Quantum criticality of the imperfect Bose gas inddimensions

Abstract

Abstract. We study the low-temperature limit of the d-dimensional imperfect Bose gas. Relying on an exact analysis of the microscopic model, we establish the existence of a second-order quantum phase transition to a phase involving the Bose-Einstein condensate. The transition is triggered by varying the chemical potential and persists at non-zero temperatures T for d > 2. We extract the exact phase diagram and identify the scaling regimes in the vicinity of the quantum critical point focusing on the behavior of the correlation length ξ. The length ξ develops an essential singularity exclusively for d = 2. We follow the evolution of the phase diagram varying d. For d > 2 our results agree with renormalization-group based analysis of the effective bosonic order-parameter models with the dynamical exponent z = 2.

Functional renormalization group in a finite volume

“…Eq. (58) entails that for large cutoff scales k T → ∞ the flow decays exponentially with exp(−k T ) in line with (30). This is expected as the cutoff used in (58) does not affect the frequency sum, and reflects the fast decay of thermal fluctuations in the presence of large mass scales.…”

“…The function A(y) is a rational function of the argument y = m gap T , and the exponential suppression with exp(−m gap T ) can be readily computed from one loop thermal perturbation theory. Evidently, similar expressions hold for the finite volume correlations, with the identification T → 1 L i in (30). For potentially vanishing correlation functions the denominator of (30) should be substituted with…”

“…The difference of free energies densities f k at finite and infinite volume relates to the Casimir force, for a FRG computation see Ref. [30]. The flow of the pressure is then given by the one of the free energy density and its volume or, equivalently, length derivative,…”

Phase diagram and correlation functions of the anisotropic imperfect Bose gas in d dimensions

“…As a result, the IBG is naturally equipped with two parameters (T and µ) to tune the transition and is well defined for T → 0. In consequence, its phase diagram realises the standard scenario of quantum criticality for T small [23,39]. This is not quite the case for the Berlin-Kac model, where a realisation of quantum criticality requires defining its quantum extension, which in practice usually amounts to adding an extra kinetic term to the Hamiltonian.…”

Non-classical critical exponents at Bose–Einstein condensation

“…However, as we show here, ideal BEC, accepted as a bona-fide second order phase transition, has been considered in a wrong universality class. That is, instead of belonging to the Spherical Model (SM) universality class, [8][9][10][11][12][13][14][15][16][17] BEC has its own universality class, a non mean-field one, with a set of non-classical exponents. The assessment of ideal BEC belonging to SM universality class resides in the work by Gunton and Buckingham (GB) [9], in which it is first assumed that the order parameter is the condensate particle wavefunction, and then, the transition is considered within a mean-field approximation.…”