Classical Limit of the Interacting-Boson Model

Jin-Quan Chen, Pieter Van Isacker

Martin R. Zirnbauer, D.M. Brink

N. Dupuis

In systems with a spontaneously broken continuous symmetry, the perturbative loop expansion is plagued by infrared divergences due to the coupling between transverse and longitudinal fluctuations. As a result, the longitudinal susceptibility diverges and the self-energy becomes singular at low energy. We study the crossover from the high-energy Gaussian regime, where perturbation theory remains valid, to the low-energy Goldstone regime characterized by a diverging longitudinal susceptibility. We consider both the classical linear O (N) model and interacting bosons at zero temperature, using a variety of techniques: perturbation theory, hydrodynamic approach (i.e., for bosons, Popov's theory), large-N limit, and nonperturbative renormalization group. We emphasize the essential role of the Ginzburg momentum scale p{G}, below which the perturbative approach breaks down. Even though the action of (nonrelativistic) bosons includes a first-order time derivative term, we find remarkable similarities in the weak-coupling limit between the classical O(N) model and interacting bosons at zero temperature.

Zhaoyu Han, Steven Allan Kivelson

We define an infinite class of ``frustration-free'' interacting lattice quantum Hamiltonians for bosons, constructed such that their exact ground states have a density distribution specified by the Boltzmann weight of a corresponding classical lattice gas problem. By appropriately choosing the classical weights, we obtain boson representations of various known solvable models, including quantum dimer and vertex models, toric code, and certain Levin-Wen string-net models. We also systematically construct solvable models with other interesting ground states, including quantum spin liquids, supersolids, ``Bose-Einstein insulators,'' Bose liquids with ``Bose surfaces,'' and Bose-Einstein condensates that permit adiabatic evolution from a noninteracting limit to a Gutzwiller-projected limit.

Luigi Accardi, Yun Gang Lu

N. M. Bogoliubov, R. Bullough, G. D. Pang

Quantum-group deformation of ordinary bosons yields the q bosons or nonlinear phonons. We solve exactly, for any real q>1, including q=\ensuremath{\infty}, a one-dimensional q-boson lattice ``hopping model,'' and calculate asymptotically its correlation functions. The model is a nonlinear model of strongly interacting ordinary bosons. Our solution solves the equivalent quantum difference differential nonlinear Schr\"odinger model. Approximation reduces this to a nonintegrable boson Hubbard-type model with q bosons as fundamental particles. One special limit q\ensuremath{\rightarrow}\ensuremath{\infty} of the hopping model is the classical $XY--- chain.