Lieb-Schultz-Mattis constraints for the insulating phases of the one-dimensional SU($N$) Kondo lattice model

Abstract

The nature of the insulating phases of the SU($N$)-generalization of the one-dimensional Kondo lattice model is investigated by means of non-perturbative approaches. By extending the Lieb-Schultz-Mattis (LSM) argument to multi-component fermion systems with translation and global SU($N$) symmetries, we derive two indices which depend on the filling and the ``SU($N$)-spin'' (representation) of the local moments. These indices strongly constrain possible insulating phases; for instance, when the local moments transform in the $N$-dimensional (defining) representation of SU($N$), a featureless Kondo insulator is possible only at filling $f=1-1/N$. To obtain further insight into the insulating phases suggested by the LSM argument, we derive low-energy effective theories by adding an antiferromagnetic Heisenberg exchange interaction among the local moments [the SU($N$) Kondo-Heisenberg model]. A conjectured global phase diagram of the SU($N$) Kondo lattice model as a function of the filling and the Kondo coupling is then obtained by a combination of different analytical approaches.

arXiv comment29 pages, 6 figures

References in corpus (89)

• Anyons in an exactly solved model and beyond
• Topological Kondo Insulators
• Dimerization and Incommensurate Spiral Spin Correlations in the Zigzag Spin Chain: Analogies to the Kondo Lattice
• Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice
• Weak Coupling Phase Diagram of the Two Chain Hubbard Model
• Ultracold Fermi Gases with Emergent SU(N) Symmetry
• Ultracold Gases of Ytterbium: Ferromagnetism and Mott States in an SU(6) Fermi System
• MATBG as Topological Heavy Fermion: I. Exact Mapping and Correlated Insulators
• 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
• Exact SO(8) Symmetry in the Weakly-Interacting Two-Leg Ladder
• Non-perturbative approach to Luttinger's theorem in one dimension
• Locality in Quantum and Markov Dynamics on Lattices and Networks
• Intrinsic and emergent anomalies at deconfined critical points
• Localized magnetic moments with tunable spin exchange in a gas of ultracold fermions
• Symmetric-Gapped Surface States of Fractional Topological Insulators
• Anomaly Manifestation of Lieb-Schultz-Mattis Theorem and Topological Phases
• Phases of one-dimensional SU(N) cold atomic Fermi gases --from molecular Luttinger liquids to topological phases
• Algebraic spin liquid in an exactly solvable spin model
• Lieb-Schultz-Mattis, Luttinger, and 't Hooft -- anomaly matching in lattice systems
• An extended massless phase and the Haldane phase in a spin-1 isotropic antiferromagnetic chain
• Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods
• Anomaly and global inconsistency matching: $\theta$-angles, $SU(3)/U(1{)}^2$ nonlinear sigma model, $SU(3)$ chains and its generalizations
• Probing the Kondo Lattice Model with Alkaline Earth Atoms
• Exact Results for 1D Kondo Lattice from Bosonization
• Pair Density Wave correlations in the Kondo-Heisenberg Model
• Fermionic magnons, non-Abelian spinons, and spin quantum Hall effect from an exactly solvable Kitaev Hamiltonian with SU(2) symmetry
• Metal-insulator transition in the one-dimensional SU(N) Hubbard model
• Lieb-Schultz-Mattis Theorem and its generalizations from the Perspective of the Symmetry Protected Topological phase
• Symmetry protection of critical phases and global anomaly in $1+1$ dimensions
• Semiclassical Solution of One Dimensional Model of Kondo Insulator
• Topological theory of Lieb-Schultz-Mattis theorems in quantum spin systems
• Kondo lattice model in magic-angle twisted bilayer graphene
• Laser-induced Kondo effect in ultracold alkaline-earth fermions
• Spin Gap in a Doped Kondo Chain
• Kondo Lattice Model of Magic-Angle Twisted-Bilayer Graphene: Hund's Rule, Local-Moment Fluctuations, and Low-Energy Effective Theory
• Lieb-Schultz-Mattis type theorems for quantum spin chains without continuous symmetry
• The one dimensional Kondo lattice model at partial band filling
• Anomaly matching and symmetry-protected critical phases in $SU(N)$ spin systems in 1+1 dimensions
• Z_3 symmetry-protected topological phases in the SU(3) AKLT model
• Surface Kondo Effect and Non-Trivial Metallic State of the Kondo Insulator YbB12
• Dimerization induced by the RKKY interaction
• Spinon confinement and the Haldane gap in SU(n) spin chains
• Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries
• ${\mathbb{Z}}_N$ Symmetries, Anomalies, and the Modular Bootstrap
• Symmetric Kondo Lattice States in Doped Strained Twisted Bilayer Graphene
• Fractionalized Fermi liquids and exotic superconductivity in the Kitaev-Kondo lattice
• Kondo Phase in Twisted Bilayer Graphene -- A Unified Theory for Distinct Experiments
• Staggered liquid phases of the 1D Kondo-Heisenberg lattice model
• Topological superconductivity in Kondo-Kitaev model
• One-dimensional electron gas interacting with a Heisenberg spin-1/2 chain
• A solvable 3D Kondo lattice exhibiting odd-frequency pairing and order fractionalization
• Sigma Models on Flags
• Chiral Haldane phases of SU(N) quantum spin chains in the adjoint representation
• Mixed global anomalies and boundary conformal field theories
• The dimerized phase of ionic Hubbard models
• Unified Phase Diagram of Antiferromagnetic SU(N) Spin Ladders
• Massless renormalization group flow in SU(N)${}_k$ perturbed conformal field theory
• Competing Orders and Hidden Duality Symmetries in Two-leg Spin Ladder Systems
• Zooming in on heavy fermions in Kondo lattice models
• Lieb-Schultz-Mattis anomalies and web of dualities induced by gauging in quantum spin chains
• Generalization of the Haldane conjecture to SU($n$) chains
• Pair-density-wave superconductor from doping Haldane chain and rung-singlet ladder
• Flag manifold sigma models: spin chains and integrable theories
• Phase diagram and dynamics of the SU($\mathbf{N}$) symmetric Kondo lattice model
• Bosonization Approach to the One-Dimensional Kondo Lattice Model at Half Filling: Reexamination
• Heavy-fermion valence-bond liquids in ultracold atoms: Cooperation of Kondo effect and geometric frustration
• From coupled-wire construction of quantum Hall states to wave functions and hydrodynamics
• Spontaneous Parity Violation in a Quantum Spin Chain
• Odd-frequency pair density wave in the Kitaev-Kondo lattice model
• Observation of spin-exchange dynamics between itinerant and localized ${}^{171}\mathrm{Yb}$ atoms
• Probing FeSi, a d-electron topological Kondo insulator candidate, with magnetic field, pressure, and microwaves
• Quadrupolar spin liquid, octupolar Kondo coupling and odd-frequency superconductivity in an exactly solvable model
• Symmetry-protected topological phases in two-leg SU(N) spin ladder with unequal spins
• Luttinger sum rules and spin fractionalization in the SU(N) Kondo Lattice
• Two-leg SU(2n) spin ladder: A low-energy effective field theory approach
• Ferromagnetism in the SU(N) Kondo lattice model -- SU(N) double exchange and supersymmetry
• Mass generation by fractional instantons in SU($n$) chains
• "Haldane" phases with ultracold fermionic atoms in double-well optical lattices
• Bosonization with a background $U(1)$ gauge field
• Symmetry protected topological phases in two-orbital SU(4) fermionic atoms
• Logarithmic corrections to finite size spectrum of SU(N) symmetric quantum chains
• The one-dimensional Kondo lattice model at quarter-filling
• Matrix Product Study of Spin Fractionalization in the 1D Kondo Insulator
• Charge Density Wave in a Doped Kondo Chain
• Flag manifold sigma models from SU($n$) chains
• Coupled dimer and bond-order-wave order in the quarter-filled one-dimensional Kondo lattice model
• Even-odd effects in the $J_1-J_2$ SU($N$) Heisenberg spin chain
• SU($\mathbf{N}$) Kondo-Heisenberg chain: Phase diagram, Ising criticality, and the coexistence of heavy quasiparticles and valence bond solid order

Cited by in corpus (2)

• Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
• Fusion rule in conformal field theories and topological orders: A unified view of correspondence and (fractional) supersymmetry and their relation to topological holography