Related papers: Complexity of the XY antiferromagnet at fixed magn…
The solution of complex many-body lattice models can often be found by defining an energy functional of the relevant density of the problem. For instance, in the case of the Hubbard model the spin-resolved site occupation is enough to…
We conjecture exact and simple formulas for physical quantities in two quantum chains. A classic result of this type is Onsager, Kaufman and Yang's formula for the spontaneous magnetization in the Ising model, subsequently generalized to…
By applying tight binding model of adatoms in graphene, we study theoretically the localized aspects of the interaction between transition metal atoms and graphene. Considering the electron-electron interaction by adding a Hubbard term in…
We solve analytically the $N\times N$ square lattice Hubbard model for even $N$ at half filling and weak coupling by a new approach. The exact ground state wave function provides an intriguing and appealing picture of the antiferromagnetic…
In the present work ferromagnetic ordering in the Hubbard model generalized by taking into account the inter-atomic exchange interaction and correlated hopping in partially filled narrow band is considered. In the case of weak…
We consider the standard repulsive Hubbard model with a flat lowest-energy band for two one-dimensional lattices (diamond chain and ladder) as well as for a two-dimensional lattice (bilayer) at half filling of the flat band. The considered…
We consider the numerical approximation of a continuum model of antiferromagnetic and ferrimagnetic materials. The state of the material is described in terms of two unit-length vector fields, which can be interpreted as the magnetizations…
We construct a multi-band Hubbard model on the lattice obtained by "decorating" a closely packed $d$-dimensional lattice $\mathcal{M}$ (such as the triangular lattice) where $d\ge2$. We take the limits in which the Coulomb interaction and…
We construct exact ground states of interacting electrons on triangle and diamond Hubbard chains. The construction requires (i) a rewriting of the Hamiltonian into positive semidefinite form, (ii) the construction of a many-electron ground…
We discuss how approximate theories for Bose-Fermi mixtures recover in the molecular limit the expected expression for Fermi-Fermi mixtures of molecules and unpaired fermions. In particular, we compare the energy of the system resulting…
For a quantum mechanical system with broken supersymmetry, we present a simple method of determining the ground state when the corresponding energy eigenvalue is sufficiently small. A concise formula is derived for the approximate ground…
We consider a microscopic model for a doped quantum ferromagnet as a test case for the systematic low-energy effective field theory for magnons and holes, which is constructed in complete analogy to the case of quantum antiferromagnets. In…
We establish the Hatsugai-Kohmoto model as a stable quartic fixed point (distinct from Wilson-Fisher) by computing the $\beta-$function in the presence of perturbing local interactions. In vicinity of the half-filled doped Mott state, the…
We consider the ground state energy of the Bose--Hubbard model on a graph with large and homogeneous coordination number. In the limit of infinite coordination number, we prove convergence of the ground state energy to the minimizer of a…
The ferromagnetic XY model on sparse random graphs in a randomly oriented field is analyzed via the belief propagation algorithm. At variance with the fully connected case and with the random field Ising model on the same topology, we find…
We present a simple method for the construction of exact ground states of generalized Hubbard models in arbitrary dimensions. This method is used to derive rigorous criteria for the stability of various ground state types, like the…
In this paper, we write exactly solvable generalizations of 1-dimensional quantum XY and Ising-like models by using $2^d$-dimensional Gamma ($\Gamma$) matrices as the degrees of freedom on each site. We show that these models result in…
Despite progress in quantum Hamiltonian complexity, little is known about the computational complexity of quantum physics at the thermodynamic limit. Even defining the problem is not straight forward. We study the complexity of estimating…
We study the fixed-magnetization ferromagnetic Ising model on random $d$-regular graphs for $d\ge 3$ and inverse temperature below the tree reconstruction threshold. Our main result is that for each magnetization $\eta$, the free energy…
We investigate the magnetic properties of a repulsive fermionic SU($3$) Hubbard model on the Lieb lattice from weak to strong interaction by means of the mean-field approximation. To validate the method we employed, we first discuss the…