The Beliaev technique for a weakly interacting Bose gas

Abstract

Abstract. Aiming at simplicity of explicit equations and, at the same time, controllable accuracy of the theory, we present our results for all the thermodynamic quantities and correlation functions for a weakly interacting Bose gas at short-to-intermediate distances obtained within an improved version of Beliaev's diagrammatic technique. With a controllably small (but essentially finite) Bogoliubov's symmetry-breaking term, Beliaev's diagrammatic technique becomes regular in the infrared limit. Up to higher-order terms (for which we present parametric order-of-magnitude estimates), the partition function and entropy of the system formally correspond to those of a non-interacting bosonic (pseudo-)Hamiltonian with a temperature-dependent Bogoliubov-type dispersion relation. Away from the fluctuation region, this approach provides the most accurate-in fact, the best possible within the Bogoliubov-type pseudoHamiltonian framework-description of the system with controlled accuracy. It produces accurate answers for the off-diagonal correlation functions up to distances where the behavior of correlators is controlled by generic hydrodynamic relations and, thus, can be accurately extrapolated to arbitrarily large scales. In the fluctuation region, the non-perturbative contributions are given by universal 7

Numerical calculation of spectral functions of the Bose-Hubbard model using bosonic dynamical mean-field theory

“…For these parameters the average occupation per site is n = 0.4968 ± 0.0005 and the average number of condensed bosons per site is b 2 = 0.4542 ± 0.0004. Since U n ≈ 0.1242 is small in comparison to the bandwidth 2zt = 6, the weak-coupling Bogoliubov approximation [42][43][44] can be expected to be applicable. The momentum resolved spectral function A(k,ω) obtained within the B-DMFT is presented in Fig.…”

Recent developments in quantum Monte Carlo simulations with applications for cold gases

“…It was also used in Ref. [43] to compare the properties of the dilute gas in 1D, 2D and 3D against an improved Beliaev diagrammatic technique. The worm algorithm also allowed for a more precise determination of the critical temperature of the 3D dilute Bose gas [245].…”

Green's-function formalism for a condensed Bose gas consistent with infrared-divergent longitudinal susceptibility and Nepomnyashchii-Nepomnyashchii identity

“…In this region, strong fluctuations dominate over the phase transition behavior [26,38,[40][41][42][43].…”

“…To obtain correct infrared behaviors in this approach, the WardTakahashi identities associated with the gauge symmetry play an important role. The infrared divergences are also removed by an artificial field that breaks U(1) gauge symmetry [26]. In this approach, one takes the limit of vanishing symmetry breaking terms after calculating physical quantities, and long-range correlations are corrected by incorporating the Popov's hydrodynamic theory.…”