Scaling of free energy and correlation functions for a Bose system

Singh, K. K.

doi:10.1103/physrevb.13.3192

Cited by 24 publications

(10 citation statements)

References 3 publications

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“…[9,10,11,12]. In D = 3, although the results of the expansion up to second order in ε are in remarkable agreement with experimental values of critical exponents (measured in He 4 experiments, but due to universality applicable in the case of Bose gases as well [13]), higher-order results diverge from the experimental values. The reason is that the ε-expansion is asymptotic, as first noted in [14], and to obtain meaningful results when higher orders in ε are included, one has to make use of resummation techniques, see e.g.…”

Section: Introductionsupporting

confidence: 62%

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The expansion in the symmetry-broken phase of an interacting Bose gas at finite temperature

Metikas

Zobay

Alber

2003

J. Phys. B: At. Mol. Opt. Phys.

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We discuss the application of the momentum-shell renormalization group method to the interacting homogeneous Bose gas in the symmetric and in the symmetry-broken phases. It is demonstrated that recently discussed discrepancies are artifacts of not taking proper care of infrared divergencies appearing at finite temperature. If these divergencies are taken into account and treated properly by means of the ε-expansion, the resulting renormalization group equations and the corresponding universal properties are identical in the symmetric and the symmetrybroken phases.The ε-expansion in the symmetry-broken phase of an interacting Bose gas 2 are sensitive to the way the resummation is performed and consequently somewhat ambiguous, see e.g. [26].An alternative method is to calculate the universal properties perturbatively as series of powers of g * (g * being the infrared stable fixed point for the interaction g) directly in D = 3, as first suggested in [27]. These series are then truncated to order g * L where L is the number of loops in which the calculation is performed. Though this method is fundamentally less satisfactory than the ε-expansion, see e.g. [15], it can be used in the regime of small but non-zero chemical potential. It has been employed for the calculation of critical exponents up to seventh order in g * for N = 0, 1, 2, 3 [28,29,26] and for arbitrary N [30, 31] where N is the number of components of the vector field. The series in g * are again asymptotic and have to be resummed. There is in general agreement with the corresponding ε-expansion results. We will be referring to this technique as the direct method.After the experimental realization of BEC in ultracold atomic gases [32,33,34], because of the renewed interest in these systems, a new generation of papers on the renormalization of Bose gases appeared. Starting with [35], a series of papers relied on the so-called momentum-shell approach [36,37,38,39]. In this method, momentum shells around the cutoff are successively integrated out directly at D = 3 according to Wilson's method, but unlike in the direct method no expansion of the critical exponents over g * is performed.This apparently new method, when applied in the symmetric (normal) phase, yields universal results which, when compared to experimental values, are worse than even the first-order ε-expansion results. However, when the momentum-shell method is applied to the symmetry-broken phase, it yields results which are far better than the firstorder ε-expansion and, in fact, as good as the results of the second-order ε-expansion. Based on this observation, it was assumed that the reliability of the momentum-shell method increases when it is used in the symmetry-broken phase, and a calculation of non-universal properties (for example transition temperature versus scattering length) from the symmetry-broken phase RG equations was attempted. For this reason, one may now wonder if applying the ε-expansion or the direct method in the symmetrybroken rather than in the symmetric phase as is us...

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Section: Introductionsupporting

confidence: 62%

“…, see equation (4). As in the classical case, this divergence is cured by performing the ε-expansion.…”

Section: ε-Expansionmentioning

confidence: 99%

The expansion in the symmetry-broken phase of an interacting Bose gas at finite temperature

Metikas

Zobay

Alber

2003

J. Phys. B: At. Mol. Opt. Phys.

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“…The reason is that the strong quantum condition (̺ ≫ 1) has been used in the derivation of inequality (77).…”

Section: Lowest Order Perturbation Theorymentioning

confidence: 99%

“…In Refs. [74,75,76,77] this was interpreted as a rescaling of the boson mass m which grows with the successive RG transformations. The fact that the quantity, to which such a rescaling should be ascribed is the thermal length λ or, equivalently, the factor (1/mT ) associated with it, has become clear later.…”

Section: Preliminary Notesmentioning

confidence: 99%

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Some basic aspects of quantum phase transitions

Shopova

Uzunov

2003

Physics Reports

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Several basic problems of the theory of quantum phase transitions are reviewed. The effect of the quantum correlations on the phase transition properties is considered with the help of basic models of statistical physics. The effect of quenched disorder on the quantum phase transitions is also discussed. The review is performed within the framework of the thermodynamic scaling theory and by the most general methods of statistical physics for the treatment of phase transitions: general lengthscale arguments, exact solutions, mean field approximation, Hubbard-Stratonovich transformation, Feynman path integral approach, and renormalization group in the field theoretical variant. Some new ideas and results are presented. Outstanding theoretical problems are mentioned.

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Gauge Invariance

2008

Gauge Field Theories

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Scaling of free energy and correlation functions for a Bose system

Cited by 24 publications

References 3 publications

The expansion in the symmetry-broken phase of an interacting Bose gas at finite temperature

The expansion in the symmetry-broken phase of an interacting Bose gas at finite temperature

Some basic aspects of quantum phase transitions

Gauge Invariance

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