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

Abstract

We discuss the Lieb-Schultz-Mattis (LSM) theorem in two-dimensional spin systems with on-site $\mathrm{U}(1)⋊{\mathbb{Z}}_2$ 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 $C_2$-rotation symmetry.

arXiv comment15 pages, 10 figures

References in corpus (38)

• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Lieb-Schultz-Mattis in Higher Dimensions
• Spectral Gap and Exponential Decay of Correlations
• Electron Localization in the Insulating State
• Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice
• Filling constraints for spin-orbit coupled insulators in symmorphic and non-symmorphic crystals
• Topological Order and Absence of Band Insulators at Integer Filling in Non-Symmorphic Crystals
• Building crystalline topological phases from lower-dimensional states
• Intrinsic and emergent anomalies at deconfined critical points
• Many-Body Electric Multipole Operators in Extended Systems
• Many-Body Order Parameters for Multipoles in Solids
• Quantized Berry Phases as Local Order Parameters of Quantum Liquids
• Symmetric-Gapped Surface States of Fractional Topological Insulators
• Anomaly Manifestation of Lieb-Schultz-Mattis Theorem and Topological Phases
• Cyclic exchange, isolated states and spinon deconfinement in an XXZ Heisenberg model on the checkerboard lattice
• Lattice Homotopy Constraints on Phases of Quantum Magnets
• Topological theory of Lieb-Schultz-Mattis theorems in quantum spin systems
• Topological Classification of Gapped Spin Chains :Quantized Berry Phase as a Local Order Parameter
• A Multi-Dimensional Lieb-Schultz-Mattis Theorem
• Difficulties in operator-based formulation of the bulk quadrupole moment
• Sum Rule of the Hall Conductance in Random Quantum Phase Transition
• Twisted boundary condition and Lieb-Schultz-Mattis ingappability for discrete symmetries
• A many-body index for quantum charge transport
• General Lieb-Schultz-Mattis type theorems for quantum spin chains
• Insensitivity of bulk properties to the twisted boundary condition
• Filling-enforced constraint on the quantized Hall conductivity on a periodic lattice
• Featureless and non-fractionalized Mott insulators on the honeycomb lattice at 1/2 site filling
• Nodal count of graph eigenfunctions via magnetic perturbation
• A generalized boundary condition applied to Lieb-Schultz-Mattis type ingappabilities and many-body Chern numbers
• Lieb-Schultz-Mattis theorems for symmetry protected topological phases
• Effective field theory for one-dimensional valence-bond-solid phases and their symmetry protection
• Geometric approach to Lieb-Schultz-Mattis theorem without translation symmetry under inversion or rotation symmetry
• Translation constraints on quantum phases with twisted boundary conditions
• Many-Body Chern Numbers of $\nu =1/3$ and $1/2$ States on Various Lattices
• Lieb-Schultz-Mattis theorem in higher dimensions from approximate magnetic translation symmetry
• Many-body multipole index and bulk-boundary correspondence
• Lieb-Schultz-Mattis Theorem for 1D Quantum Magnets with Antiunitary Translation and Inversion Symmetries
• Stability of quasi-particle creation and multiband geometry in fractional Chern insulators under magnetic fields

Cited by in corpus (1)

• Polarization-based indices in quantum many-body systems: validity and extension beyond one dimension