Projectification of point group symmetries with a background flux and Lieb-Schultz-Mattis theorem

2025/05/02 by Tada, Yasuhiro, Oshikawa, Masaki · 1 citation
#FOS: Physical sciences #Strongly Correlated Electrons (cond-mat.str-el)

paper · doi:10.48550/arxiv.2505.00927

Abstract

We discuss the Lieb-Schultz-Mattis (LSM) theorem in two-dimensional spin systems with on-site \mathrm U(1)\rtimes \mathbb Z₂ spin rotation symmetry and point group C_2v symmetry about a site. We ``twist" the point group symmetry by introducing a small uniform U(1) flux to obtain a projective symmetry, similarly to the familiar magnetic translation symmetry. The LSM theorem is proved in presence of the flux and then it is demonstrated that the theorem holds also for the flux-free system. Besides, the uniform flux enables us to show the LSM theorem for the time-reversal symmetry and the site-centered C₂-rotation symmetry.

Citations

• Ground state degeneracy in quantum spin systems protected by crystal symmetries
• Topological classification of gapped spin chains: Quantized Berry phase as a local order parameter
• Cyclic exchange, isolated states, and spinon deconfinement in anXXZHeisenberg model on the checkerboard lattice
• The planar pyrochlore: a Valence Bond Crystal
• Spectral Gaps of Quantum Hall Systems with Interactions
• Theory of quantised Hall conductivity in two dimensions
• Two soluble models of an antiferromagnetic chain

Cited by

• Quantized order parameters of approximate symmetry for metals and insulators

Related

• Revealing Spin and Spatial Symmetry Decoupling: New Insights into Magnetic Systems with Dzyaloshinskii-Moriya Interaction
• Extension of the Lieb-Schultz-Mattis and Kolb theorem
• Ground state degeneracy in quantum spin systems protected by crystal symmetries
• Symmetry-enforced quantum spin Hall insulators in π-flux models
• Modulated symmetries from generalized Lieb-Schultz-Mattis anomalies