Monte Carlo determination of the critical temperature for the two-dimensional<i>XY</i>model

Weber, Hans; Minnhagen, Petter

doi:10.1103/physrevb.37.5986

Cited by 233 publications

(224 citation statements)

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“…The first uses the finite-size scaling of r s . Weber and Minnhagen 44 have derived the finite-size scaling of the SF density at T BKT . An unbiased fit to this log-scaling form (see Methods) shows that the fit error (Fig.…”

Section: Resultsmentioning

confidence: 99%

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Proposed formation and dynamical signature of a chiral Bose liquid in an optical lattice

Paramekanti

Hemmerich

et al. 2014

Nat Commun

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Recent experiments on p-orbital atomic bosons have suggested the emergence of a spectacular ultracold superfluid with staggered orbital currents in optical lattices. This raises fundamental questions concerning the effects of thermal fluctuations as well as possible ways of directly observing such chiral order. Here we show via Monte Carlo simulations that thermal fluctuations destroy this superfluid in an unexpected two-step process, unveiling an intermediate normal phase with spontaneously broken time-reversal symmetry, dubbed a 'chiral Bose liquid'. For integer fillings (nZ2) in the chiral Mott regime, thermal fluctuations are captured by an effective orbital Ising model, and Onsager's powerful exact solution is adopted to determine the transition from this intermediate liquid to the paraorbital normal phase at high temperature. A lattice quench is designed to convert the staggered angular momentum, previously thought by experts difficult to directly probe, into coherent orbital oscillations, providing a time-resolved dynamical signature of chiral order.

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Section: Resultsmentioning

confidence: 99%

“…On finite size systems, the universal SF stiffness jump gets severely rounded, and a careful finite-size scaling is required to extract T BKT . On the basis of the KT renormalization group equations, Weber and Minnhagen have shown 44 that r s (T BKT , L) scales as…”

Section: Methodsmentioning

confidence: 99%

Proposed formation and dynamical signature of a chiral Bose liquid in an optical lattice

Paramekanti

Hemmerich

et al. 2014

Nat Commun

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“…2 yields the estimate of T KT . A more sophisticated method taking into account the logarithmic correction [18] yields a similar answer [15].…”

Section: Pacs Numbersmentioning

confidence: 99%

Nematic and Chiral Order for Planar Spins on a Triangular Lattice

et al. 2008

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We propose a variant of the antiferromagnetic XY model on the triangular lattice to study the interplay between the chiral and nematic orders in addition to the magnetic order. The model has a significant bi-quadratic interaction of the planar spins. When the bi-quadratic exchange energy dominates, a large temperature window is shown to exist over which the nematic and the chiral orders co-exist without the magnetic order, thus defining a chiral-nematic state. The phase diagram of the model and some of its critical properties are derived by means of the Monte Carlo simulation. PACS numbers:Nontrivial orders in frustrated magnets [1] are among the central issues in the field of condensed-matter physics. Besides the conventional magnetic order parameter of spin S i at a site i, there could appear various nontrivial orders such as vector [2,3] and scalar [4, 5] chiral orders [6], and nematic order [7], which might lead to additional phase transitions distinct from the one driven by magnetic order. Even the ground state itself may be characterized solely by these nontrivial orders. This issue is now attracting revived interest from the viewpoint of nontrivial glass transition of spins [8] and multiferroic behaviors [9,10], where the ferroelectricity is induced by the formation of vector spin chirality [11]. One important aspect of this problem is the interplay between the various orders. Usually the nontrivial orders become long ranged when the magnetic order sets in. For example, the spiral spin order naturally implies the vector spin chiral order through S i × S j ∼ S i × S j on the neighboring sites. Therefore, the interesting issue is whether the nontrivial order can become long ranged in the absence of the magnetic order. This issue has been studied theoretically [9], and experimentally in the quasi-one dimensional frustrated magnet [12] where the chiral order appears above the magnetic phase transition. The next important question, we argue, is the interplay between the two nontrivial orders, e.g., chiral and nematic orders, which has not been fully addressed so far.To address this issue, we study a generalized classical XY spin model on a triangular lattice,where θ ij is the angle difference θ i − θ j between the nearest neighbors ij . This model contains the usual frustration in the exchange interaction due to the triangular lattice geometry, together with the possible nematic order induced by the J 2 term. The J 2 = 0 limit has been extensively studied, and it is believed to have two phase transitions at closely spaced critical temperatures[2, 13-15]. The Kosterlitz-Thouless (KT) transition temperature T KT signaling the loss of (algebraic) magnetic order and the melting temperature of the staggered chirality, T χ , are extremely close, (T χ − T KT )/T χ 0.02 at J 2 = 0, hampering the interpretation of the intermediate, T KT < T < T χ phase as the chiral phase in which the chirality is ordered but the magnetism remains disordered. Extension of the XY model to include large J 2 interaction was considered ear...

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“…A more quantitative determination of the critical coupling and the corresponding jump in the phase stiffness can be obtained by the Weber and Minnhagen scaling analysis, which has been introduced before as an accurate method of locating the critical coupling and the universal jump of the KT transition for the ordinary XY model. 22 The phase stiffness at the transition should have a logarithmic correction given by 22…”

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Field-induced superconductor-to-insulator transition in Josephson-junction ladders

Granato

2005

Phys. Rev. B

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The superconductor-to-insulator transition is studied in a self-charging model for a ladder of Josephson junctions in the presence of an external magnetic field. Path integral Monte Carlo simulations of the equivalent ͑1+1͒-dimensional classical model are used to study the phase diagram and critical behavior. In addition to a superconducting ͑vortex-free͒ phase, a vortex phase can also occur for an increasing magnetic field and small charging energy. It is found that an intervening insulating phase separates the superconducting from the vortex phases. Surprisingly, a finite-size scaling analysis shows that the field-induced superconducting-to-insulator transition is in the KT universality class, even though the external field breaks time-reversal symmetry. DOI: 10.1103/PhysRevB.72.104521 PACS number͑s͒: 74.40.ϩk, 74.81.Fa, 73.43.Nq, 74.25.Qt Superconductor-to-insulator transitions in Josephson junction arrays have attracted considerable interest. 1-5 Such arrays can currently be fabricated in any desired geometry both in one and two dimensions 4,5 with well-controlled parameters. When charging effects due to the small capacitance of the grains or junctions dominate, strong quantum fluctuations of the phase of the superconducting order parameter may drive the system into an insulating phase at zero temperature, leading to a superconductor-to-insulator transition as a function of charging energy or an external magnetic field. In two dimensions, the universality class of these transitions have already been investigated in detail numerically, 6 both in relation to experiments 3,4 and theoretical predictions. 7-9 Nevertheless, there are also remarkable quantum phase transition scenarios 10 that can take place in a Josephson-junction ladder in a magnetic field as in Fig. 1 which have not been investigated experimentally or numerically. Interestingly, a Josephson-junction ladder provides the simplest onedimensional version of the array allowing the study of commensurability effects due to the flux lattice 10-13 or charge frustration, 14 in the presence of quantum fluctuations.An important aspect of the Josephson-junction ladder in Fig. 1 is the approximate relation to the quantum sineGordon model, 15 as first shown by Kardar. 10 For an increasing magnetic field, there is a transition from a ͑vortex-free͒ superconducting phase to a vortex phase, where flux penetrates the ladder, in the absence of quantum fluctuations. This transition is the analog of the commensurateincommensurate transition 16 described by the sine-Gordon model. For small fields, the phases in different branches of the ladder are locked to each other while in the vortex state exponentially interacting kinks ͑vortices͒ appear that unlock the phases leading to a one-dimensional vortex lattice. The inclusion of quantum fluctuations due to charging effects leads to the interesting prediction that an insulating phase should occur in the vicinity of this transition and therefore a direct transition from the ͑vortex-free͒ superconducting phase to the vort...

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Monte Carlo determination of the critical temperature for the two-dimensionalXYmodel

Cited by 233 publications

References 12 publications

Proposed formation and dynamical signature of a chiral Bose liquid in an optical lattice

Proposed formation and dynamical signature of a chiral Bose liquid in an optical lattice

Nematic and Chiral Order for Planar Spins on a Triangular Lattice

Field-induced superconductor-to-insulator transition in Josephson-junction ladders

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