Exact eigenstates of multicomponent Hubbard models: SU($N$) magnetic $\eta$ pairing, weak ergodicity breaking, and partial integrability

Abstract

We construct exact eigenstates of multicomponent Hubbard models in arbitrary dimensions by generalizing the $\eta$-pairing mechanism. Our models include the SU($N$) Hubbard model as a special case. Unlike the conventional two-component case, the generalized $\eta$-pairing mechanism permits the construction of eigenstates that feature off-diagonal long-range order and magnetic long-range order. These states form fragmented fermionic condensates due to a simultaneous condensation of multicomponent $\eta$ pairs. While the $\eta$-pairing states in the SU(2) Hubbard model are based on the $\eta$-pairing symmetry, the exact eigenstates in the $N$-component system with $N\ge 3$ arise not from symmetry of the Hamiltonian but from a spectrum generating algebra defined in a Hilbert subspace. We exploit this fact to show that the generalized $\eta$-pairing eigenstates do not satisfy the eigenstate thermalization hypothesis and serve as quantum many-body scar states. This result indicates a weak breakdown of ergodicity in the $N$-component Hubbard models for $N\ge 3$. Furthermore, we show that these exact eigenstates constitute integrable subsectors in which the Hubbard Hamiltonian effectively reduces to a non-interacting model. This partial integrability causes various multicomponent Hubbard models to weakly break ergodicity. We propose a method of harnessing dissipation to distill the integrable part of the dynamics and elucidate a mechanism of non-thermalization caused by dissipation. This work establishes the coexistence of off-diagonal long-range order and SU($N$) magnetism in excited eigenstates of the multicomponent Hubbard models, which presents a possibility of novel out-of-equilibrium pairing states of multicomponent fermions. These models unveil a unique feature of quantum thermalization of multicomponent fermions, which can experimentally be tested with cold-atom quantum simulators.

35 pages, 4 figures. v2: numerical results added, published version

References in corpus (38)

• Thermalization and its mechanism for generic isolated quantum systems
• Probing many-body dynamics on a 51-atom quantum simulator
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
• A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
• An SU(N) Mott insulator of an atomic Fermi gas realized by large-spin Pomeranchuk cooling
• Collisional stability of a three-component degenerate Fermi gas
• Ultracold Fermi Gases with Emergent SU(N) Symmetry
• Ultracold fermions and the SU(N) Hubbard model
• Fragmentation of Bose-Einstein Condensates
• Three-body recombination in a three-state Fermi gas with widely tunable interactions
• Ultracold Gases of Ytterbium: Ferromagnetism and Mott States in an SU(6) Fermi System
• Mott Insulators of Ultracold Fermionic Alkaline Earth Atoms: Underconstrained Magnetism and Chiral Spin Liquid
• Color Superfluidity and "Baryon" Formation in Ultracold Fermions
• Eta-Pairing in Hubbard Models: From Spectrum Generating Algebras to Quantum Many-Body Scars
• Hidden symmetry and quantum phases in spin-3/2 cold atomic systems
• Eta-pairing states as true scars in an extended Hubbard Model
• Metastable superfluidity of repulsive fermionic atoms in optical lattices
• Superfluidity and magnetism in multicomponent ultracold fermions
• Heating-Induced Long-Range $\eta$-Pairing in the Hubbard Model
• BCS pairing in Fermi systems with several flavors
• Trionic phase of ultracold fermions in an optical lattice: A variational study
• Pairing in a three component Fermi gas
• Coexistence of diffusive and ballistic transport in a simple spin ladder
• Emergence of Hilbert Space Fragmentation in Ising Models with a Weak Transverse Field
• Population imbalance and pairing in the BCS-BEC crossover of three-component ultracold fermions
• Observation of the Sign Reversal of the Magnetic Correlation in a Driven-Dissipative Fermi Gas in Double Wells
• New type of crossover physics in three-component Fermi gases
• Nagaoka states in the SU($n$) Hubbard model
• Pauli blocking effects and Cooper triples in three-component Fermi gases
• Photoinduced $\eta$-pairing at finite temperatures
• Superfluid state of repulsively interacting three-component fermionic atoms in optical lattices
• Exact eigenstates of extended SU($N$) Hubbard models: Generalizations of $\eta$-pairing states with $N$-particle off-diagonal long-range order
• Rigorous results on the ground state of the attractive SU($N$) Hubbard model
• Analytical Solution for the Steady States of the Driven Hubbard model
• Spontaneously symmetry breaking states in the attractive SU$(N)$ Hubbard model
• Majorana Scars as Group Singlets
• QCD-like phase diagram with Efimov trimers and Cooper pairs in resonantly interacting SU(3) Fermi gases

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• Generalized Nagaoka ferromagnetism accompanied by flavor-selective Mott states in an SU($N$) Fermi-Hubbard model
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