Shannon and Rényi mutual information in quantum critical spin chains

Stéphan, Jean-Marie

doi:10.1103/physrevb.90.045424

Cited by 60 publications

(92 citation statements)

References 70 publications

(175 reference statements)

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“…In the limit n → 1, F para (ω, n, β) (see (31)) does not depend on q 0 and ω, as expected. This holds for any β even including the effects of the replica symmetry breaking.…”

Section: A the Paramagnetic Phasesupporting

confidence: 81%

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Classical mutual information in mean-field spin glass models

2016

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We investigate the classical Rényi entropy Sn and the associated mutual information In in the SherringtonKirkpatrick (S-K) model, which is the paradigm model of mean-field spin glasses. Using classical Monte Carlo simulations and analytical tools we investigate the S-K model on the n-sheets booklet. This is obtained by gluing together n independent copies of the model, and it is the main ingredient to construct the Rényi entanglementrelated quantities. We find a glassy phase at low temperature, whereas at high temperature the model exhibits paramagnetic behavior, consistent with the regular S-K model. The temperature of the paramagnetic-glassy transition depends non-trivially on the geometry of the booklet. At high-temperatures we provide the exact solution of the model by exploiting the replica symmetry. This is the permutation symmetry among the fictitious replicas that are used to perform disorder averages (via the replica trick). In the glassy phase the replica symmetry has to be broken. Using a generalization of the Parisi solution, we provide analytical results for Sn and In, and for standard thermodynamic quantities. Both Sn and In exhibit a volume law in the whole phase diagram. We characterize the behavior of the corresponding densities Sn/N, In/N , in the thermodynamic limit. Interestingly, at the critical point the mutual information does not exhibit any crossing for different system sizes, in contrast with local spin models.

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“…In the limit n → 1, F para (ω, n, β) (see (31)) does not depend on q 0 and ω, as expected. This holds for any β even including the effects of the replica symmetry breaking.…”

Section: A the Paramagnetic Phasesupporting

confidence: 81%

“…For n = 1 Eq. (2) defines the subsystem Shannon entropy 30,31 . From S n (A), one defines the classical mutual information I n (A, B) as I n (A, B) ≡ S n (A) + S n (B) − S n (A ∪ B).…”

Section: Introductionmentioning

confidence: 99%

Classical mutual information in mean-field spin glass models

2016

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“…, and x 0 denotes the leftmost site of the chain. The computation of I x involves two-point correlation functions and it quantifies the total amount of classical and quantum correlations in the system [74][75][76][77][78][79] . The QMI for two sites has been shown to be a useful probe to detect a MIT.…”

Section: Algebraic Localizationmentioning

confidence: 99%

Algebraic many-body localization and its implications on information propagation

Tomasi

2019

Phys. Rev. B

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We probe the existence of a many-body localized phase (MBL-phase) in a spinless fermionic Hubbard chain with algebraically localized single-particle states, by investigating both static and dynamical properties of the system. This MBL-phase can be characterized by an extensive number of integrals of motion which develop algebraically decaying tails, unlike the case of exponentially localized single-particle states. We focus on the implications for the quantum information propagation through the system. We provide evidence that the bipartite entanglement entropy after a quantum quench has an unbounded algebraic growth in time, while the quantum Fisher information grows logarithmically.

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“…More recently, the wavefunctions of manybody quantum systems have been analyzed via multifractality for ground states in pure quantum spin models [80][81][82][83][84][85][86][87][88][89][90][91][92][93], as well as for excited states in MBL models [10,[94][95][96].…”

Section: Bmentioning

confidence: 99%

Many-body-localization transition: strong multifractality spectrum for matrix elements of local operators

Monthus¹

2016

J. Stat. Mech.

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For short-ranged disordered quantum models in one dimension, the Many-Body-Localization is analyzed via the adaptation to the Many-Body context [M. Serbyn, Z. Papic and D.A. Abanin, PRX 5, 041047 (2015)] of the Thouless point of view on the Anderson transition : the question is whether a local interaction between two long chains is able to reshuffle completely the eigenstates (Delocalized phase with a volume-law entanglement) or whether the hybridization between tensor states remains limited (Many-Body-Localized Phase with an area-law entanglement). The central object is thus the level of Hybridization induced by the matrix elements of local operators, as compared with the difference of diagonal energies. The multifractal analysis of these matrix elements of local operators is used to analyze the corresponding statistics of resonances. Our main conclusion is that the critical point is characterized by the Strong-Multifractality Spectrum f (0 ≤ α ≤ 2) = α 2 , well known in the context of Anderson Localization in spaces of effective infinite dimensionality, where the size of the Hilbert space grows exponentially with the volume. Finally, the possibility of a delocalized non-ergodic phase near criticality is discussed.

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Shannon and Rényi mutual information in quantum critical spin chains

Cited by 60 publications

References 70 publications

Classical mutual information in mean-field spin glass models

Classical mutual information in mean-field spin glass models

Algebraic many-body localization and its implications on information propagation

Many-body-localization transition: strong multifractality spectrum for matrix elements of local operators

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