Auxiliary field approach to dilute Bose gases with tunable interactions

Abstract

We rewrite the Lagrangian for a dilute Bose gas in terms of auxiliary fields related to the normal and anomalous condensate densities. We derive the loop expansion of the effective action in the composite-field propagators. The lowest-order auxiliary field (LOAF) theory is a conserving mean-field approximation consistent with the Goldstone theorem without some of the difficulties plaguing approximations such as the Hartree and Popov approximations. LOAF predicts a second-order phase transition. We give a set of Feynman rules for improving results to any order in the loop expansion in terms of composite-field propagators. We compare results of the LOAF approximation with those derived using the Popov approximation. LOAF allows us to explore the critical regime for all values of the coupling constant and we determine various parameters in the unitarity limit.

16 pages, 7 figures

References in corpus (10)

• Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates
• Atomic three-body loss as a dynamical three-body interaction
• Tomographic RF Spectroscopy of a Trapped Fermi Gas at Unitarity
• Quantum versus classical statistical dynamics of an ultracold Bose gas
• Particle-hole fluctuations in the BCS-BEC Crossover
• Functional renormalization for Bose-Einstein Condensation
• Non-perturbative predictions for cold atom Bose gases with tunable interactions
• Four-point vertex in the Hubbard model and partial bosonization
• Non-equilibrium dynamics of a Bose-Einstein condensate in an optical lattice
• Bose-Einstein Condensate Driven by a Kicked Rotor in a Finite Box

Cited by in corpus (19)

• Bose - Einstein condensation of triplons with a weakly broken U(1) symmetry
• Large-N approximation for single- and two-component dilute Bose gases
• Analytical limits for cold atom Bose gases with tunable interactions
• Composite-Field Goldstone States and Higgs Mechanism in Dilute Bose Gases
• Mean-field description of pairing effects, BKT physics, and superfluidity in 2D Bose gases
• Dissipative phase transition in systems with two-photon drive and nonlinear dissipation near the critical point
• The Josephson relation for the superfluid density and the connection to the Goldstone theorem in dilute Bose atomic gasses
• Quench Dynamics and Emergence of Phase Separation in Two-Component Atomic Bose Gases at Zero Temperature and above the BEC Critical Temperature
• Effects of exchange and weak Dzyaloshinsky-Moriya anisotropies on thermodynamic characteristics of spin-gapped magnets
• Phase Transitions in Three-Dimensional Bosonic Systems in Optical Lattices
• Addressing energy density functionals in the language of path-integrals I: Comparative study of diagrammatic techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• Equation of state and contact of a strongly interacting Bose gas in the normal state
• Thermodynamics and structural transition of binary atomic Bose-Fermi mixtures in box or harmonic potentials: A path-integral study
• Leading-Order Auxiliary Field Theory of the Bose-Hubbard Model
• Density and Spin Linear Response of Atomic Fermi Superfluids with Population Imbalance in BCS-BEC Crossover
• Large-$N$ properties of a non-ideal Bose gas
• Addressing energy density functionals in the language of path-integrals II: Comparative study of functional renormalization group techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• Defining a critical temperature of a crossover from BEC to the normal phase in anisotropic quantum magnets
• Critical temperature of trapped interacting bosons from large-N based theories