Weicheng Ye, Meng Guo, YinChen He, Chong Wang, Liujun Zou
SciPost Phys. 13, 066 (2022) ·
published 26 September 2022

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LiebSchultzMattis (LSM) theorems provide powerful constraints on the
emergibility problem, i.e. whether a quantum phase or phase transition can
emerge in a manybody system. We derive the topological partition functions
that characterize the LSM constraints in spin systems with $G_s\times G_{int}$
symmetry, where $G_s$ is an arbitrary space group in one or two spatial
dimensions, and $G_{int}$ is any internal symmetry whose projective
representations are classified by $\mathbb{Z}_2^k$ with $k$ an integer. We then
apply these results to study the emergibility of a class of exotic quantum
critical states, including the wellknown deconfined quantum critical point
(DQCP), $U(1)$ Dirac spin liquid (DSL), and the recently proposed
nonLagrangian Stiefel liquid. These states can emerge as a consequence of the
competition between a magnetic state and a nonmagnetic state. We identify all
possible realizations of these states on systems with $SO(3)\times
\mathbb{Z}_2^T$ internal symmetry and either $p6m$ or $p4m$ 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 spinquadrupolar liquids of which the most relevant spinful
fluctuations carry spin$2$. In particular, there is a realization of
spinquadrupolar DSL that is beyond the usual parton construction. We further
use our formalism to analyze the stability of these states under
symmetrybreaking perturbations, such as spinorbit coupling. As a concrete
example, we find that a DSL can be stable in a recently proposed candidate
material, NaYbO$_2$.
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