Related papers: Lieb's Theorem for Bose Hubbard Models
We present rigorous and universal results for the ground states of the $f=2$ spinor Bose-Hubbard model. The model includes three two-body on site interaction terms, two of which are spin dependent while the other one is spin independent. We…
We prove basic theorems about the ground states of the S=1 Bose-Hubbard model. The results are quite universal and depend only on the coefficient U_2 of the spin-dependent interaction. We show that the ground state exhibits saturated…
In 1989, Lieb proved two theorems about the Hubbard model. One showed that the ground state of the attractive model was a spin singlet state ($S=0$), was unique, and was positive definite. The other showed that the ground state of the…
We study the ground state of the attractive one-dimensional Bose-Hubbard model, and in particular the nature of the crossover between the weak interaction and strong interaction regimes for finite system sizes. Indicator properties like the…
The Bose-Hubbard model is well-defined description of a Bose solid which may be realistic for cold atoms in a periodic optical lattice. We show that contrary to accepted theories it can never have as a ground state a perfect Mott insulator…
We prove that the Hamiltonian of the model describing a spin which is linearly coupled to a field of relativistic and massless bosons, also known as the spin-boson model, admits a ground state for small values of the coupling constant…
For a large class of finite-range quantum spin models with half-integer spins, we prove that uniqueness of the ground state implies the existence of a low-lying excited state. For systems of linear size L, of arbitrary finite dimension, we…
The many-body ground state of a very general class of electron-phonon Hamiltonians is proven to contain a spin singlet (for an even number of electrons on a finite lattice). The phonons interact with the electronic system in two different…
In 1989, Elliott Lieb published a Physical Review Letter proving two theorems about the Hubbard model. This paper used the concept of spin-reflection positivity to prove that the ground state of the attractive Hubbard model was always a…
We consider the Bose-Hubbard model describing attractive bosonic particles hopping across the sites of a translation-invariant lattice, and compare the relevant ground-state properties with those of the corresponding symmetry-breaking…
We rigorously prove that an extended Hubbard model with attraction in two dimensions has an unconventional pairing ground state for any electron filling. The anisotropic spin-0 or anisotropic spin-1 pairing symmetry is realized, depending…
The study of interaction between the particle and lattice degrees of freedom is one of the central interests in the quantum many-body systems. The Z2 Bose-Hubbard model has been proposed to describe ultracold bosons in a dynamical optical…
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…
We review recent results on the existence of ground states for the infrared-critical spin boson model, which describes the interaction of a massless bosonic field with a two-state quantum system. Explicitly, we derive a critical coupling…
We construct a basis for the many-particle ground states of the positive hopping Bose-Hubbard model on line graphs of finite 2-connected planar bipartite graphs at sufficiently low filling factors. The particles in these states are…
In this work, the ground states of the Hubbard model on complete graph are studied, for a finite lattice size $L$ and arbitrary on-site energy $U$. We construct explicitly the ground states of the system when the number of the electrons…
We numerically investigate low-energy stationary states of pseudospin-1 Bose-Einstein condensates in the presence of Rashba-Dresselhaus-type spin-orbit coupling. We show that for experimentally feasible parameters and strong spin-orbit…
We show that the exact ground state of the Lieb-Mattis Hamiltonian is an equal-weight superposition of all possible classical N\'{e}el states, and provide an exact formulation of this superposition in the $z$-spin basis for both $S=1/2$ and…
The physics of strongly correlated quantum particles within a flat band was originally explored as a route to itinerant ferromagnetism and, indeed, a celebrated theorem by Lieb rigorously establishes that the ground state of the repulsive…
We show the existence of ground states in the massless spin boson model without any infrared regularization. Our proof is non-perturbative and relies on a compactness argument. It works for arbitrary values of the coupling constant under…