A quantum phase model is introduced as a limit for very strong interactions of a strongly correlated q-boson hopping model. The exact solution of the phase model is reviewed, and solutions are also provided for two correlation functions of the model. Explicit expressions, including both amplitude and scaling exponent, are derived for these correlation functions in the low temperature limit. The amplitudes were found to be related to the number of plane partitions contained in boxes of finite size.A quantum phase model is introduced as a limit for very strong interactions of a strongly correlated q-boson hopping model. The exact solution of the phase model is reviewed, and solutions are also provided for two correlation functions of the model. Explicit expressions, including both amplitude and scaling exponent, are derived for these correlation functions in the low temperature limit. The amplitudes were found to be related to the number of plane partitions contained in boxes of finite size.

Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering SciencesFeb 14, 201115 citations

Structure functions in an interacting Boson system

Vox Kalai Wong, Harvey Gould

Physics Letters AMay 1, 19724 citations

Critical Behavior for Correlated Strongly Coupled Boson Systems in 1 + 1 Dimensions

N. M. Bogoliubov, R. Bullough, JUSSI TIMONEN

The natural integrable correlated strongly coupled boson system in 1 + 1 dimensions is the $q$ -boson hopping model; we calculate its critical exponent $\ensuremath{\theta}$ and determine its correlation functions. For small couplings the $q$ -boson model has natural connections with the Bose gas and the $\mathrm{XY}$ models of very large spin for which $\ensuremath{\theta}'\mathrm{s}$ and correlators are reported. For large couplings the hopping model is a new phase of interacting bosons substantially different from the impenetrable Bose gas.The natural integrable correlated strongly coupled boson system in 1 + 1 dimensions is the $q$-boson hopping model; we calculate its critical exponent $\ensuremath{\theta}$ and determine its correlation functions. For small couplings the $q$-boson model has natural connections with the Bose gas and the $\mathrm{XY}$ models of very large spin for which $\ensuremath{\theta}'\mathrm{s}$ and correlators are reported. For large couplings the hopping model is a new phase of interacting bosons substantially different from the impenetrable Bose gas.

Physical Review LettersJun 20, 199446 citations

Density-Functional Theory for Strongly Correlated Bosonic and Fermionic Ultracold Dipolar and Ionic Gases

Francesc Malet, André Mirtschink, Christian B. Mendl +4 more

We introduce a density functional formalism to study the ground-state properties of strongly correlated dipolar and ionic ultracold bosonic and fermionic gases, based on the self-consistent combination of the weak and the strong coupling limits. Contrary to conventional density functional approaches, our formalism does not require a previous calculation of the interacting homogeneous gas, and it is thus very suitable to treat systems with tunable long-range interactions. Because of its asymptotic exactness in the regime of strong correlation, the formalism works for systems in which standard mean-field theories fail.We introduce a density functional formalism to study the ground-state properties of strongly correlated dipolar and ionic ultracold bosonic and fermionic gases, based on the self-consistent combination of the weak and the strong coupling limits. Contrary to conventional density functional approaches, our formalism does not require a previous calculation of the interacting homogeneous gas, and it is thus very suitable to treat systems with tunable long-range interactions. Because of its asymptotic exactness in the regime of strong correlation, the formalism works for systems in which standard mean-field theories fail.

arXiv:1502.01469Physical Review LettersJul 14, 201518 citations

Two-body correlations in two-dimensional boson systems

Han Guangze

AIP conference proceedingsJan 1, 20050 citations

The natural integrable correlated strongly coupled boson system in 1 + 1 dimensions is the

q

-boson hopping model; we calculate its critical exponent $\ensuremath{\theta}$ and determine its correlation functions. For small couplings the

q

-boson model has natural connections with the Bose gas and the

\mathrm{XY}

models of very large spin for which $\ensuremath{\theta}'\mathrm{s}$ and correlators are reported. For large couplings the hopping model is a new phase of interacting bosons substantially different from the impenetrable Bose gas.