Random spin-1 quantum chains

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

doi:10.1016/0038-1098(96)00082-8

Cited by 38 publications

(57 citation statements)

References 11 publications

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“…Then, the problem becomes essentially non-perturbative for arbitrary distributions of exchange interactions. For instance, considering an arbitrary spin-S REHAC, the renormalized coupling is given by the recursive relation [22] …”

Section: -Renormalization Group Approach For Random Quantum Spin Cmentioning

confidence: 99%

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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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Section: -Renormalization Group Approach For Random Quantum Spin Cmentioning

confidence: 99%

“…Application of the generalized MDH procedure here results only in the formation of singlets, with the renormalized exchange coupling reading [22] ∆ ′ = 2 9…”

Section: Iii2 -Random Biquadratic Spin-1 Chainmentioning

confidence: 99%

Entanglement entropy in random quantum spin-Schains

et al. 2007

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“…In this section, we review the predictions of the analytic theory [17,18]. Some are contrastive to our numerical results shown later.…”

Section: Review Of the Predictions With The Real-space Decimation Anamentioning

confidence: 88%

“…It is quite suggestive that the realspace decimation theory becomes inapplicable for the cases other than S = 1/2. In order to adapt the decimation procedure even for the case S = 1, several authors proposed schemes to map the random S = 1 chain to an effective S = 1/2 model [17,18]. Their theory and the consequences are reviewed afterwards.…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of the bond-random antiferromagnetic S=1 Heisenberg chain

Nishiyama

1998

Physica A: Statistical Mechanics and its Applications

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Ground state of the bond-random antiferromagnetic S = 1 Heisenberg chain with the biquadratic interaction −β i (S i · S i+1 ) 2 is investigated by means of the exact-diagonalization method and the finite-size-scaling analysis. It is shown that the Haldane phase β ≈ 0 persists against the randomness; namely, no randomness-driven phase transition is observed until at a point of extremelybroad-bond distribution. We found that in the Haldane phase, the magnetic correlation length is kept hardly changed. These results are contrastive to those of an analytic theory which predicts a second-order phase transition between the Haldane and the random-singlet phases at a certain critical randomness.

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“…The existence of a gap in the excitation spectrum is not sufficient to guarantee the robustness of pure chain behavior with respect to the effects of disorder. For gapped biquadratic chains, any amount of disorder drives the system to a random singlet phase or infinite randomness fixed point [3]. If this is not the case for Haldane chains there may be a unique property of integer chains which confers them a special stability with respect to the introduction of disorder.…”

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confidence: 99%

Phase Diagram of the Random Heisenberg Antiferromagnetic Spin-1 Chain

2002

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We present a new perturbative real space renormalization group (RG) to study random quantum spin chains and other one-dimensional disordered quantum systems. The method overcomes problems of the original approach which fails for quantum random chains with spins larger than S = 1/2. Since it works even for weak disorder we are able to obtain the zero temperature phase diagram of the random antiferromagnetic Heisenberg spin-1 chain as a function of disorder. We find a random singlet phase for strong disorder and as disorder decreases, the system shows a crossover from a Griffiths to a disordered Haldane phase.The study of the effects of disorder on quantum systems is an actual and important area of research [1]- [17]. Intensive work on the last decades has deepened our understanding of the phase transitions which occur in pure quantum systems [18]. Now the main effort is concentrated in understanding the role of randomness in these transitions. This gives rise to new and interesting phenomena as the existence of Griffiths phases [2,7]. In this connection random quantum spin chains have been intensive investigated. In the pure case their behavior is well known [19]. Also for spin−1/2 quantum antiferromagnetic chains a perturbative approach developed by Ma, Dasgupta and Hu (M DH) [1] and extended by Fisher [2] allows to obtain results which are essentially exact for this system. The picture which emerges for these chains is described by a random singlet phase (RSP ) where spins are coupled in pairs over arbitrary distances. In the renormalization group approach this random singlet phase is governed by an infinite randomness fixed point [2,7,17]. A straightforward extension of the M DH method for biquadratic spin−1 chains has shown that in the Heisenberg case the perturbative RG approach may fail even for the case of strong disorder [3]. The reason is that in the elimination process of strong interactions, in which consists the M DH approach, interactions stronger than those eliminated are generated. This failure is better demonstrated when the method is extended to finite temperatures where it gives rise to non-physical behavior as negative specific heat and so on [6]. Several proposals have been put forward to extend the M DH method for quantum spin chains, with S > 1/2 [11]-[14], without undisputed success. The challenge in the case of quantum integer spin chains is particularly exciting as it deals with the question of the fate of the Haldane phase [20] in the presence of disorder. The existence of a gap in the excitation spectrum is not sufficient to guarantee the robustness of pure chain behavior with respect to the effects of disorder. For gapped biquadratic chains, any amount of disorder drives the system to a random singlet phase or infinite randomness fixed point [3]. If this is not the case for Haldane chains there may be a unique property of integer chains which confers them a special stability with respect to the introduction of disorder. In fact Hida [16] using a density matrix renormalization group app...

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Random spin-1 quantum chains

Cited by 38 publications

References 11 publications

Entanglement entropy in random quantum spin-Schains

Entanglement entropy in random quantum spin-Schains

Numerical analysis of the bond-random antiferromagnetic S=1 Heisenberg chain

Phase Diagram of the Random Heisenberg Antiferromagnetic Spin-1 Chain

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