We develop finite-temperature strong-coupling expansions for the $\mathrm{SU}(N)$ Hubbard model in powers of $\ensuremath{\beta}t, w=exp(\ensuremath{-}\ensuremath{\beta}U)$ and $\frac{1}{\ensuremath{\beta}U}$ for arbitrary filling. The expansions are done in the grand canonical ensemble and are most useful at a density of one particle per site, where for $U$ larger than or of order of the bandwidth, the expansions converge over a wide temperature range ${t}^{2}/U\phantom{\rule{4pt}{0ex}}\ensuremath{\lesssim}\phantom{\rule{4pt}{0ex}}T\phantom{\rule{4pt}{0ex}}\ensuremath{\lesssim}\phantom{\rule{4pt}{0ex}}10U$. By taking the limit $w\ensuremath{\rightarrow}0$, valid at temperatures much less than $U$ , the expansions turn into a high-temperature expansion for a dressed $\mathrm{SU}(N)$ Heisenberg model that includes nearest-neighbor exchange, further neighbor exchanges, and ring exchanges known from the $T=0$ perturbation theory of the SU(2) Hubbard model. Below a filling of one particle per site, the $w\ensuremath{\rightarrow}0$ limit corresponds to an effective $t\text{\ensuremath{-}}J$ model. The onset of strong correlations can be identified by a plateaulike behavior in the entropy as a function of temperature. At small deviations from one particle per site, the expansions can be arranged in powers of a small parameter $\ensuremath{\delta}=1\ensuremath{-}n$, the deviation from one particle per site, where the leading $\ensuremath{\beta}t$-dependent terms correspond to holes sloshing around in a disordered $\mathrm{SU}(N)$ background. We use these expansions to calculate the thermodynamic properties of the model at moderate and high temperatures over a wide parameter range.We develop finite-temperature strong-coupling expansions for the $\mathrm{SU}(N)$ Hubbard model in powers of $\ensuremath{\beta}t, w=exp(\ensuremath{-}\ensuremath{\beta}U)$ and $\frac{1}{\ensuremath{\beta}U}$ for arbitrary filling. The expansions are done in the grand canonical ensemble and are most useful at a density of one particle per site, where for $U$ larger than or of order of the bandwidth, the expansions converge over a wide temperature range ${t}^{2}/U\phantom{\rule{4pt}{0ex}}\ensuremath{\lesssim}\phantom{\rule{4pt}{0ex}}T\phantom{\rule{4pt}{0ex}}\ensuremath{\lesssim}\phantom{\rule{4pt}{0ex}}10U$. By taking the limit $w\ensuremath{\rightarrow}0$, valid at temperatures much less than $U$, the expansions turn into a high-temperature expansion for a dressed $\mathrm{SU}(N)$ Heisenberg model that includes nearest-neighbor exchange, further neighbor exchanges, and ring exchanges known from the $T=0$ perturbation theory of the SU(2) Hubbard model. Below a filling of one particle per site, the $w\ensuremath{\rightarrow}0$ limit corresponds to an effective $t\text{\ensuremath{-}}J$ model. The onset of strong correlations can be identified by a plateaulike behavior in the entropy as a function of temperature. At small deviations from one particle per site, the expansions can be arranged in powers of a small parameter $\ensuremath{\delta}=1\ensuremath{-}n$, the deviation from one particle per site, where the leading $\ensuremath{\beta}t$-dependent terms correspond to holes sloshing around in a disordered $\mathrm{SU}(N)$ background. We use these expansions to calculate the thermodynamic properties of the model at moderate and high temperatures over a wide parameter range.

arXiv:2201.06677Physical Review AMar 24, 20227 citations

The high temperature series for the Hubbard model

正人多田

Jan 1, 19830 citations

Strong-coupling thermodynamics of the Hubbard model

D. Grensing, Heinz Koppe

The European Physical Journal BJun 1, 19765 citations

Onset of charge incompressibility and Mott gaps in the honeycomb-lattice SU(4) Hubbard model: Lessons for twisted bilayer graphene systems

Rahul Hingorani, J. Oitmaa, Rajiv R. P. Singh

We use finite-temperature strong coupling expansions to calculate thermodynamic properties of the honeycomb-lattice SU(4) Hubbard model. We present numerical results for various properties including chemical potential, compressibility, entropy and specific heat as a function of temperature and density at several $U/t$ values. We study the onset of charge incompressibility and Mott gaps as the temperature is lowered at integer densities. In the incompressible Mott regime, the expansions are recast into a high-temperature expansion for a generalized spin model with SU(4) symmetry, which is then used to study the convergence of strong coupling expansions in $t/U$ . We discuss lessons that can be drawn from high-temperature properties of a simple Hubbard model regarding twisted bilayer graphene and other magic-angle flat-band systems.We use finite-temperature strong coupling expansions to calculate thermodynamic properties of the honeycomb-lattice SU(4) Hubbard model. We present numerical results for various properties including chemical potential, compressibility, entropy and specific heat as a function of temperature and density at several $U/t$ values. We study the onset of charge incompressibility and Mott gaps as the temperature is lowered at integer densities. In the incompressible Mott regime, the expansions are recast into a high-temperature expansion for a generalized spin model with SU(4) symmetry, which is then used to study the convergence of strong coupling expansions in $t/U$. We discuss lessons that can be drawn from high-temperature properties of a simple Hubbard model regarding twisted bilayer graphene and other magic-angle flat-band systems.

arXiv:2203.14356Physical review. B./Physical review. BJun 23, 20221 citation

We develop finite-temperature strong-coupling expansions for the

\mathrm{SU}(N)

Hubbard model in powers of $\ensuremath{\beta}t, w=exp(\ensuremath{-}\ensuremath{\beta}U)$ and $\frac{1}{\ensuremath{\beta}U}$ for arbitrary filling. The expansions are done in the grand canonical ensemble and are most useful at a density of one particle per site, where for

U

larger than or of order of the bandwidth, the expansions converge over a wide temperature range ${t}^{2}/U\phantom{\rule{4pt}{0ex}}\ensuremath{\lesssim}\phantom{\rule{4pt}{0ex}}T\phantom{\rule{4pt}{0ex}}\ensuremath{\lesssim}\phantom{\rule{4pt}{0ex}}10U$. By taking the limit $w\ensuremath{\rightarrow}0$, valid at temperatures much less than

U

, the expansions turn into a high-temperature expansion for a dressed

\mathrm{SU}(N)

Heisenberg model that includes nearest-neighbor exchange, further neighbor exchanges, and ring exchanges known from the

T=0

perturbation theory of the SU(2) Hubbard model. Below a filling of one particle per site, the $w\ensuremath{\rightarrow}0$ limit corresponds to an effective $t\text{\ensuremath{-}}J$ model. The onset of strong correlations can be identified by a plateaulike behavior in the entropy as a function of temperature. At small deviations from one particle per site, the expansions can be arranged in powers of a small parameter $\ensuremath{\delta}=1\ensuremath{-}n$, the deviation from one particle per site, where the leading $\ensuremath{\beta}t$-dependent terms correspond to holes sloshing around in a disordered

\mathrm{SU}(N)

background. We use these expansions to calculate the thermodynamic properties of the model at moderate and high temperatures over a wide parameter range.

U/t

values. We study the onset of charge incompressibility and Mott gaps as the temperature is lowered at integer densities. In the incompressible Mott regime, the expansions are recast into a high-temperature expansion for a generalized spin model with SU(4) symmetry, which is then used to study the convergence of strong coupling expansions in

t/U

. We discuss lessons that can be drawn from high-temperature properties of a simple Hubbard model regarding twisted bilayer graphene and other magic-angle flat-band systems.