Entanglement renormalization for disordered systems

Goldsborough, Andrew M.; Evenbly, Glen

doi:10.1103/physrevb.96.155136

Cited by 23 publications

(20 citation statements)

References 44 publications

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“…1. It would also be interesting to try to apply an adaptation of the dMera of [58] to answer the question regarding the scaling of the EE in our disordered system.…”

Section: Discussionmentioning

confidence: 99%

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Strange metal from local quantum chaos

Ben-Zion

McGreevy

2018

Phys. Rev. B

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How to make a model of a non-Fermi-liquid metal with efficient current dissipation is a long-standing problem. Results from holographic duality suggest a framework where local critical fermionic degrees of freedom provide both a source of decoherence for the Landau quasiparticle, and a sink for its momentum. This leads us to study a Kondo lattice type model with SYK models in place of the spin impurities. We find evidence for a stable phase at intermediate couplings.1 For a review of the large literature, see [1]. 2 For a more leisurely discussion of these issues, see also §5 of [7].The model is a rather direct and crude discretization of the AdS 2 × R d near-horizon

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“…1. It would also be interesting to try to apply an adaptation of the dMera of [58] to answer the question regarding the scaling of the EE in our disordered system.…”

Section: Discussionmentioning

confidence: 99%

“…Another possiblity is that the apparent rejoining with the free fermion value is related to a previously-observed difficulty in the use of DMRG algorithms for disordered critical systems [58]. If we parametrize the EE as…”

Section: Numerical Analysismentioning

confidence: 99%

Strange metal from local quantum chaos

Ben-Zion

McGreevy

2018

Phys. Rev. B

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“…Since Tensor-Networks have become very popular in recent years, it is interesting to point out that the SDRG actually corresponds to a special type of Multi-scale-Entanglement-Renormalization-Ansatz (MERA) (see section IV of the review [140]) and has been integrated into various tensor-network algorithms [48,[141][142][143][144]. Recently, in analogy with SDRG, a Strong-Disorder-Disentangling procedure [145] has been introduced : at each step, one chooses the most strongly entangled pair of sites, in order to construct iteratively the appropriate unitary circuit that transforms a given quantum state into an unentangled product state.…”

Section: Relations Between Sdrg and Entanglement-algorithmsmentioning

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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“…[41] selections of blocks for the renormalization were adjusted to the specific models under consideration; in Ref. [42] optimization using variational energy minimization after coarse-graining was introduced, as an extension of tSDRG and the multiscale entanglement renormalization ansatz (MERA) [43,44]. An interesting question is whether these improved tSDRG methods can obtain the logarithmic corrections found in QMC calculations.…”

Section: Summary and Discussionmentioning

confidence: 99%

Tensor network renormalization group study of spin-1 random Heisenberg chains

2020

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We use a tensor network strong-disorder renormalization group (tSDRG) method to study spin-1 random Heisenberg antiferromagnetic chains. The ground state of the clean spin-1 Heisenberg chain with uniform nearest-neighbor couplings is a gapped phase known as the Haldane phase. Here we consider disordered chains with random couplings, in which the Haldane gap closes in the strong disorder regime. As the randomness strength is increased further and exceeds a certain threshold, the random chain undergoes a phase transition to a critical random-singlet phase. The strong-disorder renormalization group method formulated in terms of a tree tensor network provides an efficient tool for exploring ground-state properties of disordered quantum many-body systems. Using this method we detect the quantum critical point between the gapless Haldane phase and the randomsinglet phase via the disorder-averaged string order parameter. We determine the critical exponents related to the average string order parameter, the average end-to-end correlation function and the average bulk spin-spin correlation function, both at the critical point and in the random-singlet phase. Furthermore, we study energy-length scaling properties through the distribution of energy gaps for a finite chain. Our results are in closer agreement with the theoretical predictions than what was found in previous numerical studies. As a benchmark, a comparison between tSDRG results for the average spin correlations of the spin-1/2 random Heisenberg chain with those obtained by using unbiased zero-temperature QMC method is also provided.

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Entanglement renormalization for disordered systems

Cited by 23 publications

References 44 publications

Strange metal from local quantum chaos

Strange metal from local quantum chaos

Strong disorder RG approach – a short review of recent developments

Tensor network renormalization group study of spin-1 random Heisenberg chains

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