We have recently shown (]) that the one-dimensional ( ld) Hubbard model possesses an infinite number of conservation laws by identifying a 2d classical statistical model for which a one-parameter family of transfer matrices commutes with the Hamiltonian. Reference2 contains a demonstrat ion that the one-parameter family of transfer matrices commute mutually and hence we have a new completely in...

A new lattice model of interacting electrons is presented. It can be viewed as a classical Hubbard model in which the energy associated to electron itinerance is proportional to the total number of possible electron jumps. Symmetry properties of the Hubbard model are preserved. In the half-filled band with strong interaction the model becomes the Ising model. The main features of the magnetic b...

An exact boson mapping of the reduced BCS (equal strength) pairing Hamiltonian is considered. In the mapping, fermion pair operators are mapped exactly to the corresponding bosons. The image of the mapping results in a Bose-Hubbard model with level dependent hopping. Though the resultant Bose-Hubbard Hamiltonian is non-Hermitian, all eigenvalues are real when Uk/t < 1, where k is the total numb...

Bose Hubbard model is presented and basic natures of Mott insulating phase and superfluid phase are studied in this essay. Also how and when this quantum phase transition occurs is discussed. Experimental supports from ultracold atoms physics are explained, while some miscellaneous topics are touched in the end.

Recently a new type of algorithms for numerical simulations of models with dynamical fermions has been proposed by M. Lüscher [1]. The idea is based on the approximation of a fermionic determinant by the path integral over some number of bosonic fields, which allows ones to elegantly avoid the main difficulty coming from the nonlocality of the fermionic determinant. The complexity of a sweep of...

We demonstrate that polaritons in an array of interacting microcavities with strong atom–photon coupling can form a two-component Bose–Hubbard model in which both polariton species are protected against spontaneous emission as their atomic part is stored in two ground states of the atoms. The parameters of the effective model can be tuned via the driving strength of external lasers and include ...

We consider a theoretical model of a four-mode Bose-Hubbard model consisting of two pairs of wells coupled via two processes with two different rates. The model is naturally divided into two subsystems with strong intrasystem coupling and much weaker coupling between the two subsystems and has previously been introduced as a model for Josephson heat oscillations by Strzys and Anglin [Phys. Rev....

J. K. Freericks, H. R. Krishnamurthy, Yasuyuki Kato, Naoki Kawashima, and Nandini Trivedi Department of Physics, Georgetown University, 37th and O Streets NW, Washington, D.C. 20057, USA Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India Condensed Matter Theory Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore ...

J. K. Freericks,1,* V. Turkowski,2,† H. R. Krishnamurthy,3,4,‡ and M. Knap5 1Department of Physics, Georgetown University, Washington, D.C. 20057, USA 2Physics Department and Nanoscience Technology Center, University of Central Florida, Orlando, Florida 32816, USA 3Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India 4Condensed Matter T...