Phase Diagram of the Random Heisenberg Antiferromagnetic Spin-1 Chain

Saguia, A.; Boechat, B.; Continentino, M. A.

doi:10.1103/physrevlett.89.117202

Cited by 35 publications

(41 citation statements)

References 23 publications

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“…Based on a modified strong disorder RG approach 8,9,14 and different numerical calculations, 11,12,13 the following scenario of the phase transition in the model is conjectured with increasing strength of disorder.…”

Section: Disorder-induced Phasesmentioning

confidence: 99%

Disorder-induced phases in theS=1antiferromagnetic Heisenberg chain

Lajkó

Carlon²,

Rieger

et al. 2005

Phys. Rev. B

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We use extensive density matrix renormalization group (DMRG) calculations to explore the phase diagram of the random S = 1 antiferromagnetic Heisenberg chain with a power-law distribution of the exchange couplings. We use open chains and monitor the lowest gaps, the end-to-end correlation function and the string order parameter. For this distribution, at weak disorder the system is in the gapless Haldane phase with a disorder dependent dynamical exponent, z, and z = 1 signals the border between the nonsingular and singular regions of the local susceptibility. For strong enough disorder, which approximately corresponds to a uniform distribution, a transition into the random singlet phase is detected, at which the string order parameter as well as the average end-toend correlation function are vanishing and at the same time the dynamical exponent is divergent. Singularities of physical quantities are found to be somewhat different in the random singlet phase and in the critical point.

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Section: Disorder-induced Phasesmentioning

confidence: 99%

Disorder-induced phases in theS=1antiferromagnetic Heisenberg chain

Lajkó

Carlon²,

Rieger

et al. 2005

Phys. Rev. B

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“…In order to solve this problem, a generalization of the MDH method was proposed in Refs. [23,24]. This modified MDH method consists in either of the following procedures shown in Fig.…”

Section: -Renormalization Group Approach For Random Quantum Spin Cmentioning

confidence: 99%

Entanglement entropy in random quantum spin-Schains

et al. 2007

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We discuss the scaling of entanglement entropy in the random singlet phase (RSP) of disordered quantum magnetic chains of general spin-S. Through an analysis of the general structure of the RSP, we show that the entanglement entropy scales logarithmically with the size of a block and we provide a closed expression for this scaling. This result is applicable for arbitrary quantum spin chains in the RSP, being dependent only on the magnitude S of the spin. Remarkably, the logarithmic scaling holds for the disordered chain even if the pure chain with no disorder does not exhibit conformal invariance, as is the case for Heisenberg integer spin chains. Our conclusions are supported by explicit evaluations of the entanglement entropy for random spin-1 and spin-3/2 chains using an asymptotically exact real-space renormalization group approach. I -INTRODUCTIONQuantum information science provides fruitful connections between different branches of physics. In this context, the relationship between entanglement, which is a fundamental resource for quantum information applications [1], and the theory of quantum critical phenomena [2,3] has been a focus of intensive research. Specifically, entanglement measures have been proposed as a tool to characterize quantum phase transitions (See, e.g., Refs. [4,5,6,7,8]). In this direction, a successful approach has been the analysis of bipartite entanglement in quantum systems as measured by the von Neumann entropy. Given a quantum system in a pure state |ψ and a bipartition of the system into two blocks A and B, entanglement between A and B can be measured by the von Neumann entropy S of the reduced density matrix of either block, i.e.,where ρ A = Tr B ρ and ρ B = Tr A ρ denote the reduced density matrices of blocks A and B, respectively, with ρ = |ψ ψ|. By evaluating S for quantum spin systems, Ref.[6] numerically found that entanglement displays a logarithmic scaling with the size of the block in critical (gapless) chains and saturates to a constant value in chains with a gap for excitations. The logarithmic scaling was proven in general for one-dimensional quantum models exhibiting conformal invariance [9,10], with the scaling governed by a universal factor, given by the central charge of the associated conformal field theory. Indeed, for a block of spins of length L in a quantum chain, von Neumann entropy S(L) scales aswhere c is the central charge and k is a non-universal constant. Recently, the behavior of entanglement entropy in critical spin chains has also been discussed in presence of disorder [11,12,13,14,15]. Disorder appears as an essential feature in a number of condensed matter systems, motivating a great deal of theoretical and experimental research (e.g., see [16,17]). Moreover, disorder usually introduces a further effect, namely, the breaking of conformal symmetry in a critical model. Remarkably, Refael and Moore [11] have shown that, even in the absence of conformal invariance, due to disorder, the logarithmic scaling given by Eq. (2) holds for the spin-1/2 rand...

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“…5-7 Recently, this technique has been extended to higher-spin cases, [8][9][10][11] where two of the main debates are on the robustness of the Haldane gap 12 against disorder and on the presence of the spin-1 RS phase. A number of numerical studies have also been carried out [13][14][15][16] to establish a quantitative phase diagram.…”

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confidence: 99%

Randomness-driven Quantum Phase Transition in Bond-alternating Haldane Chain

2005

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The effect of bond randomness on the spin-gapped ground state of the spin-1 bond-alternating antiferromagnetic Heisenberg chain is discussed. By using the loop cluster quantum Monte Carlo method, we investigate the stability of topological order in terms of the recently proposed twist order parameter [M. Nakamura and S. Todo: Phys. Rev. Lett. 89 (2002) 077204]. It is observed that the dimer phases as well as the Haldane phase of the spin-1 Heisenberg chain are robust against a weak randomness, though the valence-bond-solid-like topological order in the latter phase is destroyed by introducing a disorder stronger than the critical value.KEYWORDS: Haldane chain, bond randomness, quantum phase transitions, random-singlet phase, quantum Monte Carlo, loop algorithm, topological order, twist order parameterDisorder effects on low-dimensional quantum magnets have been investigated extensively in recent theoretical studies. In particular, impurity effects on spin-gapped Heisenberg antiferromagnets 1 have aroused much interest in relation to the impurity-induced antiferromagnetic (AF) long-range order observed experimentally in real materials.2 It has been established by recent numerical simulations 3, 4 that in two dimensions or higher, there are two classes of disorder, that affect spin-gapped states in essentially different ways. Site dilution and bond dilution are representatives of each class. The former induces localized moments around impurity sites. There exist strong correlations between such effective spins retaining the staggeredness with respect to the original lattice, and therefore the AF long-range order emerges by an infinitesimal concentration of dilution. In the bonddilution case, on the other hand, localized moments are always induced in pairs and they form a singlet again by AF interactions through the two-or three-dimensional shortest paths as long as the concentration of bond dilution is smaller than a finite critical value.In one dimension, since quantum fluctuations are much stronger than those in higher-dimensional systems, novel quantum critical phenomena are observed under disorder at the magnitude of coupling constants (bond randomness). Theoretically, the decimation renormalization group (DRG) approaches have achieved great success in predicting rich physics, such as the random-singlet (RS) phase for spin-1 2 chains.5-7 Recently, this technique has been extended to higher-spin cases, [8][9][10][11] where two of the main debates are on the robustness of the Haldane gap 12 against disorder and on the presence of the spin-1 RS phase. A number of numerical studies have also been carried out [13][14][15][16] to establish a quantitative phase diagram. However, this problem has not been sufficiently clarified yet. One of the main difficulties in simulating random quantum systems is the extremely wide energy scale that has to be taken into account. Another difficulty * Present address: Speech Interface Technology Group, NEC Corporation, Kawasaki 211-8666, Japan. † E-mail address: wistaria@ap.t.u-to...

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Phase Diagram of the Random Heisenberg Antiferromagnetic Spin-1 Chain

Cited by 35 publications

References 23 publications

Disorder-induced phases in theS=1antiferromagnetic Heisenberg chain

Disorder-induced phases in theS=1antiferromagnetic Heisenberg chain

Entanglement entropy in random quantum spin-Schains

Randomness-driven Quantum Phase Transition in Bond-alternating Haldane Chain

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