Topological characterization of LiebSchultzMattis constraints and applications to symmetryenriched quantum criticality
Abstract
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$_2$.
 Publication:

arXiv eprints
 Pub Date:
 November 2021
 arXiv:
 arXiv:2111.12097
 Bibcode:
 2021arXiv211112097Y
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 Condensed Matter  Quantum Gases;
 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 23 pages of main text + appendices + ancillary files