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Ebey, P. S.; Finley, P. T.; Hallock, R. B.

doi:10.1023/a:1022591707583

Cited by 15 publications

(5 citation statements)

References 10 publications

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“…The fit is extremely good-20 points for the critical density at U ≤ 2.5 and Lm(U T ) 1/2 > 15, each calculated with relative accuracy of order 10 −4 , are described with the confidence level of 62 %. Experiments on helium films often report that the ratio n s (T c )/n s (0) = n s (T c )/n c = 2mT c /πn c is close to 0.75 [14,15]. Our simulation predicts that this ratio is given by…”

Section: And Thus Can Writementioning

confidence: 55%

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Critical Point of a Weakly Interacting Two-Dimensional Bose Gas

2001

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We study the Berezinskii-Kosterlitz-Thouless transition in a weakly interacting 2D quantum Bose gas using the concept of universality and numerical simulations of the classical |ψ| 4 -model on a lattice. The critical density and chemical potential are given by relations nc = (mT /2πh2 ) ln(ξh 2 /mU ) and µc = (mT U/πh 2 ) ln(ξµh 2 /mU ), where T is the temperature, m is the mass, and U is the effective interaction. The dimensionless constant ξ = 380 ± 3 is very large and thus any quantitative analysis of the experimental data crucially depends on its value. For ξµ our result is ξµ = 13.2 ± 0.4. We also report the study of the quasi-condensate correlations at the critical point.An accurate microscopic expression for the critical temperature of the Berezinskii-Kosterlitz-Thouless (BKT) transition [1] has been a weak point of the theory of weakly interacting two-dimensional Bose gas. The theory of Ref.[2] (see also [3,4] and analysis below), suggests that the critical density of the BKT transition in the weakly interacting system reads (we seth = 1)However, the value of ξ cannot be obtained within standard analytical treatments since ξ is related to the system behavior in the fluctuation region where the perturbative expansion in powers of U does not work. With unknown ξ, one finds Eq. (1) rather inaccurate unless mU is exponentially small. Moreover, as we will find in this Letter, the value of ξ is very large: ξ ≈ 380. This means that for all experimentally available up to date (quasi-)2D weakly interacting Bose gases [5,6] the quantitative analysis of the data for the critical ratio n c /T c requires a precise value of ξ. In the system of spin-polarized atomic hydrogen on helium film [5], the value of mU is of order unity [3]; in the recently created quasi-2D system of sodium atoms [6], mU is of order 10 −2 , according to the formula of Ref. [7].To quantitatively describe the BKT transition in a weakly interacting Bose gas, it is sufficient to solve a classical-field |ψ| 4 -model with the effective long-wave Hamiltonian [2]where µ ′ is the chemical potential, and ψ is the classical complex field.In this Letter, we first discuss the origin of the relation (1) in the limit of small U , and how quantum and classical models relate to each other. Then we present our numeric results (for the critical density, critical chemical potential, and quasi-condensate correlations at the BKT point) obtained by simulating the critical behavior of the 2D |ψ| 4 -model on a lattice using recently developed Worm algorithm [8] for classical statistical models. In particular, we show that the quasi-condensate correlations are very strong at T c , in agreement with the experimental observation in the spin-polarized atomic hydrogen [5] and quantum Monte Carlo simulations [9].A simple dimensional analysis of the Hamiltonian (2) allows to write a generic formula for the critical point in a weakly interacting 2D |ψ| 4 -model. The routine itself is completely analogous to that in the 3D case (see, e.g., [10,11]), but final results naturally ...

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Section: And Thus Can Writementioning

confidence: 55%

“…The fitting procedure yields A = (6.07±0.05)·10 3 , A µ = (211 ± 6), which, according to Eq. (15), means that…”

Section: And Thus Can Writementioning

confidence: 99%

Critical Point of a Weakly Interacting Two-Dimensional Bose Gas

2001

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“…For helium films on various substrates [19,20], and spin-polarized atomic hydrogen on helium film [21], the value of mU is most probably of order unity [5].…”

Section: Discussionmentioning

confidence: 99%

Two-dimensional weakly interacting Bose gas in the fluctuation region

2002

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We study the crossover between the mean-field and critical behavior of the two-dimensional Bose gas throughout the fluctuation region of the Berezinskii-Kosterlitz-Thouless phase transition point. We argue that this crossover is described by universal (for all weakly interacting |ψ| 4 models ) relations between thermodynamic parameters of the system, including superfluid and quasi-condensate densities. We establish these relations with high-precision Monte Carlo simulations of the classical |ψ| 4 model on a lattice, and check their asymptotic forms against analytic expressions derived on the basis of the mean-field theory.

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“…For instance, when random disorder is added to paradigmatic condensed matter models, such as the Bose-Hubbard model or the BCS model for superconductivity, it gives rise to disorder-driven phase transitions from a conducting to an insulating phase, resulting from the localization of bosons and cooper pairs, respectively [3][4][5][6]. While disorder driven phase transitions have been observed in a wide range of experimental systems such as films of adsorbed 4 He on substrates [7,8], bosonic magnets [9][10][11], and thin superconducting films [12,13], and in spite of a remarkable theoretical effort [14][15][16][17][18][19][20][21], a thorough understanding of the effects of disorder in interacting quantum many body systems is lacking. On the one hand these systems are challenging to study theoretically, on the other poor control over experimental condensed matter systems does not allow for thorough experimental investigation of these systems.…”

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confidence: 99%

Equilibrium phases of two-dimensional bosons in quasiperiodic lattices

2015

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We report on results of Quantum Monte Carlo simulations for bosons in a two dimensional quasiperiodic optical lattice. We study the ground state phase diagram at unity filling and confirm the existence of three phases: superfluid, Mott insulator, and Bose glass. At lower interaction strength, we find that sizable disorder strength is needed in order to destroy superfluidity in favor of the Bose glass. On the other hand, at large enough interaction superfluidity is completely destroyed in favor of the Mott insulator (at lower disorder strength) or the Bose glass (at larger disorder strength). At intermediate interactions, the system undergoes an insulator to superfluid transition upon increasing the disorder, while a further increase of disorder strength drives the superfluid to Bose glass phase transition. While we are not able to discern between the Mott insulator and the Bose glass at intermediate interactions, we study the transition between these two phases at larger interaction strength and, unlike what reported in [1] for random disorder, find no evidence of a Mott-glass-like behavior.Introduction: Condensed matter systems, either manufactured or occurring in nature, posses, in general, a certain degree of disorder. Studying physical phenomena such as Anderson [2] localization, resulting from the presence of disorder, is therefore of crucial importance. Anderson localization pertains to the case of non-interacting fermions. More realistic systems, though, consist of interacting particles. For interacting systems, the interplay between disorder and interaction may result in novel physical effects. For instance, when random disorder is added to paradigmatic condensed matter models, such as the Bose-Hubbard model or the BCS model for superconductivity, it gives rise to disorder-driven phase transitions from a conducting to an insulating phase, resulting from the localization of bosons and cooper pairs, respectively [3][4][5][6]. While disorder driven phase transitions have been observed in a wide range of experimental systems such as films of adsorbed 4 He on substrates [7,8], bosonic magnets [9][10][11], and thin superconducting films [12,13], and in spite of a remarkable theoretical effort [14][15][16][17][18][19][20][21], a thorough understanding of the effects of disorder in interacting quantum many body systems is lacking. On the one hand these systems are challenging to study theoretically, on the other poor control over experimental condensed matter systems does not allow for thorough experimental investigation of these systems.

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Cited by 15 publications

References 10 publications

Critical Point of a Weakly Interacting Two-Dimensional Bose Gas

Critical Point of a Weakly Interacting Two-Dimensional Bose Gas

Two-dimensional weakly interacting Bose gas in the fluctuation region

Equilibrium phases of two-dimensional bosons in quasiperiodic lattices

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