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

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${}_2$.

23 pages of main text + appendices + ancillary files

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• Universal entanglement spectrum in gapless symmetry protected topological states
• Non-zero momentum requires long-range entanglement
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• Topological physics in quantum critical systems
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• Anomaly of $(2+1)$-Dimensional Symmetry-Enriched Topological Order from $(3+1)$-Dimensional Topological Quantum Field Theory
• Bosonization and Anomaly Indicators of (2+1)-D Fermionic Topological Orders
• Generalized Li-Haldane Correspondence in Critical Dirac-Fermion Systems
• Entanglement-enabled symmetry-breaking orders
• Entanglement area law and Lieb-Schultz-Mattis theorem in long-range interacting systems, and symmetry-enforced long-range entanglement
• Crystallography, Group Cohomology, and Lieb-Schultz-Mattis Constraints
• When Wannier centers jump: Critical points between atomic insulating phases
• Anomalous Dynamical Scaling at Topological Quantum Criticality