Properties of the random-singlet phase: From the disordered Heisenberg chain to an amorphous valence-bond solid

Shu, Yu-Rong; Yao, Dao‐Xin; Ke, Chih-Wei; Lin, Yueh-hsiang; Sandvik, Anders W.

doi:10.1103/physrevb.94.174442

Cited by 29 publications

(48 citation statements)

References 56 publications

(107 reference statements)

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“…Motivated by the entanglement entropy in the random singlet phase of the random S = 1/2 spin chain, entanglement measure through valence bond entanglement has been proposed for SU (2) quantum systems [131], which can be efficiently measured through quantum MC calculations both in one-and two-dimensions [132,133].…”

Section: A Random Quantum Chainsmentioning

confidence: 99%

Strong disorder RG approach – a short review of recent developments

Iglói

Monthus

2018

Eur. Phys. J. B

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Relations between SDRG and Entanglement-Algorithms 10 VI. Localized and Many-Body-Localized Phases of quantum spin chains 11 A. RSRG-X for excited eigenstates 11 B. RSRG-t for the unitary dynamics 11 C. Non-equilibrium dynamical scaling of observables 12 D. Comparison with other RG procedures existing in the field of Many-Body-Localization 13 VII. Floquet dynamics of periodically driven chains in their localized phases 13 VIII. Open dissipative quantum spin chains 13 A. Quantum spin chains coupled to a bath of quantum oscillators 13 B. Lindblad dynamics for random quantum spin chains 14 IX. Anderson localization models 14 X. Random contact process 14 A. Strong disorder RG rules 15 B. Long range spreading 15 C. Temporal disorder 15 XI. Classical master equations 16 A. Real-space renormalization for random walks in random media 16 B. RG in configuration-space for the dynamics of classical many-body models 16 XII. Random classical oscillators 17 A. Random elastic networks 17 B. Synchronisation of interacting non-linear dissipative classical oscillators 17 XIII. Other classical models 17 A. Equilibrium properties of random systems 17 B. Extremes of stochastic processes 18 XIV. Conclusion 18

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Section: A Random Quantum Chainsmentioning

confidence: 99%

Strong disorder RG approach – a short review of recent developments

Iglói

Monthus

2018

Eur. Phys. J. B

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“…Surprisingly, we have determined an accurate scaling as quantified in Eqs. (14) and (17) for the mean transverse correlations and the typical ones, respectively. In general, these prefactors and their scaling with a crossover length depend on the dimensions of the related relevant and irrelevant operators.…”

Section: Discussionmentioning

confidence: 99%

“…Corrections to the SDRG prediction were reported in the literature over the years, ranging from non-universal critical exponents [41] to logarithmic corrections [14,43]. Here, we have Finally, and just for completeness, we end our study on the mean correlations by focusing only on the main culprits for their behavior: the rare singlet pairs of the random-singlet state (depicted in Fig.…”

Section: Iii13 Mimicking Logarithmic Correctionsmentioning

confidence: 97%

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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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“…52 Recently, a Quantum Monte Carlo study proposed a logarithmic correction to the correlation function for the Heisenberg model. 22 It is not within the scope of the present work to further investigate this feature which would require longer chains and better statistics. Here, we simply report that our data are also compatible with it as shown in Fig.…”

Section: Dmrg Studymentioning

confidence: 95%

Adaptive density matrix renormalization group for disordered systems

2018

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We propose a simple modification of the density matrix renormalization group (DMRG) method in order to tackle strongly disordered quantum spin chains. Our proposal, akin to the idea of the adaptive time-dependent DMRG, enables us to reach larger system sizes in the strong disorder limit by avoiding most of the metastable configurations which hinder the performance of the standard DMRG method. We benchmark our adaptive method by revisiting the random antiferromagnetic XXZ spin-1/2 chain for which we compute the randomsinglet ground-state average spin-spin correlation functions and von Neumann entanglement entropy. We then apply our method to the bilinear-biquadratic random antiferromagnetic spin-1 chain tuned to the antiferromagnet and gapless highly symmetric SU(3) point. We find the new result that the mean correlation function decays algebraically with the same universal exponent φ = 2 as the spin-1/2 chain. We then perform numerical and analytical strong-disorder renormalization-group calculations, which confirm this finding and generalize it for any highly symmetric SU(N) random-singlet state.

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Properties of the random-singlet phase: From the disordered Heisenberg chain to an amorphous valence-bond solid

Cited by 29 publications

References 56 publications

Strong disorder RG approach – a short review of recent developments

Strong disorder RG approach – a short review of recent developments

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

Adaptive density matrix renormalization group for disordered systems

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