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arXiv:2112.10420 · Physical review. B./Physical review. B

Adaptive density matrix renormalization group study of the disordered antiferromagnetic spin- 12 Heisenberg chain

Alexander H. O. Wada, José A. Hoyos

Published Mar 24, 2022• 7 citations
arXivHTMLPDF

Abstract

Using an adaptive strategy which enables the study of quenched disordered system via the density-matrix renormalization-group method, we compute the various ground-state spin-spin correlation measures of the spin-$\frac{1}{2}$ antiferromagnetic Heisenberg chain with random coupling constants, namely, the mean values of the bulk and of the end-to-end correlations, the typical value of the bulk correlations, and the distribution of the bulk correlations. Our results are in agreement with the predictions of the strong-disorder renormalization-group method. We do not find any hint of logarithmic corrections either in the bulk average correlations, which were recently reported by Shu et al. [Phys. Rev. B 94, 174442 (2016)], or in the end-to-end average correlations. We report the existence of a logarithmic correction on the end-to-end correlations of the clean chain. Finally, we have determined that the distribution of the bulk correlations, when properly rescaled by an associated Lyapunov exponent, is a narrow and universal (disorder-independent) probability function.

DOI
10.1103/physrevb.105.104205

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Using an adaptive strategy which enables the study of quenched disordered system via the density-matrix renormalization-group method, we compute the various ground-state spin-spin correlation measures of the spin-12\frac{1}{2}21​ antiferromagnetic Heisenberg chain with random coupling constants, namely, the mean values of the bulk and of the end-to-end correlations, the typical value of the bulk correlations, and the distribution of the bulk correlations. Our results are in agreement with the predictions of the strong-disorder renormalization-group method. We do not find any hint of logarithmic corrections either in the bulk average correlations, which were recently reported by Shu et al. [Phys. Rev. B 94, 174442 (2016)], or in the end-to-end average correlations. We report the existence of a logarithmic correction on the end-to-end correlations of the clean chain. Finally, we have determined that the distribution of the bulk correlations, when properly rescaled by an associated Lyapunov exponent, is a narrow and universal (disorder-independent) probability function.
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We revisit the spin-reduction transition in the random spin-3/23/23/2 antiferromagnetic Heisenberg chain using the tensor-network strong-disorder renormalization group (tSDRG). The predicted transition separates two random-singlet (RS) phases: one formed by effective spin-1/21/21/2 moments at weaker disorder and the other by full spin-3/23/23/2 moments at stronger disorder. Within the Damle--Huse classification, this transition corresponds to an emergent permutation-symmetric P4P_4P4​ multicritical point on a P2P_2P2​ critical line associated with the RS phases. We first derive the critical exponents governing the disorder-averaged bulk and end-to-end correlation functions in the PnP_nPn​ universality classes within the Damle--Huse framework. Using these theoretical predictions, together with a diagnostic constructed from the mean and variance of the energy-gap distribution, we identify the P4P_4P4​ transition point and the reentrant behavior of the RS phase.
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