Helicity Modulus, Superfluidity, and Scaling in Isotropic Systems

Fisher, Michael E.; Barber, Michael N.; Jasnow, David

doi:10.1103/physreva.8.1111

Cited by 602 publications

(462 citation statements)

References 47 publications

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“…Our results are compatible with predictions η A = 1, 28 γ A = ν, 14 and υ = ν. 14,25,27 These results, together with the Fisher scaling relation (72), imply that the photon mass (or the penetration depth λ) scaling exponent ν ′ must be equal to the XY model critical exponent: ν ′ = ν XY . 8 Our results support this prediction, but only in extremely close proximity to the critical point.…”

Section: Discussionmentioning

confidence: 99%

“…By duality, this is exactly the scaling of Υ near the critical point in the XY model, and the value of υ is indeed entirely consistent with arguments that Υ scales with the exponent ν. 25 The amplitude value A Υ could also be compared directly with the XY model, but we are not aware of helicity modulus data for the Villain action.…”

Section: Susceptibilitiesmentioning

confidence: 99%

“…Another important quantity in the XY model is the helicity modulus, 25 which characterizes the response of the free energy to a twist of the spins by an amount δθ along, say, the z direction. Instead of period boundary conditions for θ, we would instead have θ(x, y, z + N ) = θ(x, y, z) + δθ.…”

Section: B Helicity Modulusmentioning

confidence: 99%

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Numerical study of duality and universality in a frozen superconductor

Neuhaus¹,

Rajantie

Rummukainen

2003

Phys. Rev. B

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The three-dimensional integer-valued lattice gauge theory, which is also known as a "frozen superconductor," can be obtained as a certain limit of the Ginzburg-Landau theory of superconductivity, and is believed to be in the same universality class. It is also exactly dual to the three-dimensional XY model. We use this duality to demonstrate the practicality of recently developed methods for studying topological defects, and investigate the critical behaviour of the phase transition using numerical Monte Carlo simulations of both theories. On the gauge theory side, we concentrate on the vortex tension and the penetration depth, which map onto the correlation lengths of the order parameter and the Noether current in the XY model, respectively. We show how these quantities behave near the critical point, and that the penetration depth exhibits critical scaling only very close to the transition point. This may explain the failure of superconductor experiments to see the inverted XY model scaling.

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Section: Discussionmentioning

confidence: 99%

Section: Susceptibilitiesmentioning

confidence: 99%

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Numerical study of duality and universality in a frozen superconductor

Neuhaus¹,

Rajantie

Rummukainen

2003

Phys. Rev. B

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“…83 The detailed knowledge of their exact values (some of which have been computed in the dilute limit in earlier sections of this paper) is not required to understand general features of topological excitations.…”

Section: A Atomic Superfluidmentioning

confidence: 99%

Superfluidity and phase transitions in a resonant Bose gas

2008

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The atomic Bose gas is studied across a Feshbach resonance, mapping out its phase diagram, and computing its thermodynamics and excitation spectra. It is shown that such a degenerate gas admits two distinct atomic and molecular superfluid phases, with the latter distinguished by the absence of atomic off-diagonal long-range order, gapped atomic excitations, and deconfined atomic π-vortices. The properties of the molecular superfluid are explored, and it is shown that across a Feshbach resonance it undergoes a quantum Ising transition to the atomic superfluid, where both atoms and molecules are condensed. In addition to its distinct thermodynamic signatures and deconfined half-vortices, in a trap a molecular superfluid should be identifiable by the absence of an atomic condensate peak and the presence of a molecular one.

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“…Replacing the superfluid velocity v s with the phase gradient according to Eq. (1) leads to a fundamental relation for the superfluid fraction [3,4] …”

mentioning

confidence: 99%

Superfluidity and interference pattern of ultracold bosons in optical lattices

2003

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We present a study of the superfluid properties of atomic Bose gases in optical lattice potentials using the Bose-Hubbard model. To do this, we use a microscopic definition of the superfluid fraction based on the response of the system to a phase variation imposed by means of twisted boundary conditions. We compare the superfluid fraction to other physical quantities, i.e., the interference pattern after ballistic expansion, the quasi-momentum distribution, and number fluctuations. We have performed exact numerical calculations of all these quantities for small one-dimensional systems. We show that the superfluid fraction alone exhibits a clear signature of the Mott-insulator transition. Observables like the fringe visibility, which probe only ground state properties, do not provide direct information on superfluidity and the Mott-insulator transition.PACS numbers: 03.75. Fi, 05.30.Jp, 73.43.Nq, Ultracold atomic gases in optical lattices provide a unique framework for the experimental study of fundamental quantum phenomena in interacting many-body systems. This is especially true for the exploration of quantum phase transitions such as the superfluid to Mott-insulator transition observed in a recent pioneering experiment [1]. The remarkable degree of experimental control over all the relevant parameters-density, interaction strength, lattice geometry and dimensionalityallows much more detailed studies of the complicated mechanisms behind quantum phase transition than conventional solid state systems.It is clearly the case that the most important quantity for characterizing the superfluid-to-insulator transition is the superfluid density or superfluid fraction f s . The aim of this paper is to set up the general theoretical framework for the calculation of the superfluid fraction within the Bose-Hubbard model and to compare it, on the formal level, with quantities being measured at the moment. These include the interference pattern after ballistic expansion, the quasi-momentum distribution as well as the number fluctuations which are important in applications. We perform exact numerical calculations for the Mott-insulator transition in an one-dimensional system to demonstrate the relationship, and more importantly the differences, between the superfluid fraction and various ground state observables, most notably the visibility of the interference pattern.Superfluidity. The concept of superfluidity is closely related to the existence of a condensate in the interacting many-boson system [2]. Formally, the one-body density matrix ρ (1) ( x, x ′ ) has to have exactly one macroscopic eigenvalue which defines the number of particles N 0 in the condensate; the corresponding eigenvector describes the condensate wave function φ 0 ( x) = e iθ( x) |φ 0 ( x)|. A spatially varying condensate phase θ( x) is associated with a velocity field for the condensate byThis irrotational velocity field is identified with velocity of the superfluid flow v s ( x) ≡ v 0 ( x) [2] and enables us to derive an expression for the superfluid fra...

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Helicity Modulus, Superfluidity, and Scaling in Isotropic Systems

Cited by 602 publications

References 47 publications

Numerical study of duality and universality in a frozen superconductor

Numerical study of duality and universality in a frozen superconductor

Superfluidity and phase transitions in a resonant Bose gas

Superfluidity and interference pattern of ultracold bosons in optical lattices

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