Phase transition of trapped interacting Bose gases and the renormalization group

Metikas, Georgios; Zobay, O.; Alber, Gernot

doi:10.1103/physreva.69.043614

Cited by 14 publications

(29 citation statements)

References 48 publications

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“…A basic aspect of Bose-Einstein condensation is the actual order of the transition. In the non-interacting case it is third order (within the Ehrenfest classification), On the other hand, order-parameter based studies of dilute Bose systems [8,9,10,11,12,13,14,15,16] as well as related effective low-energy bosonic models for underlying Fermi systems [6,17,18,19] typically truncate the effective action at quartic order biasing the system towards a second-order transition. It is however well known that different fluctuation-related effects tend to change the order of both thermal and quantum phase transitions [5,20,21,22,23,24,25,26,27,28], and often destabilize them towards first-order.…”

Section: Introductionmentioning

confidence: 99%

Quantum criticality of the imperfect Bose gas inddimensions

Jakubczyk¹,

Napiórkowski²

2013

J. Stat. Mech.

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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.

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Section: Introductionmentioning

confidence: 99%

Quantum criticality of the imperfect Bose gas inddimensions

Jakubczyk¹,

Napiórkowski²

2013

J. Stat. Mech.

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“…These equations, however, do not yield the correct behavior for, e.g., the critical temperature [37]. After clarifying the relation between the flow equations for the condensed and the uncondensed phase [38], the latter were successfully used to investigate the critical temperature of trapped Bose gases [39,40].…”

mentioning

confidence: 99%

“…As discussed in detail in Refs. [39] and [41], the approach has some shortcomings: it is only approximate, and some of the underlying assumptions and approximations are not fully controllable and difficult to improve systematically. Never-theless, these problems are outweighed by the advantages of the method.…”

mentioning

confidence: 99%

“…(5) and (6) and further discussions can be found in Refs. [34,38,39,41]. Similar equations were also used, e.g., in Refs.…”

mentioning

confidence: 99%

“…This puts limitations on the practical feasibility of the procedure described in (i). For v(â) this issue is not severe, since the initial conditions M (0) and b(0) can easily be calculated to very high accuracy by means of a bisection routine [39]. For δ(â), however, one has to evaluate the derivative of the thermodynamic potential (7) which adds a significant amount of numerical noise.…”

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Condensation temperature of interacting Bose gases with and without disorder

Zobay

2006

Phys. Rev. A

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The momentum-shell renormalization group ͑RG͒ is used to study the condensation of interacting Bose gases without and with disorder. First of all, for the homogeneous disorder-free Bose gas the interactioninduced shifts in the critical temperature and chemical potential are determined up to second order in the scattering length. The approach does not make use of dimensional reduction and is thus independent of previous derivations. Secondly, the RG is used together with the replica method to study the interacting Bose gas with delta-correlated disorder. The flow equations are derived and found to reduce, in the high-temperature limit, to the RG equations of the classical Landau-Ginzburg model with random-exchange defects. The random fixed point is used to calculate the condensation temperature under the combined influence of particle interactions and disorder.The realization of Bose-Einstein condensation in ultracold atomic gases has renewed the interest in the quantumstatistical properties of interacting Bose gases around the phase transition. One particular focus of theoretical work in this area concerns the calculation of the critical temperature T c of the homogeneous Bose gas as a function of the scattering length a. Due to its nonperturbative character, this apparently simple problem turned out to present a considerable theoretical challenge. For a long time, the leading-order functional dependence of the shift in T c on the scattering length remained highly controversial. It was even unclear whether the interactions lead to an upward or downward shift in the critical temperature ͓1͔. Only recently, a generally accepted result has emerged ͓2-4͔. It was shown that the critical temperature of an interacting Bose gas with spatial density n obeys the relation T c T c 0 = 1 + c 1 an 1/3 + ͓c 2 Ј ln͑an 1/3 ͒ + c 2 Љ͔a 2 n 2/3 + O͑a 3 n͒, ͑1͒where T c 0 denotes the critical temperature of an ideal Bose gas with the same density. To calculate the coefficients c i , one can make use of dimensional reduction ͓1,5͔ and perturbatively match the full quantum-mechanical problem to a classical field theory with a lower-͑i.e., three-͒ dimensional action ͓4͔. The coefficient c 2 Ј can then be determined by perturbation theory alone, whereas the evaluation of c 1 and c 2 Љ requires nonperturbative input from the classical theory. This input was calculated in Refs. ͓6-8͔ with so far unsurpassed accuracy by means of Monte Carlo lattice simulations.Even after the qualitative and quantitative behavior of the T c shift had been solidly established ͓2-4,6,8͔, a large number of papers continued to appear that presented further calculations of critical properties of interacting Bose gases. The main purpose of these works was not to correct or improve the previous results, but to introduce, test, and refine alternative approaches. The applied methods comprise, e.g., linear ␦ expansion ͓9-14͔, variational perturbation theory ͓15-17͔, and the exact renormalization group ͓18-20͔.The present paper follows this research line of investigat...

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Finite-size effects on the Bose–Einstein condensation critical temperature in a harmonic trap

Noronha

2016

Physics Letters A

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We obtain second and higher order corrections to the shift of the Bose-Einstein critical temperature due to finite-size effects. The confinement is that of a harmonic trap with general anisotropy. Numerical work shows the high accuracy of our expressions. We draw attention to a subtlety involved in the consideration of experimental values of the critical temperature in connection with analytical expressions for the finite-size corrections.

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Phase transition of trapped interacting Bose gases and the renormalization group

Cited by 14 publications

References 48 publications

Quantum criticality of the imperfect Bose gas inddimensions

Quantum criticality of the imperfect Bose gas inddimensions

Condensation temperature of interacting Bose gases with and without disorder

Finite-size effects on the Bose–Einstein condensation critical temperature in a harmonic trap

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