Gappability Index for Quantum Many-Body Systems

Abstract

We propose an index ${\mathcal{I}}_G$ which characterizes the degree of ingappability, namely the difficulty to induce a unique ground state with a nonvanishing excitation gap, in the presence of a symmetry $G$. ${\mathcal{I}}_G$ represents the dimension of the subspace of ambient uniquely-gapped in the entire $G$-invariant "theory space". The celebrated Lieb-Schultz-Mattis theorem corresponds, in our formulation, to the case ${\mathcal{I}}_G=0$ (completely ingappable) for the symmetry $G$ including the lattice translation symmetry. We illustrate the usefulness of the index by discussing the phase diagram of spin-$1/2$ antiferromagnets in various dimensions, which do not necessarily have the translation symmetry.

arXiv comment3 figures

References in corpus (32)

• Topological Insulators in Three Dimensions
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Magnetization plateaus in spin chains: ``Haldane gap'' for half-integer spins
• Lieb-Schultz-Mattis in Higher Dimensions
• Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice
• Classification of Interacting Topological Floquet Phases in One Dimension
• Classification of topological phases in periodically driven interacting systems
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications II
• Quantum Criticality without Tuning in the Mixed Valence Compound beta-YbAlB4
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications I
• Phase Structure of 1d Interacting Floquet Systems I: Abelian SPTs
• Translational symmetry and microscopic constraints on symmetry-enriched topological phases: a view from the surface
• Filling constraints for spin-orbit coupled insulators in symmorphic and non-symmorphic crystals
• Abelian Floquet symmetry-protected topological phases in one dimension
• Order Parameter to Characterize Valence-Bond-Solid States in Quantum Spin Chains
• Floquet topological phases with symmetry in all dimensions
• Lattice Homotopy Constraints on Phases of Quantum Magnets
• Symmetry protection of critical phases and global anomaly in $1+1$ dimensions
• Topological theory of Lieb-Schultz-Mattis theorems in quantum spin systems
• Berry Phase in Quantum Field Theory: Diabolical Points and Boundary Phenomena
• Lieb-Schultz-Mattis type theorems for quantum spin chains without continuous symmetry
• Twisted boundary condition and Lieb-Schultz-Mattis ingappability for discrete symmetries
• General Lieb-Schultz-Mattis type theorems for quantum spin chains
• Anomaly matching and symmetry-protected critical phases in $SU(N)$ spin systems in 1+1 dimensions
• Higher-dimensional generalizations of the Berry curvature
• DMRG studies of critical SU(N) spin chains
• A generalized boundary condition applied to Lieb-Schultz-Mattis type ingappabilities and many-body Chern numbers
• Effective field theory for one-dimensional valence-bond-solid phases and their symmetry protection
• Quantum Criticality in Dimerized Spin Ladders

Cited by in corpus (7)

• Generalized Thouless Pumps in 1+1-dimensional Interacting Fermionic Systems
• Ferromagnets, a New Anomaly, Instantons, and (noninvertible) Continuous Translations
• Higher Berry curvature from matrix product states
• Anomalous Continuous Translations
• Modulating Hamiltonian Approach to Quantum Many-Body Systems and Crystalline Topological Phases Protected by Generalized Magnetic Translations
• Equivariant Parameter Families of Spin Chains: A Discrete MPS Formulation
• Anisotropy-induced spin parity effects