Renormalization group study of the two-dimensional random transverse-field Ising model

Kovács, I.; Iglói, Ferenc

doi:10.1103/physrevb.82.054437

Cited by 102 publications

(185 citation statements)

References 52 publications

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“…One possibility is that the the model looks more and more disordered at larger length scales near criticality. This is the case for random transverse field Ising models in one and two dimensions 19,26,27 . In such cases, the model flows towards infinite randomness, and the strong disorder renormalization group becomes asymptotically exact near criticality 18 .…”

Section: Strong Disorder Renormalization Of the 2d Disordered Romentioning

confidence: 95%

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Mott glass to superfluid transition for random bosons in two dimensions

2012

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We study the zero temperature superfluid-insulator transition for a two-dimensional model of interacting, lattice bosons in the presence of quenched disorder and particle-hole symmetry. We follow the approach of a recent series of papers by Altman, Kafri, Polkovnikov, and Refael, in which the strong disorder renormalization group is used to study disordered bosons in one dimension. Adapting this method to two dimensions, we study several different species of disorder and uncover universal features of the superfluid-insulator transition. In particular, we locate an unstable finite disorder fixed point that governs the transition between the superfluid and a gapless, glassy insulator. We present numerical evidence that this glassy phase is the incompressible Mott glass and that the transition from this phase to the superfluid is driven by percolation-type process. Finally, we provide estimates of the critical exponents governing this transition.

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Section: Strong Disorder Renormalization Of the 2d Disordered Romentioning

confidence: 95%

“…For large clusters, the link decimation rule for addition of charging energies (26) implies that U ∼ s −1 , and therefore:…”

Section: Glassmentioning

confidence: 99%

Mott glass to superfluid transition for random bosons in two dimensions

2012

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“…As a final remark, we should stress the difference with the strong disorder renormalization method (see [51] for a review) that has been developed for disordered quantum short-ranged spin models either in d = 1 [52] or in d = 2, 3, 4 [53][54][55][56][57][58][59][60][61][62][63]. In these quantum spin models, the idea is to decimate the strongest coupling J max remaining in the whole system : the renormalized couplings obtained via second order perturbation theory of quantum mechanics are typically much weaker than the decimated coupling J max , so that the procedure is consistent and the typical renormalized couplings decays as J typ L ∝ e −L ψ .…”

Section: Ementioning

confidence: 99%

One-dimensional Ising spin-glass with power-law interaction: real-space renormalization at zero temperature

Monthus¹

2014

J. Stat. Mech.

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For the one-dimensional long-ranged Ising spin-glass with random couplings decaying with the distance r as J(r) ∼ r −σ and distributed with the Lévy symmetric stable distribution of index 1 < µ ≤ 2 (including the usual Gaussian case µ = 2), we consider the region σ > 1/µ where the energy is extensive. We study two real space renormalization procedures at zero temperature, namely a simple box decimation that leads to explicit calculations, and a strong disorder decimation that can be studied numerically on large sizes. The droplet exponent governing the scaling of the renormalized couplings JL ∝ L θµ(σ) is found to be θµ(σ) = 2 µ −σ whenever the long-ranged couplings are relevant θµ(σ) ≥ −1. For the statistics of the ground state energy E GS L over disordered samples, we obtain that the droplet exponent θµ(σ) governs the leading correction to extensivity of the averaged value E GS L ≃ Le0 + L θµ (σ) e1. The characteristic scale of the fluctuations around this average is of order L 1 µ , and the rescaledGaussian distributed for µ = 2, or displays the negative power-law tail in 1/(−u) 1+µ for u → −∞ in the Lévy case 1 < µ < 2. Finally we apply the zero-temperature renormalization procedure to the related Dyson hierarchical spin-glass model where the same droplet exponent appears.

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“…Spin glasses are the paradigmatic models of such theoretical challenge and, presumably, their phase transitions should govern by the IRFP [6]. Although recent theoretical works [7][8][9] support this conjecture, old Monte Carlo studies concluded that for two [10] and three [11] dimensions, the quantum phase transition of such systems is instead conventional (with z takes a finite value). Subsequent simulation research has explored this same problem concluding that in two dimensions and at the critical point, several observables (different versions of the Binder cumulant and the correlation length) do not follow a conventional dynamic scaling [12].…”

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confidence: 99%

Unconventional critical activated scaling of two-dimensional quantum spin glasses

Matoz-Fernandez

Romá

2016

Phys. Rev. B

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We study the critical behavior of two-dimensional short-range quantum spin glasses by numerical simulations. Using a parallel tempering algorithm, we calculate the Binder cumulant for the Ising spin glass in a transverse magnetic field with two different short-range bond distributions, the bimodal and the Gaussian ones. Through an exhaustive finite-size analysis, we show that the cumulant probably follows an unconventional activated scaling, which we interpret as new evidence supporting the hypothesis that the quantum critical behavior is governed by an infinite randomness fixed point. PACS numbers: 75.10.Nr, 64.70.Tg, 75.40.Mg, 75.50.Lk Quantum phase transitions in condensed matter have been a subject of special interest though many decades [1]. This phenomenon manifests itself in systems where quantum instead of thermal fluctuations are relevant. An order-disorder phase transition can occur even at zero temperature, if a suitable parameter (a magnetic field, for example) is tuned externally through the critical region. Simple models, e. g. the pure Ising ferromagnet chain in a transverse field, have been used as prototypes for testing our understanding in the vicinity of such critical points [2]. More interesting still is the criticality found in disordered systems. It has been established that the quantum phase transition in diluted and random Ising models in a transverse field, is controlled by the so-called infinite randomness fixed point (IRFP) [3] which, among other things, is characterized by a divergent dynamical exponent z and an unconventional dynamic scaling [2,4,5].The critical behavior of the quantum disordered and frustrated systems, however, is very poorly understood [1]. Spin glasses are the paradigmatic models of such theoretical challenge and, presumably, their phase transitions should govern by the IRFP [6]. Although recent theoretical works [7][8][9] support this conjecture, old Monte Carlo studies concluded that for two [10] and three [11] dimensions, the quantum phase transition of such systems is instead conventional (with z takes a finite value). Subsequent simulation research has explored this same problem concluding that in two dimensions and at the critical point, several observables (different versions of the Binder cumulant and the correlation length) do not follow a conventional dynamic scaling [12]. Such disagreements are still an open question, which often is circumvented in favor of the IRFP scenario by noting that small system sizes were used in these numerical works. Being that the simulations of disordered and highly frustrated systems as spin glasses inevitably suffer from this drawback, at first sight this obstacle seems impossible to overcome without the use of an alternative strategy.In this paper, we use a quantum parallel-tempering Monte Carlo algorithm to simulate the two-dimensional Ising spin glass model in a transverse magnetic field. Through an exhaustive finite-size scaling analysis of the Binder cumulants, we present new evidence for the existence of an IRFP i...

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Renormalization group study of the two-dimensional random transverse-field Ising model

Cited by 102 publications

References 52 publications

Mott glass to superfluid transition for random bosons in two dimensions

Mott glass to superfluid transition for random bosons in two dimensions

One-dimensional Ising spin-glass with power-law interaction: real-space renormalization at zero temperature

Unconventional critical activated scaling of two-dimensional quantum spin glasses

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