## Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality

Weicheng Ye, Meng Guo, Yin-Chen He, Chong Wang, Liujun Zou

SciPost Phys. 13, 066 (2022) · published 26 September 2022

- doi: 10.21468/SciPostPhys.13.3.066
- Submissions/Reports

### Abstract

Lieb-Schultz-Mattis (LSM) theorems provide powerful constraints on the emergibility 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 $G_s\times G_{int}$ 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 well-known deconfined quantum critical point (DQCP), $U(1)$ 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 $SO(3)\times \mathbb{Z}_2^T$ 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 spin-quadrupolar liquids of which the most relevant spinful fluctuations carry spin-$2$. 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$_2$.

### Cited by 19

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}^{2}Weicheng Ye, -
^{1}^{3}Meng Guo, -
^{1}Yin-Chen He, -
^{1}Chong Wang, -
^{1}Liujun Zou

^{1}Institut Périmètre de physique théorique / Perimeter Institute [PI]^{2}University of Waterloo [UW]^{3}University of Toronto