Classical mutual information in mean-field spin glass models

Alba, Vincenzo; Inglis, Stephen; Pollet, Lode

doi:10.1103/physrevb.93.094404

Cited by 7 publications

(11 citation statements)

References 57 publications

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“…The non-equilibrium features of the entanglement in these random spin chains are also under intensive investigation 51,[68][69][70][71][72][73][74][75] . The behavior of entanglement related quantities in classical disordered spin systems has been explored 76 .…”

Section: Introductionmentioning

confidence: 99%

Entanglement negativity in random spin chains

2016

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We investigate the logarithmic negativity in strongly-disordered spin chains in the random-singlet phase. We focus on the spin-1/2 random Heisenberg chain and the random XX chain. We find that for two arbitrary intervals the disorder-averaged negativity and the mutual information are proportional to the number of singlets shared between the two intervals. Using the strong-disorder renormalization group (SDRG), we prove that the negativity of two adjacent intervals grows logarithmically with the intervals length. In particular, the scaling behavior is the same as in conformal field theory, but with a different prefactor. For two disjoint intervals the negativity is given by a universal simple function of the cross ratio, reflecting scale invariance. As a function of the distance of the two intervals, the negativity decays algebraically in contrast with the exponential behavior in clean models. We confirm our predictions using a numerical implementation of the SDRG method. Finally, we also implement DMRG simulations for the negativity in open spin chains. The chains accessible in the presence of strong disorder are not sufficiently long to provide a reliable confirmation of the SDRG results.

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Section: Introductionmentioning

confidence: 99%

Entanglement negativity in random spin chains

2016

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“…A relation to the Casimir energy problem is also established in 14,15 . The FP can be also used to find the Shannon entropy with plethora of applications in the studies of quantum phase transitions, see [18][19][20][21][22][23][24][25][26][27][28] .…”

Section: Introductionmentioning

confidence: 99%

Formation probabilities and statistics of observables as defect problems in free fermions and quantum spin chains

Najafi

Rajabpour

2020

Phys. Rev. B

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We show that the computation of formation probabilities (FP) in the configuration basis and the full counting statistics (FCS) of observables in the quadratic fermionic Hamiltonians are equivalent to the calculation of emptiness formation probability (EFP) in the Hamiltonian with a defect. In particular, we first show that the FP of finding a particular configuration in the ground state is equivalent to the EFP of the ground state of the quadratic Hamiltonian with a defect. Then, we show that the probability of finding a particular value for any quadratic observable is equivalent to a FP problem and ultimately leads to the calculation of EFP in the ground state of a Hamiltonian with a defect. We provide new exact determinant formulas for the FP in the generic quadratic fermionic Hamiltonians. As applications of our formalism we study the statistics of the number of particles and kinks. Our conclusions can be extended also to the quantum spin chains that can be mapped to the free fermions via Jordan-Wigner (J-W) transformtion. In particular, we provide an exact solution to the problem of the transverse field XY chain with a staggered line defect. We also study the distribution of magnetization and kinks in the transverse field XY chain and show how the dual nature of these quantities manifest itself in the distributions.

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“…This method has been successfully applied in a number of classical systems. [11][12][13][14][15][16][17][18][19] The physical reason for information quantities to be able to detect phase transitions is the deep connection between certain measurable thermodynamic quantities and principles of information theory. In fact, information can be quantified in terms of entropy, which in turn can be defined from thermodynamic observables.…”

Section: Introductionmentioning

confidence: 99%

Critical scaling of the mutual information in two-dimensional disordered Ising models

Sriluckshmy¹,

Mandal²

2018

J. Stat. Mech.

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Rényi Mutual information (RMI), computed from second Rényi entropies, can identify classical phase transitions from their finite-size scaling at the critical points. We apply this technique to examine the presence or absence of finite temperature phase transitions in various two-dimensional models on a square lattice, which are extensions of the conventional Ising model by adding a quenched disorder. When the quenched disorder causes the nearest neighbor bonds to be both ferromagnetic and antiferromagnetic, (a) a spin glass phase exists only at zero temperature, and (b) a ferromagnetic phase exists at a finite temperature when the antiferromagnetic bond distributions are sufficiently dilute. Furthermore, finite temperature paramagnetic-ferromagnetic transitions can also occur when the disordered bonds involve only ferromagnetic couplings of random strengths. In our numerical simulations, the "zero temperature only" phase transitions are identified when there is no consistent finite-size scaling of the RMI curves, while for finite temperature critical points, the curves can identify the critical temperature Tc by their crossings at Tc and 2 Tc. arXiv:1711.02352v2 [cond-mat.dis-nn]

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Classical mutual information in mean-field spin glass models

Cited by 7 publications

References 57 publications

Entanglement negativity in random spin chains

Entanglement negativity in random spin chains

Formation probabilities and statistics of observables as defect problems in free fermions and quantum spin chains

Critical scaling of the mutual information in two-dimensional disordered Ising models

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