Violation of the Bell inequality in quantum critical random spin-1/2 chains

Getelina, João C.; Oliveira, Thiago R. de; Hoyos, José A.

doi:10.1016/j.physleta.2018.08.003

Cited by 7 publications

(9 citation statements)

References 39 publications

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“…7. Surprisingly, the observed data (not shown here) exhibits a drop in the correlations (due to the inability of capturing the longest and weakest coupled spin pairs) compatible with a logarith- mic correction of type (15) with negative exponent of order 1, compatible with that reported in Ref. 43.…”

Section: Iii13 Mimicking Logarithmic Correctionssupporting

confidence: 88%

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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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Section: Iii13 Mimicking Logarithmic Correctionssupporting

confidence: 88%

“…Mean transverse correlation function C xx (r) plotted according to Eq (15). for even separations r, considering various disorder strengths D and chain sizes L. The upturn for L = 100 is due to the periodic boundary condition.…”

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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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“…The SDRG approach has also been used to study the critical properties of aperiodic quantum spin chains [116][117][118][119] and their entanglement entropy is calculated in the strong aperiodicity limit [120,121]. Other entanglement measures have been also studied in random quantum chains, like the entanglement [122,123] or the concurrence [124] between distant pairs of q-bits, the full entanglement spectrum of random singlet critical points [125], the Rényi entropies [126], the fluctuations of the entanglement entropy [127], the full probability distribution of the entanglement entropy [128], the Schmidtgap ( i.e. the difference between the two largest eigenvalues of the entanglement spectrum) for the RTIM and for the S = 1 random spin chain [129].…”

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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“…Ultimately, non-locality is only manifest when considering a scenario involving multiple physical systems, be them black-boxes in the device independent scenario or actual quantum systems. In particular, non-locality in many-body quantum systems has been extensively explored [5][6][7][8][9][10][11][12][13][14][15][16][17][18], see [19] for a review. For instance, it has been discussed in the literature how to use nonlocality measurements as an indicator of quantum phase transitions (QPT's) in several many-body systems models [12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Bell Non-Locality in Many Body Quantum Systems with Exponential Decay of Correlations

Vieira,

Duarte,

Drumond

et al. 2020

Preprint

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Using Bell-inequalities as a tool to explore non-classical physical behaviours, in this paper we analyse what one can expect to find in many-body quantum physics. Concretely, framing the usual correlation scenarios as a concrete spin-lattice, we want know whether or not it is possible to violate a Bell-inequality restricted to this scenario. Using clustering theorems, we are able to show that a large family of quantum many-body systems behave almost locally, violating Bell-inequalities (if so) only by a non-significant amount. We also provide examples, explain some of our assumptions via counter-examples and present all the proofs for our theorems. We hope the paper is self-contained.

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Violation of the Bell inequality in quantum critical random spin-1/2 chains

Cited by 7 publications

References 39 publications

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

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

Strong disorder RG approach – a short review of recent developments

Bell Non-Locality in Many Body Quantum Systems with Exponential Decay of Correlations

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