Renormalization theory of a two dimensional Bose gas: quantum critical point and quasi-condensed state

Abstract

We present a renormalization group construction of a weakly interacting Bose gas at zero temperature in the two-dimensional continuum, both in the quantum critical regime and in the presence of a condensate fraction. The construction is performed within a rigorous renormalization group scheme, borrowed from the methods of constructive field theory, which allows us to derive explicit bounds on all the orders of renormalized perturbation theory. Our scheme allows us to construct the theory of the quantum critical point completely, both in the ultraviolet and in the infrared regimes, thus extending previous heuristic approaches to this phase. For the condensate phase, we solve completely the ultraviolet problem and we investigate in detail the infrared region, up to length scales of the order $({\lambda }^3{\rho }_0{)}^{-1/2}$ (here $\lambda$ is the interaction strength and ${\rho }_0$ the condensate density), which is the largest length scale at which the problem is perturbative in nature. We exhibit violations to the formal Ward Identities, due to the momentum cutoff used to regularize the theory, which suggest that previous proposals about the existence of a non-perturbative non-trivial fixed point for the infrared flow should be reconsidered.

arXiv comment88 pages, 25 figures; some references added, some typos corrected

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Cited by in corpus (6)

• Asymptotic expansion of low-energy excitations for weakly interacting bosons
• Longitudinal fluctuations in the Berezinskii-Kosterlitz-Thouless phase
• The excitation spectrum of two dimensional Bose gases in the Gross-Pitaevskii regime
• Bose particles in a box I. A convergent expansion of the ground state of a three-modes Bogoliubov Hamiltonian
• Complex Bosonic Many-body Models: Overview of the Small Field Parabolic Flow
• The Condensation of Ideal Dunkl-Bose Gas in Power-Law Traps