Phase transitions in the Hubbard model and ionic Hubbard model at half-filling on the honeycomb lattice are investigated in the strong-coupling perturbation theory which corresponds to an expansion in powers of the hopping $t$ around the atomic limit. Within this formulation we find analytic expressions for the single-particle spectrum, whereby the calculation of the insulating gap is reduced to a simple root finding problem. This enables high-precision determination of the insulating gap that does not require any extrapolation procedure. The critical value of Mott transition on the honeycomb lattice is obtained to be ${U}_{c}\ensuremath{\approx}2.38t$. Studying the ionic Hubbard model at the lowest order, we find two insulating states, one with Mott character at large $U$ and another with single-particle gap character at large ionic potential $\mathrm{\ensuremath{\Delta}}$. The present approach gives a critical gapless state at $U=2\mathrm{\ensuremath{\Delta}}$ at lowest order. By systematically improving on the perturbation expansion, the density of states around this critical gapless phase reduces.Phase transitions in the Hubbard model and ionic Hubbard model at half-filling on the honeycomb lattice are investigated in the strong-coupling perturbation theory which corresponds to an expansion in powers of the hopping $t$ around the atomic limit. Within this formulation we find analytic expressions for the single-particle spectrum, whereby the calculation of the insulating gap is reduced to a simple root finding problem. This enables high-precision determination of the insulating gap that does not require any extrapolation procedure. The critical value of Mott transition on the honeycomb lattice is obtained to be ${U}_{c}\ensuremath{\approx}2.38t$. Studying the ionic Hubbard model at the lowest order, we find two insulating states, one with Mott character at large $U$ and another with single-particle gap character at large ionic potential $\mathrm{\ensuremath{\Delta}}$. The present approach gives a critical gapless state at $U=2\mathrm{\ensuremath{\Delta}}$ at lowest order. By systematically improving on the perturbation expansion, the density of states around this critical gapless phase reduces.

arXiv:1509.09076Physical review. B./Physical review. BFeb 10, 20169 citations

MOTT TRANSITION IN THE HUBBARD MODEL

B. Sriram Shastry

WORLD SCIENTIFIC eBooksApr 1, 19930 citations

The Mott transition and the strong correlation problem

Gabriel Kotliar

Physica A Statistical Mechanics and its ApplicationsMay 1, 20001 citation

Rashba-metal to Mott-insulator transition

Valentina Brosco, Massimo Capone

The recent discovery of materials featuring strong Rashba spin-orbit coupling (RSOC) and strong electronic correlation raises questions about the interplay of Mott and Rashba physics. In this work, we employ cluster perturbation theory to investigate the spectral properties of the two-dimensional Hubbard model in the presence of a significant or large RSOC. We show that RSOC strongly favors metallic phases and competes with Mott localization, leading to an unconventional scenario for the Mott transition, which is no longer controlled by the ratio between the Hubbard $U$ and an effective bandwidth. The results show a strong sensitivity to the value of the RSOC.The recent discovery of materials featuring strong Rashba spin-orbit coupling (RSOC) and strong electronic correlation raises questions about the interplay of Mott and Rashba physics. In this work, we employ cluster perturbation theory to investigate the spectral properties of the two-dimensional Hubbard model in the presence of a significant or large RSOC. We show that RSOC strongly favors metallic phases and competes with Mott localization, leading to an unconventional scenario for the Mott transition, which is no longer controlled by the ratio between the Hubbard $U$ and an effective bandwidth. The results show a strong sensitivity to the value of the RSOC.

arXiv:1811.12034Physical review. B./Physical review. BJun 22, 20209 citations

Effect of correlations on the mott transition

Börje Johansson

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimentoAug 1, 19700 citations

Strong-coupling perturbative study of the disordered Hubbard model on the honeycomb lattice

Alireza Habibi, Elaheh Adibi, Somaye Jafari

We study the Anderson disordered Hubbard model on the honeycomb lattice. The Hubbard term is handled with strong-coupling perturbation theory which encodes the information about Mott transition physics into a rich dynamical local self-energy. The local nature of the self-energy allows us to combine it with kernel polynomial and transfer matrix methods which consequently enables us to study lattices with millions of sites. The transfer matrix method, which in the ribbon geometry is essentially free from finite-size errors, can be employed to perform finite-size scaling on the width of the ribbon. This enables us to rule out the possibility of metallic phase between the Mott and Anderson insulating phases which has been claimed in the literature. Therefore, we find a direct transition between Anderson and Mott insulators when the disorder strength $W$ is comparable to the Hubbard interaction $U$ . For a fixed disorder strength $W$ , we obtain an interaction-dependent nonmonotonic behavior of the localization length which reflects the interaction-induced enhancement of the localization length for weak and intermediate interaction strengths. Eventually, at strong interactions $U$ , the Mott localization takes over, and the localization length becomes comparable to the lattice scale. This phenomenon is reminiscent of the holographic determination of the Mott state where the system at infrared recognizes its ultraviolet lattice scale.We study the Anderson disordered Hubbard model on the honeycomb lattice. The Hubbard term is handled with strong-coupling perturbation theory which encodes the information about Mott transition physics into a rich dynamical local self-energy. The local nature of the self-energy allows us to combine it with kernel polynomial and transfer matrix methods which consequently enables us to study lattices with millions of sites. The transfer matrix method, which in the ribbon geometry is essentially free from finite-size errors, can be employed to perform finite-size scaling on the width of the ribbon. This enables us to rule out the possibility of metallic phase between the Mott and Anderson insulating phases which has been claimed in the literature. Therefore, we find a direct transition between Anderson and Mott insulators when the disorder strength $W$ is comparable to the Hubbard interaction $U$. For a fixed disorder strength $W$, we obtain an interaction-dependent nonmonotonic behavior of the localization length which reflects the interaction-induced enhancement of the localization length for weak and intermediate interaction strengths. Eventually, at strong interactions $U$, the Mott localization takes over, and the localization length becomes comparable to the lattice scale. This phenomenon is reminiscent of the holographic determination of the Mott state where the system at infrared recognizes its ultraviolet lattice scale.

arXiv:1806.07969Physical review. B./Physical review. BDec 3, 20185 citations

t

around the atomic limit. Within this formulation we find analytic expressions for the single-particle spectrum, whereby the calculation of the insulating gap is reduced to a simple root finding problem. This enables high-precision determination of the insulating gap that does not require any extrapolation procedure. The critical value of Mott transition on the honeycomb lattice is obtained to be ${U}_{c}\ensuremath{\approx}2.38t$. Studying the ionic Hubbard model at the lowest order, we find two insulating states, one with Mott character at large

U

and another with single-particle gap character at large ionic potential $\mathrm{\ensuremath{\Delta}}$. The present approach gives a critical gapless state at $U=2\mathrm{\ensuremath{\Delta}}$ at lowest order. By systematically improving on the perturbation expansion, the density of states around this critical gapless phase reduces.

U

and an effective bandwidth. The results show a strong sensitivity to the value of the RSOC.

W

is comparable to the Hubbard interaction

U

. For a fixed disorder strength

W

, we obtain an interaction-dependent nonmonotonic behavior of the localization length which reflects the interaction-induced enhancement of the localization length for weak and intermediate interaction strengths. Eventually, at strong interactions

U

, the Mott localization takes over, and the localization length becomes comparable to the lattice scale. This phenomenon is reminiscent of the holographic determination of the Mott state where the system at infrared recognizes its ultraviolet lattice scale.