recently proposed candidate material,
NaYbO_22.
Funder
Government of Canada
Natural Sciences and Engineering Research Council
Subject
General Physics and Astronomy
Cited by
9 articles.
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