Solving the Bose-Hubbard model in new ways

Abstract

We introduce a new method for analysing the Bose-Hubbard model for an array of bosons with nearest neighbor interactions. It is based on a number-theoretic implementation of the creation and annihilation operators that constitute the model. One of the advantages of this approach is that it facilitates computation with arbitrary accuracy, enabling nearly perfect numerical experimentation. In particular, we provide a rigorous computer assisted proof of quantum phase transitions in finite systems of this type. Furthermore, we investigate properties of the infinite array via harmonic analysis on the multiplicative group of positive rationals. This furnishes an isomorphism that recasts the underlying Fock space as an infinite tensor product of Hecke spaces, i.e., spaces of square-integrable periodic functions that are a superposition of non-negative frequency harmonics. Under this isomorphism, the number-theoretic creation and annihilation operators are mapped into the Kastrup model of the harmonic oscillator on the circle. It also enables us to highlight a kinship of the model at hand with an array of spin moments with a local anisotropy field. This identifies an interesting physical system that can be mapped into the model at hand.

arXiv comment12 pages, 3 figures; submitted; accepted in Quantum

References in corpus (16)

• Quantum Superposition States of Bose-Einstein Condensates
• The one-dimensional Bose-Hubbard Model with nearest-neighbor interaction
• Phases of the one-dimensional Bose-Hubbard model
• Phase diagram of spin-1 bosons on one-dimensional lattices
• Yang-Baxter integrable models in experiments: from condensed matter to ultracold atoms
• Ground-state properties of the attractive one-dimensional Bose-Hubbard model
• Quantum dynamics of a model for two Josephson-coupled Bose--Einstein condensates
• Dynamical Mean Field Theory for the Bose-Hubbard Model
• Quantization of the Optical Phase Space S^2 = {phi mod 2pi, I > 0} in Terms of the Group SO(1,2)
• Quantum Critical Behavior of Two Coupled Bose-Einstein Condensates
• The two-site Bose--Hubbard model
• Bose-Hubbard model with attractive interactions
• Quantum signatures of self-trapping transition in attractive lattice bosons
• Nonlinear Phenomenology from Quantum Mechanics: Soliton in a Lattice
• Quantum phases of a one-dimensional Majorana-Bose-Hubbard model
• Superfluid weight and polarization amplitude in the one-dimensional bosonic Hubbard model