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.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.

arXiv:2412.18864Physical review. B./Physical review. BDec 23, 20243 citations

Local entropies across the Mott transition in an exactly solvable model

Luke Yeo, Philip Phillips

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 ${s}_{1}$ and ${s}_{2}$ , 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 ${s}_{1}$ and $s$ increase continuously into the metal, across a first-order Mott transition. In the Hatsugai-Kohmoto model, ${s}_{1}$ acquires the constant value ln 4 even at the Mott transition. On the other hand, ${s}_{2}$ 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, ${s}_{2}$ and $s$ exhibit kinks at the transition while in two dimensions, only $s$ exhibits a kink.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 ${s}_{1}$ and ${s}_{2}$, 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 ${s}_{1}$ and $s$ increase continuously into the metal, across a first-order Mott transition. In the Hatsugai-Kohmoto model, ${s}_{1}$ acquires the constant value ln 4 even at the Mott transition. On the other hand, ${s}_{2}$ 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, ${s}_{2}$ and $s$ exhibit kinks at the transition while in two dimensions, only $s$ exhibits a kink.

arXiv:1901.07037Physical review. D/Physical review. D.May 22, 201918 citations

MOTT TRANSITION IN THE HUBBARD MODEL

B. Sriram Shastry

WORLD SCIENTIFIC eBooksApr 1, 19930 citations

Scaling close to a Mott transition in an exactly soluble model

M. A. Contínentino, Mauricio D. Coutinho-Filho

Solid State CommunicationsJun 1, 199422 citations

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.

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

{s}_{1}

and

{s}_{2}

, 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

{s}_{1}

and

s

increase continuously into the metal, across a first-order Mott transition. In the Hatsugai-Kohmoto model,

{s}_{1}

acquires the constant value ln 4 even at the Mott transition. On the other hand,

{s}_{2}

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,

{s}_{2}

and

s

exhibit kinks at the transition while in two dimensions, only

s

exhibits a kink.