On the Divergence of the Ferromagnetic Susceptibility in the SU(N) Nagaoka-Thouless Ferromagnet

Abstract

Using finite temperature strong coupling expansions for the SU(N) Hubbard Model, we calculate the thermodynamic properties of the model in the infinite-$U$ limit for arbitrary density $0\le \rho \le 1$ and all $N$. We express the ferromagnetic susceptibility of the model as a Curie term plus a $\Delta \chi$, an excess susceptibility above the Curie-behavior. We show that, on a bipartite lattice, graph by graph the contributions to $\Delta \chi$ are non-negative in the limit that the hole density $\delta =1-\rho$ goes to zero. By summing the contributions from all graphs consisting of closed loops we find that the low hole-density ferromagnetic susceptibility diverges exponentially as $\exp \Delta /T$ as $T\to 0$ in two and higher dimensions. This demonstrates that Nagaoka-Thouless ferromagnetic state exists as a thermodynamic state of matter at low enough density of holes and sufficiently low temperatures. The constant $\Delta$ scales with the SU(N) parameter $N$ as $1/N$ implying that ferromagnetism is gradually weakened with increasing $N$ as the characteristic temperature scale for ferromagnetic order goes down.

arXiv comment5 pages, 1 figure

References in corpus (24)

• 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
• 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
• Lattice dependence of saturated ferromagnetism in the Hubbard model
• Phases of the infinite U Hubbard model
• Ferromagnetism in Correlated Electron Systems: Generalization of Nagaoka's Theorem
• Violation of Luttinger's Theorem in the Two-Dimensional t-J Model
• Nagaoka ferromagnetism in the two-dimensional infinite-U Hubbard model
• Stability of Ferromagnetism in Hubbard Models with Nearly-Flat Bands
• Neel order, ring exchange and charge fluctuations in the half-filled Hubbard model
• A dynamical mean-field theory study of Nagaoka ferromagnetism
• Universal thermodynamics of an SU($N$) Fermi-Hubbard Model
• Nagaoka states in the SU($n$) Hubbard model
• Selective insulators and anomalous responses in correlated fermions with synthetic extra dimensions
• Exact Results on Itinerant Ferromagnetism and the 15-puzzle Problem
• Incipient order in the t-J model at high temperatures
• The breakdown of the Nagaoka phase in the 2D t-J model
• Finite Temperature Strong Coupling Expansions for the SU(N) Hubbard Model

Cited by in corpus (3)

• Many-body Physics of Ultracold Alkaline-Earth atoms with SU($N$)-symmetric interactions
• Itinerant ferromagnetism in an SU(3) Fermi-Hubbard model at finite temperatures: A dynamical mean-field theory study
• Generalized Nagaoka ferromagnetism accompanied by flavor-selective Mott states in an SU($N$) Fermi-Hubbard model