Disorder Induced Cross-Over Effects at Quantum Critical Points

Carlon, Enrico; Lajkó, Péter; Iglói, Ferenc

doi:10.1103/physrevlett.87.277201

Cited by 50 publications

(62 citation statements)

References 36 publications

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“…These problems can not be directly studied by the simple strong disorder RG method, however, from arguments considering the sign of z dis − z pure and from analogous investigations on quantum spin chains 31,32,44 we can suggest the following picture. Originally gapped phases could stay gapped for weak disorder and become gapless only if the strength of disorder exceed some finite limiting value, as seen for the random conventional ladder.…”

Section: Discussionmentioning

confidence: 99%

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Strongly disordered spin ladders

Mélin¹,

Lin

Lajkó

et al. 2002

Phys. Rev. B

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The effect of quenched disorder on the low-energy properties of various antiferromagnetic spin ladder models is studied by a numerical strong disorder renormalization group method and by density matrix renormalization. For strong enough disorder the originally gapped phases with finite topological or dimer order become gapless. In these quantum Griffiths phases the scaling of the energy, as well as the singularities in the dynamical quantities are characterized by a finite dynamical exponent, z, which varies with the strength of disorder. At the phase boundaries, separating topologically distinct Griffiths phases the singular behavior of the disordered ladders is generally controlled by an infinite randomness fixed point.

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Section: Discussionmentioning

confidence: 99%

“…However, a precise numerical calculation of a small ∆ by the DMRG method is very difficult, therefore we used another strategy, as described in details in Refs. 37,44. By this method one considers the equivalent AF chain with random first-and second-neighbor couplings (see Fig.…”

Section: Random Zig-zag Laddersmentioning

confidence: 99%

Strongly disordered spin ladders

Mélin¹,

Lin

Lajkó

et al. 2002

Phys. Rev. B

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“…For the RTIM, where the RW mapping can be generalized for weaker disorder, any small amount of randomness seems to bring the system into the IRFP [12], which claim is checked by intensive numerical calculations [25,22,23]. There are, however, several other models (random quantum clock-model, Ashkin-Teller model [19], directed percolation [18], S = 1 random antiferromagnetic spin chains [16], etc.) where weak disorder is not sufficient to bring the system into the IRFP.…”

Section: B Strong Disorder: Mapping To Random Walksmentioning

confidence: 99%

“…Here we mention recent calculations on the random transverse-field Ising model (RTIM) [12,13], random quantum Potts and clock models [14], random antiferromagnetic Heisenberg spin chains [15,16] and ladders [17] and also non-equilibrium phase transitions in the presence of quenched disorder [18]. In many cases a cross-over between weak and strong disorder regimes has been observed and a general scaling scenario has been proposed [19].…”

Section: Introductionmentioning

confidence: 99%

Percolation in a random environment

Juhász

Iglói

2002

Phys. Rev. E

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We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the system with varying degree of disorder is governed by new, random fixed points with anisotropic scaling properties. For weaker disorder both the magnetization and the anisotropy exponents are non-universal, whereas for strong enough disorder the system scales into an infinite randomness fixed point in which the critical exponents are exactly known.

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“…QPTs arise from the subtle interplay between short-range interactions on one hand and quantum fluctuations on the other [4]. Since the latter are particularly strong in one dimension, quantum spin chains have emerged as a generic model to investigate QPTs [5,6,7,8]. The additional presence of disorder has profound effects on the properties of low dimensional systems [9,10] as it competes with the subtle effects of quantum fluctuations.…”

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confidence: 99%

Disorder Induced Quantum Phase Transition in Random-Exchange Spin-1/2Chains

2002

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We investigate the effect of quenched bond-disorder on the anisotropic spin-1/2 (XXZ) chain as a model for disorder induced quantum phase transitions. We find non-universal behavior of the average correlation functions for weak disorder, followed by a quantum phase transition into a strongly disordered phase with only short-range xy-correlations. We find no evidence for the universal strong-disorder fixed point predicted by the real-space renormalization group, suggesting a qualitatively different view of the relationship between quantum fluctuations and disorder.PACS numbers: 05.70. Jk,64.60.cn,75.40.Mg The existence and nature of quantum phase transitions (QPTs) [1,2,3] has in recent years emerged as one of the most interesting aspects of low-dimensional quantum systems. QPTs arise from the subtle interplay between short-range interactions on one hand and quantum fluctuations on the other [4]. Since the latter are particularly strong in one dimension, quantum spin chains have emerged as a generic model to investigate QPTs [5,6,7,8]. The additional presence of disorder has profound effects on the properties of low dimensional systems [9,10] as it competes with the subtle effects of quantum fluctuations. Its effect on QPTs has been the subject of recent intense and controversial discussion [7,8,11,12,13,14,15,16].In one-dimension the strong-disorder renormalization (SDRG) [17,18] group offers potentially exact results for a variety of models. Of particular interest is the prediction of a universal infinite randomness fixed point (IRFP) for disordered spin chains. In many systems SDRG studies suggest the relevance a random-singlet (RS) phase [19,20] as the ground state for fairly general disorder. In this RS phase the average spin correlations are predicted to obey a universal isotropic power-law de-, where the overbar denotes a configurational average over many random chains (replicas). The Luttinger (or spin-liquid) continuum of critical ground states of the ordered chain is thus predicted to collapse to a single point. Numerical results consistent with the RS picture were reported for relatively short (N ≤ 18) XXZ chains Recent numerical advances, in particular the development of the density matrix renormalization group [21], now offer a framework to investigate the relevance of the IRFP to realistic one-dimensional spin systems [22]. In this Letter we investigate the influence of exchange disorder on the anisotropic spin 1/2 Heisenberg chain (XXZ model), one of the best-known model systems for QPTs in one dimension. We find a qualitatively different scenario for the interplay of quantum fluctuations and disorder. Our results indicate that the spin correlations do not obey the universal parameter independent decay law suggested by the RS picture. Instead we find a disorderinduced QPT for finite disorder strength, whose nature can be illustrated by an exactly solvable model.In this paper we present results of a density matrix renormalization group study of XXZ chains with randomness in the transverse nearest...

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Disorder Induced Cross-Over Effects at Quantum Critical Points

Cited by 50 publications

References 36 publications

Strongly disordered spin ladders

Strongly disordered spin ladders

Percolation in a random environment

Disorder Induced Quantum Phase Transition in Random-Exchange Spin-1/2Chains

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