Integrable Model of a Superconductor with non-Fermi liquid and Mott Phases

Abstract

We present and analyze an exactly solvable interacting fermionic pairing model, which features interactions that entangle states at momenta $\mathbf{k}$ and $-\mathbf{k}$. These interactions give rise to novel correlated ground states, leading to a rich phase diagram that includes superconducting, multiple metallic, and Mott-insulating phases. At finite interaction strengths, we observe the emergence of multiple many-body Fermi surfaces, which violate Luttinger's theorem and challenge the conventional Landau-Fermi liquid paradigm. A distinguishing feature of our model is that it remains quantum integrable, even with the addition of pairing interactions of various symmetries, setting it apart from the Hatsugai-Kohmoto model. Our results provide an analytically tractable framework for studying strong correlation effects that give rise to fractionalized excitations and unconventional superconductivity, offering valuable insights into a broad class of integrable many-body systems.

25 pages, 12 figures, To appear in Physical Review B

References in corpus (8)

• Quantum criticality
• Critical fermi surfaces and non-fermi liquid metals
• Many-body characterization of topological superconductivity: The Richardson-Gaudin-Kitaev chain
• Doped Mott Insulators Break ${\mathbb{Z}}_2$ Symmetry of a Fermi Liquid: Stability of Strongly Coupled Fixed Points
• 1/4 is the new 1/2 when topology is intertwined with Mottness
• Thermodynamics of an Exactly Solvable Model for Superconductivity in a Doped Mott Insulator
• Two-stage superconductivity in the Hatsugai-Kohmoto-BCS model
• Integrable Model of Topological SO(5) Superfluidity