Adaptive density matrix renormalization group for disordered systems

Xavier, J. C.; Hoyos, José A.; Miranda, E.

doi:10.1103/physrevb.98.195115

Cited by 11 publications

(7 citation statements)

References 54 publications

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“…Therefore, the mean C µ i,j and typical C µ,typ i,j values of the correlation function are those of the SU(N ) symmetric models, already reported in the literature. 36,44 Thus,…”

Section: Emergent Su(n) Symmetrymentioning

confidence: 99%

Highly symmetric random one-dimensional spin models

et al. 2019

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The interplay of disorder and interactions is a challenging topic of condensed matter physics, where correlations are crucial and exotic phases develop. In one spatial dimension, a particularly successful method to analyze such problems is the strong-disorder renormalization group (SDRG). This method, which is asymptotically exact in the limit of large disorder, has been successfully employed in the study of several phases of random magnetic chains. Here we develop an SDRG scheme capable to provide in-depth information on a large class of strongly disordered one-dimensional magnetic chains with a global invariance under a generic continuous group. Our methodology can be applied to any Lie-algebra valued spin Hamiltonian, in any representation. As examples, we focus on the physically relevant cases of SO(N) and Sp(N) magnetism, showing the existence of different randomness-dominated phases. These phases display emergent SU(N) symmetry at low energies and fall in two distinct classes, with meson-like or baryon-like characteristics. Our methodology is here explained in detail and helps to shed light on a general mechanism for symmetry emergence in disordered systems. arXiv:1711.04783v2 [cond-mat.str-el]

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“…Therefore, the mean C µ i,j and typical C µ,typ i,j values of the correlation function are those of the SU(N ) symmetric models, already reported in the literature. 36,44 Thus,…”

Section: Emergent Su(n) Symmetrymentioning

confidence: 99%

Highly symmetric random one-dimensional spin models

et al. 2019

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“…The universality of the exponent η was disputed some years ago [41], but there is now a consensus that this is an exact result [10,[42][43][44]. Numerical confirmations of the constants c e,o,α are much more difficult [12,34].…”

Section: Ii2 Some Known Results For the Case Of Uncorrelated Couplingsmentioning

confidence: 99%

The correlation functions of certain random antiferromagnetic spin-1∕2 critical chains

Getelina

Hoyos

2020

Eur. Phys. J. B

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We study the spin-spin correlations in two distinct random critical XX spin-1/2 chain models via exact diagonalization. For the well-known case of uncorrelated random coupling constants, we study the non-universal numerical prefactors and relate them to the corresponding Lyapunov exponent of the underlying single-parameter scaling theory. We have also obtained the functional form of the correct scaling variables important for describing even the strongest finite-size effects. Finally, with respect to the distribution of the correlations, we have numerically determined that they converge to a universal (disorder-independent) non-trivial and narrow distribution when properly rescaled by the spin-spin separation distance in units of the Lyapunov exponent. With respect to the less known case of correlated coupling constants, we have determined the corresponding exponents and shown that both typical and mean correlations functions decay algebraically with the distance. While the exponents of the transverse typical and mean correlations are nearly equal, implying a narrow distribution of transverse correlations, the longitudinal typical and mean correlations critical exponents are quite distinct implying much broader distributions. Further comparisons between this models are given.

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“…In order to circumvent this problem, we employ the recently introduced adaptive DMRG (aDMRG) method [29] to obtain the ground-state spin-spin correlation function. The idea is to apply the standard DMRG method to a clean or nearly clean system (where it works efficiently well) in order to obtain a good representation of the ground state |ψ D 0 and then modify it adiabatically by increasing the disorder strength D in small steps D → D + δD.…”

Section: Disorder Description and Methodsmentioning

confidence: 99%

Adaptive Density-Matrix Renormalization-Group study of the disordered antiferromagnetic spin-1/2 Heisenberg chain

Wada,

Hoyos

2021

Preprint

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Using the recently introduced adaptive density-matrix renormalization-group method, we study the many spin-spin correlations of the spin-1/2 antiferromagnetic Heisenberg chain with random coupling constants, namely, the mean value 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 striking agreement with the predictions of the strong-disorder renormalization group method. We do not find any hint of logarithmic corrections neither in the bulk average correlations, which were recently reported by Shu et al. [Phys. Rev. B 94,174442 (2016)], nor in the end-to-end average correlations. We report computed the existence of logarithmic correction on the end-toend 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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Adaptive density matrix renormalization group for disordered systems

Cited by 11 publications

References 54 publications

Highly symmetric random one-dimensional spin models

Highly symmetric random one-dimensional spin models

The correlation functions of certain random antiferromagnetic spin-1∕2 critical chains

Adaptive Density-Matrix Renormalization-Group study of the disordered antiferromagnetic spin-1/2 Heisenberg chain

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