We establish the Hatsugai-Kohmoto model as a stable quartic fixed point (distinct from Wilson-Fisher) by computing the $\ensuremath{\beta}$ function in the presence of perturbing local interactions. In vicinity of the half-filled doped Mott state, the $\ensuremath{\beta}$ function vanishes for all local interactions regardless of their sign. The only flow away from the HK model is through the superconducting channel which lifts the spin degeneracy as does any ordering tendency. The superconducting instability is identical to that established previously [Phillips et al., Nat. Phys. 16, 1175 (2020)]. A corollary of this work is that any system in which the spectral weight bifurcates into lower and upper bands such as the Hubbard model with repulsive interactions flows into the HK stable fixed point in the vicinity of half-filling. Consequently, although the HK model has all-to-all interactions, the bifurcation of the spectral weight is stable as nothing local destroys it. The consilience with Hubbard arises because both models break the
Z2 symmetry on a Fermi surface, the HK model being the simplest to do so. Indeed, the simplicity of the HK model belies its robustness and generality.
We investigate the Hatsugai-Kohmoto (HK) model on a square lattice, which describes both a Mott insulator at half-filling and a non-Fermi liquid phase on doping. Through the solution of this exactly solvable model with the inclusion of pairing interactions, we demonstrate the emergence of strong pair-density-wave (PDW) fluctuations associated with center-of-mass momentum $\mathbf{Q}=(\ensuremath{\pi},\ensuremath{\pi})$ at finite temperatures for low dopings up to a critical doping and intermediate
U interaction. Furthermore, we also confirm that a superconducting instability appears in the model within a wide regime of interaction
U and doping parameter
x. In view of the fact that it has been recently put forward that the metal-insulator transition of the HK model belongs to the same universality class as the Mott transition of the paradigmatic Hubbard model [Huang et al., Nat. Phys. 18, 511 (2022)], our work may thus shed light on an interesting scenario regarding the emergence of a fluctuating PDW phase on doping a Mott insulator, which has been argued to be relevant for understanding the physics of the cuprate superconductors in the underdoped regime.
The Hatsugai-Kohmoto interaction model has gained a lot of attention in recent years, due to the fact it is exactly solvable in momentum space in any dimension while capturing some key features of the Mott phase. Here a one-dimensional lattice model with this interaction is approached from the real-space perspective, to explore how breaking the translation invariance of a lattice affects the intuition built by studying the exact solution in
k space. The ground state properties of chains with periodic and open boundary conditions are calculated and compared with both the exact solution in momentum space as well as with analogous solutions of the Hubbard model. The results show that introducing hard edges enhances the ferromagnetic correlations and the system undergoes a magnetic transition before reaching the strong coupling limit. Understanding the impact of hard edges is a crucial step toward answering the looming question of the existence of edge states and other topological phenomena in systems with this type of interaction.
We study entanglement in the Hatsugai-Kohmoto model, which exhibits a continuous interaction-driven Mott transition. By virtue of the all-to-all nature of its center-of-mass-conserving interactions, the model lacks dynamical spectral weight transfer, which is the key to the intractability of the Hubbard model for
d>1. In order to maintain a nontrivial Mott-like electron propagator, SU(2) symmetry is preserved in the Hamiltonian, leading to a ground state that is mixed on both sides of the phase transition. Because of this mixture, even the metal in this model is unentangled between any pair of sites, unlike free fermions whose ground state carries a filling-dependent site-site entanglement. We focus on the scaling behavior of the one- and two-site entropies
s1 and
s2, as well as the entropy density
s, of the ground state near the Mott transition. At low temperatures in the two-dimensional Hubbard model, Walsh et al. [Phys. Rev. B 99, 075122 (2019)] observed numerically that
s1 and
s increase continuously into the metal, across a first-order Mott transition. In the Hatsugai-Kohmoto model,
s1 acquires the constant value ln 4 even at the Mott transition. On the other hand,
s2 and
s each act as a sharp signal of the Mott transition, in any dimension, by decreasing at the transition into the metal. Specifically, we find that in one dimension,
s2 and
s exhibit kinks at the transition while in two dimensions, only
s exhibits a kink.
Interacting fermions on the half-filled honeycomb lattice with short-range repulsions have been suggested to host a variety of interesting many-body ground states, e.g., a topological Mott insulator. A number of recent studies of the spinless case in terms of exact diagonalization, the infinite density matrix renormalization group, and the functional renormalization group, however, indicate a suppression of the topological Mott insulating phase in the whole range of interaction parameters. Here, we complement the previous studies by investigating the quantum many-body instabilities of the physically relevant case of spin-1/2 fermions with onsite, nearest-neighbor, and second-nearest-neighbor repulsion. To this end, we employ the multipatch functional renormalization group for correlated fermions with refined momentum resolution observing the emergence of an antiferromagnetic spin-density wave and a charge-density wave for dominating onsite and nearest-neighbor repulsions, respectively. For dominating second-nearest neighbor interaction our results favor an ordering tendency towards a charge-modulated ground state over the topological Mott insulating state. The latter evades a stabilization as the leading instability by the additional onsite interaction.
This pedagogic review aims to give a gentle introduction to an exactly solvable model, the Hatsugai-Kohmoto (HK) model, which has infinite-ranged interaction but conserves the center of mass. Although this model is invented in 1992, intensive studies on its properties ranging from unconventional superconductivity, topological ordered states to non-Fermi liquid behaviors are made since 2020. We focus on its emergent non-Fermi liquid behavior and provide discussion on its thermodynamics, single-particle and two-particle correlation functions. Perturbation around solvable limit has also been explored with the help of perturbation theory, renormalization group and exact diagonalization calculation. We hope the present review will be helpful for graduate students or researchers interested in HK-like models or more generic strongly correlated electron systems.