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arXiv:2310.20306

Emergence of diverse array of phases in an exactly solvable model

Zhipeng Sun, Hai-Qing Lin

Published Oct 31, 2023• 0 citations
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Abstract

We propose an exactly solvable lattice model, motivated by the significance of the extended Hubbard model ($t-U-V$ model) and inspired by the work of Hatsugai and Kohmoto. The ground state exhibits a diverse array of phases, including the charge-$4e$ condensed phase, the charge-$2e$ superconducting phase, the half-filled insulating phase, the quarter-filled insulating phase, the metallic phase, and an unconventional metallic phase. Among them, the unconventional metallic phase could be of particular significance, for the coexistence of electrons and pairs at zero energy. These findings are poised to advance our understanding and exploration of strongly correlated physics.

DOI
10.48550/arxiv.2310.20306

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We propose an exactly solvable lattice model, motivated by the significance of the extended Hubbard model (t−U−Vt-U-Vt−U−V model) and inspired by the work of Hatsugai and Kohmoto. The ground state exhibits a diverse array of phases, including the charge-4e4e4e condensed phase, the charge-2e2e2e superconducting phase, the half-filled insulating phase, the quarter-filled insulating phase, the metallic phase, and an unconventional metallic phase. Among them, the unconventional metallic phase could be of particular significance, for the coexistence of electrons and pairs at zero energy. These findings are poised to advance our understanding and exploration of strongly correlated physics.
Numerical solvers for strongly correlated electronic systems poses a significant challenge in condensed matter theory. In recent years, extensive exploration of strongly correlated effects has been carried out based on exactly solvable Hatsugai-Kohmoto-like models. In this work, we investigate a simple two-site cluster extension of the Hatsugai-Kohmoto model. The model exhibits a rich variety of phases, including the charge-4e4e4e phase, charge-2e2e2e phase, metallic phase, pseudogap phase, and Luttinger liquid phase. These findings contribute to the understanding of strongly correlated physics and superconducting physics.
We present and analyze an exactly solvable interacting fermionic pairing model, which features interactions that entangle states at momenta k\mathbf{k}k and −k-\mathbf{k}−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.
We present an exactly solvable Hamiltonian which consists of nearest neighbor hopping and long-range interaction. The ground state and the thermodynamic quantities are analytically obtained in any dimensions. In a repulsive case, the Luttinger's theorem breaks down and the hypothesis of the adiabatic continuation no longer holds. At half filling, we show the existence of a metal-insulator transition as a function of the strength of the interaction. The zero energy excitation disappears at the critical value of the interaction when we increase the interaction. In this case, the system is an insulator. The charge compressibility behaves as κ≈|1-ρ| 1-2/ d near half filling in d dimensions where ρ is the density of electrons. At other fillings, there is always a zero energy excitation and the system is metallic. When the interaction is attractive, the ground state is composed of pairs of electrons with opposite spins. The low energy excitations, however, is not a particle-hole type of a non-interacting case but a pairwise excitation across the Fermi surface.
The ground-state phase diagram of the one-dimensional Hubbard chain with pair-hopping interaction is studied. The analysis of the model is performed using the continuum-limit field theory approach and exact diagonalization studies. At half-filling the phase diagram is shown to consist of two superconducting states with Cooper-pair center-of-mass momentum $Q=0 (\mathrm{BCS}\ensuremath{-}{\ensuremath{\eta}}_{0}$ phase) and $Q=\ensuremath{\pi} ({\ensuremath{\eta}}_{\ensuremath{\pi}}$ phase) and four insulating phases corresponding to the Mott antiferromagnet, the Peierls dimerized phase, the charge-density-wave (CDW) insulator, and an unconventional insulating phase characterized by the coexistence of a CDW and a bond-located staggered magnetization. Away from half-filling the phase diagram consists of the superconducting $\mathrm{BCS}\ensuremath{-}{\ensuremath{\eta}}_{0}$ and ${\ensuremath{\eta}}_{\ensuremath{\pi}}$ phases and the metallic Luttinger-liquid phase. The $\mathrm{BCS}\ensuremath{-}{\ensuremath{\eta}}_{0}$ phase exhibits a smooth crossover from a weak-coupling BCS type to a strong-coupling local-pair regime. The ${\ensuremath{\eta}}_{\ensuremath{\pi}}$ phase shows the properties of the doublon (zero-size Cooper-pair) superconductor with Cooper-pair center-of-mass momentum $Q=\ensuremath{\pi}.$ The transition into the ${\ensuremath{\eta}}_{\ensuremath{\pi}}$-paired state corresponds to an abrupt change in the ground-state structure. After the transition the conduction band is completely destroyed and a new ${\ensuremath{\eta}}_{\ensuremath{\pi}}$-pair band, corresponding to the strongly correlated doublon motion, is created.
Multiband superconductivity gives rise to a rich landscape of possible pairing states. Here we study superconductivity emerging from a half-filled normal state in a two-orbital extension of the Hatsugai-Kohmoto model, an exactly solvable model of correlated electrons with momentum-local interactions, which provides a minimal framework to explore the interplay of strong correlations, orbital structure and pairing symmetry. For a system with point-group symmetry D4h\rm D_{4h}D4h​, we classify the symmetry-allowed superconducting gap structures, taking into account spin, orbital and momentum degrees of freedom. We further compute the critical temperature and the superconducting order parameter for selected pairing channels as functions of interaction and pairing strength within a mean-field treatment. Our results provide a systematic framework for analyzing superconductivity in the orbital Hatsugai-Kohmoto model and extend symmetry-based approaches to correlated multiband settings.
A one-dimensional model of interacting electrons with on-site U, nearest-neighbor V, and correlated-hopping interaction T∗{T}^{*}T∗ is studied at half filling using the continuum-limit field theory approach. The ground-state phase diagram is obtained for a wide range of coupling constants. In addition to the insulating spin- and charge-density wave phases for large U and V, respectively, we identify bond-located ordered phases corresponding to an enhanced Peierls instability in the system for ${T}^{*}>0, |U\ensuremath{-}2V|<{8T}^{*}/\ensuremath{\pi}$ and to a staggered magnetization located on bonds between sites for ${T}^{*}<0, |U\ensuremath{-}2V|<8|{T}^{*}|/\ensuremath{\pi}.$ The general ground-state phase diagram including insulating, metallic, and superconducting phases is discussed.