Numerical study of vortex matter using the Bose model: First-order melting and entanglement

Nordborg, Henrik; Blatter, G.

doi:10.1103/physrevb.58.14556

Cited by 37 publications

(51 citation statements)

References 69 publications

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“…Applying this result to YBCO, for which γ ∼ 7, we conclude that ξ z (T c ) ≃ 0.86a v , or ξ z ≃ 0.023µ for a field of B ≃ H = 4T. Our result above may be compared with that of recent "2D boson" simulations of Nordborg and Blatter [7], which yielded ξ vz (T c ) = 1.7γ −1 a v . If we take from Except for the case f = 1/100, our numerical results are all in the limit of sufficiently large f , such that T c (f, η) lies well below the zero field critical point T c (0, η).…”

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confidence: 53%

Correlation Lengths in the Vortex Line Liquid of a High-TcSuperconductor

Olsson

Teitel

1999

Phys. Rev. Lett.

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We use the three dimensional uniformly frustrated XY model, as a model for a high temperature superconductor in an applied magnetic field, to explicitly measure the longitudinal correlation length ξz in the vortex line liquid phase. We determine the scaling of ξz with magnetic field and system anisotropy close to the vortex lattice melting transition. We apply our results to determine the extent of longitudinal correlations in YBCO just above melting. 64. 60-i, 74.60-w, 74.76-w It is now generally accepted that thermal fluctuations in the high T c superconductors lead, for a clean sample in the mixed state, to a first order melting of the vortex line lattice into a vortex line liquid. Nordborg and Blatter [7] within the "two dimensional (2D) boson" approximation, as well as general theoretical considerations [8], predict a correlation length ξ z ∼ γ −1 a v , where γ ≡ λ z /λ ⊥ is the anisotropy ratio and a v = φ 0 /B is the average spacing between vortex lines. However analyses of experiments on untwinned single crystal YBCO by Righi et al. [9] and by Moore [10] have suggested that longitudinal correlations may be of the surprisingly larger micron scale.To investigate this issue, we carry out extensive new simulations of the frustrated 3D XY model for different values of applied flux density f and anisotropy η, explicitly measuring the longitudinal correlation length ξ z as determined by several different criteria. We find a good scaling of ξ z with f and η in the continuum limit, allowing us to estimate ξ z (T c ) in real YBCO single crystal samples. We find that longitudinal correlations at melting are enhanced with respect to the 2D boson approximation, but not dramatically so. We also address several additional questions. We show, contrary to recent claims [11], that there is only a single transition even in the isotropic model. In the very anisotropic limit ξ z (T c ) < d, where a cross over to 2D behavior has been predicted [8,12], we find no qualitative differences from the less anisotropic cases. We find that thermally excited vortex loops, which become important at low magnetic fields, can be described by an effective renormalization of the interaction between field induced vortex lines, and we find no evidence for a recently proposed transition within the vortex line liquid phase [13,14].Our model is the uniformly frustrated 3D XY model [15], given by the Hamiltonianwhere the sum is over the sites i of a cubic grid of points with unit basis vectorsμ =x,ŷ,ẑ. θ i is the phase angle of the superconducting wavefunction on site i, andA · dl is the integral of the magnetic vector potential on the specified bond. The unit of the grid spacing alongẑ is taken as d, the spacing between the weakly coupled CuO planes; the unit of the grid spacing in the xy plane is taken as ξ ⊥0 , the bare vortex core size in the plane. The Hamiltonian (1) results from making the London approximation to the discretized GinzburgLandau energy, and assuming λ/a v → ∞ so that the internal magnetic field B can be taken as frozen...

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confidence: 53%

Correlation Lengths in the Vortex Line Liquid of a High-TcSuperconductor

Olsson

Teitel

1999

Phys. Rev. Lett.

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“…One question is what happens to the excitation spectrum at this inverted solidification transition, is there a kind of symmetry compared with the normal solidification at lower density or not? Another question is how this high density fluid evolves toward the 2D unscreened Coulomb system in which [16,17] phonons are replaced by plasmons and BEC is suppressed to zero. Above a critical value of Λ * solidification disappears and the system is fluid at all densities.…”

Section: Discussionmentioning

confidence: 99%

“…The main focus of those studies was the phase diagram of the system, and the calculation of ground-state equilibrium properties. In previous work [16,17] only a scant attention was given to dynamical properties. In this work we present the first study of dynamical properties of the 2D-SC Bose system in the fluid phase using state-of-the-art quantum Monte Carlo and analytic continuation techniques.…”

Section: Introductionmentioning

confidence: 99%

“…Below a critical threshold, the system is solid for intermediate values of the density and fluid at both very low and high density. The 2D-SC Bose system at T = 0 K has been studied by variational theory [13] and by exact ground-state methods, diffusion Monte Carlo [14] and shadow path integral ground state (SPIGS) simulations [15], and by exact finite-temperature path integral Monte Carlo simulations [16,17]. The main focus of those studies was the phase diagram of the system, and the calculation of ground-state equilibrium properties.…”

Section: Introductionmentioning

confidence: 99%

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Roton Excitations and the Fluid–Solid Phase Transition in Superfluid 2D Yukawa Bosons

et al. 2016

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We compute several groundstate properties and the dynamical structure factor of a 0-temperature system of Bosons interacting with the 2D screened Coulomb (2D-SC) potential. We resort to the exact shadow path-integral ground-state (SPIGS) quantum Monte Carlo method to compute the imaginary-time correlation function of the model, and to the genetic algorithm via falsification of theories (GIFT) to retrieve the dynamical structure factor. We provide a detailed comparison of groundstate properties and collective excitations of 2D-SC and 4 He atoms. The roton energy of the 2D-SC system is an increasing function of density, and not a decreasing one as in 4 He. This result is in contrast with the view that the roton is the soft mode of the fluid-solid transition. We uncover a remarkable quasi-universality of backflow and of other properties when expressed in terms of the amount of short range order as quantified by the height of the first peak of the static structure factor.

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“…It is a nice feature of multilevel Monte Carlo that one can implement flux cutting and permutations 14,15,17,20 , so that flux lines with PBC in the z direction don't end on themselves but form loops that wind more than once across the system. We term such loops non- It is sometimes argued that one can not implement permutations in a molecular dynamic simulation as the motion through permutation space is discrete and molecular dynamics involves continuous evolution.…”

Section: Details Of the Simulationsmentioning

confidence: 99%

Molecular dynamics of pancake vortices with realistic interactions: Observing the vortex lattice melting transition

Goldschmidt

2005

Phys. Rev. B

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In this paper we describe a version of London Langevin molecular dynamics simulations that allows for investigations of the vortex lattice melting transition in the highly anisotropic hightemperature superconductor material Bi 2 Sr 2 CaCu 2 O 8+δ . We include the full electromagnetic interaction as well as the Josephson interaction among pancake vortices. We also implement periodic boundary conditions in all directions, including the z-axis along which the magnetic field is applied. We show how to implement flux cutting and reconnection as an analog to permutations in the multilevel Monte Carlo scheme and demonstrate that this process leads to flux entanglement that proliferates in the vortex liquid phase. The first-order melting transition of the vortex lattice is observed to be in excellent agreement with previous multilevel Monte Carlo simulations.

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Numerical study of vortex matter using the Bose model: First-order melting and entanglement

Cited by 37 publications

References 69 publications

Correlation Lengths in the Vortex Line Liquid of a High-TcSuperconductor

Correlation Lengths in the Vortex Line Liquid of a High-TcSuperconductor

Roton Excitations and the Fluid–Solid Phase Transition in Superfluid 2D Yukawa Bosons

Molecular dynamics of pancake vortices with realistic interactions: Observing the vortex lattice melting transition

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