Related papers: Thermal stability of the Nagaoka-Thouless theorems
Nagaoka's theorem on ferromagnetism in the Hubbard model is extended to the Holstein-Hubbard model. This shows that Nagaoka's ferromagnetism is stable even if the electron-phonon interaction is taken into account. We also prove that…
The Aizenman--Lieb theorem for the $\mathrm{SU}(2)$ Hubbard model expands upon the Nagaoka--Thouless theorem for the ground state to encompass finite temperatures. It can be succinctly stated that the magnetization $m(\beta, b)$ of the…
We construct a model-independent framework describing stabilities of ferromagnetism in strongly correlated electron systems; Our description relies on the operator theoretic correlation inequalities. Within the new framework, we reinterpret…
Nagaoka's theorem on ferromagnetism in the Hubbard model with one electron less than half filling is generalized to the case where all possible nearest-neighbor Coulomb interactions (the density-density interaction $V$, bond-charge…
We prove that Nagaoka's theorem, that the large-$U$ Hubbard model with exactly one hole is ferromagnetic, holds for any balanced Hamiltonian. Simply put, if a positive bond encodes friendship and a negative bond encodes enmity, then balance…
We apply a result from graph theory to prove exact results about itinerant ferromagnetism. Nagaoka's theorem of ferromagnetism is extended to all non-separable graphs except single polygons with more than four vertices by applying the…
We prove Hohenberg-Kohn theorems for several models of quantum mechanics. First, we show that the pair correlation function of any ground state contains the information of the interactions and of the external potentials. Then, in the…
The Hofstadter-Hubbard model captures the physics of strongly correlated electrons in an applied magnetic field, which is relevant to many recent experiments on Moir\'e materials. Few large-scale, numerically exact simulations exists for…
While the exact phase diagram of the Fermi-Hubbard model remains poorly understood despite decades of progress, nearly 60 years ago, Nagaoka proved that a single dopant in an otherwise half-filled Hubbard system can bring about…
We revisit Nagaoka ferromagnetism in the U=oo Hubbard model within the dynamical mean-field theory (DMFT) using the recently developed continuous time quantum Monte Carlo method as the impurity solver. The stability of Nagaoka…
We present the first rigorous examples of non-singular Hubbard models which exhibit ferromagnetism at zero temperature. The models are defined in arbitrary dimensions, and are characterized by finite-ranged hoppings, dispersive bands, and…
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 $0\leq \rho \leq 1$ and all $N$. We express the…
The Kondo lattice model (KLM) is a typical model describing heavy fermion systems. In this paper, we consider the interaction of phonons with the system described by the one-electron KLM. Magnetic properties of the ground state of this…
The angular momentum vector of a Heisenberg ferromagnet with isotropic exchange interaction is conserved, while under uniaxial crystalline anisotropy the projection of the total spin along the easy axis is a constant of motion. Using…
It is well known that the Hubbard model on a line graph has a flat band and ferromagnetic ground states in a certain density range. We show that for a Hubbard model on a line graph of a planar bipartite graph the ferromagnetic ground state…
We investigate an SU(3) Fermi-Hubbard model on a hypercubic lattice at finite temperatures, combining dynamical mean-field theory with continuous-time quantum Monte Carlo simulations. Taking strong correlations into account carefully, we…
We study finite-temperature properties of a Hubbard model including sites of a particle bath which was proposed as a microscopic model to show itinerant ferromagnetism at finite electron density. We use direct numerical methods, such as…
The microscopic basis for the stability of itinerant ferromagnetism in correlated electron systems is examined. To this end several routes to ferromagnetism are explored, using both rigorous methods valid in arbitrary spatial dimensions, as…
The Hubbard model is a "highly oversimplified model" for electrons in a solid which interact with each other through extremely short ranged repulsive (Coulomb) interaction. The Hamiltonian of the Hubbard model consists of two pieces; H_hop…
We study the effect of inhomogeneities in the magnetic field on the thermal entanglement of a two spin system. We show that in the ferromagnetic case a very small inhomogeneity is capable to produce large values of thermal entanglement.…