Finite Temperature Strong Coupling Expansions for the SU(N) Hubbard Model

Abstract

We develop finite temperature strong coupling expansions for the SU(N) Hubbard Model in powers of $\beta t$, $w=\exp (-\beta U)$ and $\frac{1}{\beta U}$ 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 the Bandwidth, the expansions converge over a wide temperature range $t^2/U\lesssim T\lesssim 10U$. By taking the limit $w\to 0$, valid at temperatures much less than $U$, the expansions turn into a high temperature expansion for a dressed 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 $w\to 0$ limit corresponds to an effective $t-J$ model. The onset of strong correlations can be identified by a plateau-like 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 $\delta =1-n$, the deviation from one particle per site, where the leading $\beta t$ dependent terms correspond to holes sloshing around in a disordered 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 comment8 pages 7 figures

References in corpus (16)

• Experimental realization of a long-range antiferromagnet in the Hubbard model with ultracold atoms
• Fermionic transport in a homogeneous Hubbard model: Out-of-equilibrium dynamics with ultracold atoms
• Observation of Spatial Charge and Spin Correlations in the 2D Fermi-Hubbard Model
• Ultracold fermions and the SU(N) Hubbard model
• Bad metallic transport in a cold atom Fermi-Hubbard system
• Imaging magnetic polarons in the doped Fermi-Hubbard model
• Numerical Linked-Cluster Approach to Quantum Lattice Models
• Direct probing of the Mott crossover in the SU($N$) Fermi-Hubbard model
• Effective spin model for the spin-liquid phase of the Hubbard model on the triangular lattice
• Quantum gas microscopy of an attractive Fermi-Hubbard system
• Violation of Luttinger's Theorem in the Two-Dimensional t-J Model
• Neel order, ring exchange and charge fluctuations in the half-filled Hubbard model
• Universal thermodynamics of an SU($N$) Fermi-Hubbard Model
• Selective insulators and anomalous responses in correlated fermions with synthetic extra dimensions
• Incipient order in the t-J model at high temperatures
• Rigorous results on the ground state of the attractive SU($N$) Hubbard model

Cited by in corpus (6)

• Equation of State and Thermometry of the 2D SU($N$) Fermi-Hubbard Model
• Many-body Physics of Ultracold Alkaline-Earth atoms with SU($N$)-symmetric interactions
• Enhancement of chiral edge currents in ($d$+1)-dimensional atomic Mott-band hybrid insulators
• On the Divergence of the Ferromagnetic Susceptibility in the SU(N) Nagaoka-Thouless Ferromagnet
• Trion formation and ordering in the attractive SU(3) Fermi-Hubbard model
• Onset of charge incompressibility and Mott gaps in the Honeycomb-Lattice SU(4) Hubbard Model: Lessons for Twisted Bilayer Graphene systems