Bose-Einstein condensation temperature of a homogenous weakly interacting Bose gas in variational perturbation theory through seven loops

We study a three-dimensional Bose-Einstein condensate in an isotropic harmonic trapping potential with an additional delta-correlated disorder potential at both zero and finite temperature and investigate the emergence of a Bose-glass phase for increasing disorder strength. To this end, we revisit a quite recent non-perturbative approach towards the dirty boson problem, which relies on the Hartree-Fock mean-field theory and is worked out on the basis of the replica method, and extend it from the homogeneous case to a harmonic confinement. At first, we solve the zero-temperature selfconsistency equations for the respective density contributions, which are obtained via the HartreeFock theory within the Thomas-Fermi approximation. Additionally we use a variational ansatz, whose results turn out to coincide qualitatively with those obtained from the Thomas-Fermi approximation. In particular, a first-order quantum phase transition from the superfluid phase to the Bose-glass phase is detected at a critical disorder strength, which agrees with findings in the literature. Afterwards, we consider the three-dimensional dirty boson problem at finite temperature. This allows us to study the impact of both temperature and disorder fluctuations on the respective components of the density as well as their Thomas-Fermi radii. In particular, we find that a superfluid region, a Bose-glass region, and a thermal region coexist for smaller disorder strengths. Furthermore, depending on the respective system parameters, three phase transitions are detected, namely, one from the superfluid to the Bose-glass phase, another one from the Bose-glass to the thermal phase, and finally one from the superfluid to the thermal phase.

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“…[61,62], and has been confirmed by extensive MC simulations [63]. For the weakly interacting Bose gas in Fig.…”

Section: A Homogeneous Casementioning

confidence: 59%

Dirty bosons in a three-dimensional harmonic trap

Khellil

Pelster

2017

J. Stat. Mech.

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“…This shift has two contributions: The finite size of the system reduces the critical temperature [27], but it is also modified by the interactions. This second contribution as been extensively discussed in the literature, see the recent publication [28] and references therein. For the exponent we find β ≈ 1.70, which is 15% smaller than for the ideal trapped gas.…”

Section: Ground State Populationmentioning

confidence: 99%

Coherence properties of the two-dimensional Bose-Einstein condensate

Gies

Hutchinson

2004

Phys. Rev. A

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We present a detailed finite-temperature Hartree-Fock-Bogoliubov (HFB) treatment of the twodimensional trapped Bose gas. We highlight the numerical methods required to obtain solutions to the HFB equations within the Popov approximation, the derivation of which we outline. This method has previously been applied successfully to the three-dimensional case and we focus on the unique features of the system which are due to its reduced dimensionality. These can be found in the spectrum of low-lying excitations and in the coherence properties. We calculate the Bragg response and the coherence length within the condensate in analogy with experiments performed in the quasione-dimensional regime [Richard et al., Phys. Rev. Lett. 91, 010405 (2003)] and compare to results calculated for the one-dimensional case. We then make predictions for the experimental observation of the quasicondensate phase via Bragg spectroscopy in the quasi-two-dimensional regime.

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“…In practice, these exponents are calculated by taking the t-derivative of Eqs. (41,42). The procedure is then repeated for a set of initial conditions that bring the system closer and closer to the critical point.…”

Section: A Numerical Extraction Of Critical Exponentsmentioning

confidence: 99%

Nonperturbative renormalization group preserving full-momentum dependence: Implementation and quantitative evaluation

Benitez

Blaizot²,

Chaté³

et al. 2012

Phys. Rev. E

105

128

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We present in detail the implementation of the Blaizot-Méndez-Wschebor (BMW) approximation scheme of the nonperturbative renormalization group, which allows for the computation of the full momentum dependence of correlation functions. We discuss its signification and its relation with other schemes, in particular the derivative expansion. Quantitative results are presented for the testground of scalar O(N ) theories. Besides critical exponents which are zero-momentum quantities, we compute in three dimensions in the whole momentum range the two-point function at criticality and, in the high temperature phase, the universal structure factor. In all cases, we find very good agreement with the best existing results.

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Bose-Einstein condensation temperature of a homogenous weakly interacting Bose gas in variational perturbation theory through seven loops

Cited by 91 publications

References 54 publications

Dirty bosons in a three-dimensional harmonic trap

Dirty bosons in a three-dimensional harmonic trap

Coherence properties of the two-dimensional Bose-Einstein condensate

Nonperturbative renormalization group preserving full-momentum dependence: Implementation and quantitative evaluation

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