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arXiv:cond-mat/0111027 · Physical Review Letters

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

Kay Hamacher, Joachim Stolze, Wolfgang Wenzel

Published Aug 28, 2002• 23 citations
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Abstract

We investigate the effect of quenched bond disorder on the anisotropic antiferromagnetic spin-1/2 (XXZ) chain as a model for disorder-induced quantum phase transitions. We find nonuniversal 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.

DOI
10.1103/physrevlett.89.127202

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Comment on “Disorder Induced Quantum Phase Transition in Random-Exchange Spin- 1/2 Chains”

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arXiv:cond-mat/9308026•Physical review. B, Condensed matter•Nov 1, 1993•16 citations
We investigate the effect of quenched bond disorder on the anisotropic antiferromagnetic spin-1/2 (XXZ) chain as a model for disorder-induced quantum phase transitions. We find nonuniversal 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.
The zero-temperature phase diagram of the anisotropic, strongly disordered antiferromagnetic quantum spin-1 chain is investigated, within the framework of a real-space renormalization-group approach. In the presence of uniform anisotropy there occurs a phase transition from a random singlet phase to an Ising antiferromagnetic phase controlled by a fixed point that does not have Heisenberg symmetry. We find evidence of a fixed point due to randomness in the anisotropy similar to that which occurs for quantum Heisenberg spin-12\frac{1}{2}21​ chains.
We reconsider the random bond antiferromagnetic spin-1/2 chain for weak disorder and demonstrate the existence of crossover length scale x_W that diverges with decreasing strength of the disorder. Recent DMRG calculations [Phys. Rev. Lett. 89, 127202 (2002); cond-mat/0111027] claimed to have found evidence for a non-universal behavior in this model and found no indications of a universal infinite randomness fixed point (IRFP) scenario. We show that these data are not in the asymptotic regime since the system sizes that have been considered are of the same order of magnitude or much smaller than the crossover length x_W. We give a scaling form for the xx-spin-correlation function that takes this crossover length into account and that is compatible with the IRFP scenario and a random singlet phase.
We have carried out Monte Carlo studies of a random-exchange antiferromagnetic spin-(1/2) chain. For systems with XY-like (anisotropic) and with Heisenberg (isotropic) coupling, our results confirm the existence of a disorder-induced low-temperature (T) divergence in the long-wavelength Sz{S}^{z}Sz-Sz{S}^{z}Sz susceptibility \ensuremath{\chi} which was previously predicted by real-space renormalization-group (RSRG) treatments. Over the finite temperature range studied, these results are consistent with a 1/(T ln2{\mathrm{ln}}^{2}ln2T) behavior of \ensuremath{\chi}, and hence in qualitative agreement with the RSRG results. As in the XY-Heisenberg regime, we also find a disorder-induced enhancement of the low-T susceptibility for a system with Ising-like exchange coupling which, over the finite temperature range studied, is again consistent with RSRG results. However, there are inconsistencies between the RSRG predictions in the Ising-like regime at very low temperatures, and the exact results for the random-exchange Ising chain and the low-temperature behavior of \ensuremath{\chi} in the Ising-like regime may in fact be more complicated than predicted by RSRG. Finally, we also present results for the antiferromagnetic susceptibility and structure factor. For both Heisenberg and Ising-like systems, we find that disorder suppresses the long-range antiferromagnetic correlations at low T.
We analyze the zero-temperature phase diagram of the spin-1/2 quantum XXZ chain in the presence of weak disorder. The effects of various random perturbations are considered, including random fields and random exchange. For random perturbations that preserve the XY symmetry, we find a phase transition, as the anisotropy parameter is varied, from a ground state with quasi-long-range order (as in the pure system) to one in which typical correlation functions decay rapidly. The critical behavior at this transition is shown to be in the universality class of the Giamarchi-Schulz transition for one-dimensional bosons in a random potential. Random perturbations that break the XY symmetry are found always to destroy the quasi-long-range order of the ground state. Properties of the resulting random phases are also discussed.
Spin chains with quenched disorder exhibit rich critical behavior, often captured by real-space renormalization group (RSRG) techniques. However, the physics of such systems in the presence of random measurements (i.e., non-Hermitian dephasing) remains largely unexplored. The interplay between measurements and unitary dynamics gives rise to novel phases and phase transitions in monitored quantum systems. In this work, we investigate the disordered XX spin chain subject to stochastic local measurements in the XXX and YYY bases. By mapping the monitored chain to a non-Hermitian spin ladder with complex couplings, we propose an RSRG-for-excited-states (RSRG-X) approach for this open-system setting. Our analysis reveals a new class of strongly disordered fixed points that emerge due to non-unitarity, broadening the landscape of critical phenomena accessible via RSRG.
The one-dimensional XXZ model is studied in the presence of disorder in the Heisenberg exchange integral. Recent predictions obtained from renormalization-group calculations are investigated numerically using a Lanczos algorithm on chains of up to 18 sites. It is found that in the presence of strong X-Y-symmetric random-exchange couplings, a ``random singlet'' phase with quasi-long-range order in the spin-spin correlations persists. As the planar anisotropy is varied, the full zero-temperature phase diagram is obtained and compared with predictions of Doty and Fisher [Phys. Rev. B 45, 2167 (1992)]. In addition, we observed a novel reentrant transition of the ordered phases when exchange disorder is included.