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

Abstract

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...

Disorder-induced phases in theS=1antiferromagnetic Heisenberg chain

“…This latter system is studied in great detail by Fisher 4 with the asymptotically exact strong disorder RG method and these results have been confronted with detailed numerical investigations. 28,29,30 Here we repeat that in the RS phase there is infinite disorder scaling, so that relations in Eqs. (13) and (14) are valid with an exponent, ψ = 1/2.…”

Some basic aspects of quantum phase transitions

“…A density matrix RG theory [196] was applied to the one-dimensional (chain) randomexchange spin-1/2 XXZ model [197]. The interplay of quantum fluctuations and disorder results in a disorder-induced quantum phase transition that exhibits a nonuniversal behaviour of the spin correlations.…”

Crossover effects in the random-exchange spin-12antiferromagnetic chain

“…(4)]. However, a recent density matrix renormalization group (DMRG) calculation 18 for chains (with free boundary conditions) defined by Eq. (3) with weak randomness in the planar exchanges caused a debate, 19 which we intend to settle in this paper.…”