Permutation-symmetric critical phases in disordered non-Abelian anyonic chains

Fidkowski, Lukasz; Lin, Haijin; Titum, Paraj; Refael, Gil

doi:10.1103/physrevb.79.155120

Cited by 28 publications

(38 citation statements)

References 19 publications

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“…Non-abelian order is a particular feature in twodimensional quantum systems and non-abelian excitations are present in fractional quantum Hall states. Chains of interacting anyonic quasiparticles are introduced recently and their properties in the presence of quenched disorder has been studied through the SDRG method [73][74][75][76].…”

Section: Disordered Non-abelian Anyonic 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: Disordered Non-abelian Anyonic Chainsmentioning

confidence: 99%

Strong disorder RG approach – a short review of recent developments

Iglói

Monthus

2018

Eur. Phys. J. B

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“…For k odd, it was shown in Ref. [45] that all fixed points arising in these models (i.e., nearest neighbor random chains) are indeed infinite randomness fixed points. A bit disappointingly, all of these fixed points belong to the Damle-Huse hierarchy; the permutation symmetric points of spin-s Heisenberg models are realized in k = 2s + 1 truncated SU(2) k models; some intuition to this relationship is that the types of nonabelian anyons are mapped into domains in the spin-models.…”

Section: 43mentioning

confidence: 99%

“…As non-abelian anyons are expected to appear as defects in quantum Hall states such as 5/2 or 12/5 [38,39], it is natural to ask how a disordered system of such anyons behaves. The study of random non-abelian chains as started with the consideration of the random-singlet phase of Majorana fermions, and Fibonacci anyons [28,44], and continued with the study of infinite randomness fixed points in the more general class of non-abelian chains, the truncated SU(2) k systems [45].…”

Section: Infinite-randomness Fixed Points Of Non-abelian Anyonsmentioning

confidence: 99%

Criticality and entanglement in random quantum systems

Refael¹,

Moore²

2009

J. Phys. A: Math. Theor.

101

102

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Abstract. We review studies of entanglement entropy in systems with quenched randomness, concentrating on universal behavior at strongly random quantum critical points. The disorder-averaged entanglement entropy provides insight into the quantum criticality of these systems and an understanding of their relationship to non-random ("pure") quantum criticality. The entanglement near many such critical points in one dimension shows a logarithmic divergence in subsystem size, similar to that in the pure case but with a different universal coefficient. Such universal coefficients are examples of universal critical amplitudes in a random system. Possible measurements are reviewed along with the one-particle entanglement scaling at certain Anderson localization transitions. We also comment briefly on higher dimensions and challenges for the future.Criticality and entanglement in random quantum systems 2

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“…Previous studies of thermalization in the pinned nonAbelian anyons models have been restricted to the strongly disordered context [43][44][45][46][47][48] . All these works suggest that it is hard to localize energy in anyon chains.…”

Section: Introductionmentioning

confidence: 99%

The eigenstate thermalization hypothesis in constrained Hilbert spaces: A case study in non-Abelian anyon chains

2016

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Many phases of matter, including superconductors, fractional quantum Hall fluids and spin liquids, are described by gauge theories with constrained Hilbert spaces. However, thermalization and the applicability of quantum statistical mechanics has primarily been studied in unconstrained Hilbert spaces. In this article, we investigate whether constrained Hilbert spaces permit local thermalization. Specifically, we explore whether the eigenstate thermalization hypothesis (ETH) holds in a pinned Fibonacci anyon chain, which serves as a representative case study. We first establish that the constrained Hilbert space admits a notion of locality, by showing that the influence of a measurement decays exponentially in space. This suggests that the constraints are no impediment to thermalization. We then provide numerical evidence that ETH holds for the diagonal and offdiagonal matrix elements of various local observables in a generic disorder-free non-integrable model. We also find that certain non-local observables obey ETH.

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Permutation-symmetric critical phases in disordered non-Abelian anyonic chains

Cited by 28 publications

References 19 publications

Strong disorder RG approach – a short review of recent developments

Strong disorder RG approach – a short review of recent developments

Criticality and entanglement in random quantum systems

The eigenstate thermalization hypothesis in constrained Hilbert spaces: A case study in non-Abelian anyon chains

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