Shared information in stationary states at criticality

Alcaraz, Francisco C.; Rittenberg, V.

doi:10.1088/1742-5468/2010/03/p03024

Cited by 20 publications

(27 citation statements)

References 25 publications

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“…Some results on the finitesize scaling of entanglement in 1D critical non-conformal systems have been already reported [45][46][47][48] . The function Y (x) for S α must however satisfy simple symmetry constraints.…”

Section: B Finite-size Effectsmentioning

confidence: 96%

Entanglement spectrum of random-singlet quantum critical points

2011

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The entanglement spectrum, i.e., the full distribution of Schmidt eigenvalues of the reduced density matrix, contains more information than the conventional entanglement entropy and has been studied recently in several many-particle systems. We compute the disorder-averaged entanglement spectrum, in the form of the disorder-averaged moments Trρ α A of the reduced density matrix ρA, for a contiguous block of many spins at the random-singlet quantum critical point in one dimension. The result compares well in the scaling limit with numerical studies on the random XX model and is also expected to describe the (interacting) random Heisenberg model. Our numerical studies on the XX case reveal that the dependence of the entanglement entropy and spectrum on the geometry of the Hilbert space partition is quite different than for conformally invariant critical points.

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Section: B Finite-size Effectsmentioning

confidence: 96%

Entanglement spectrum of random-singlet quantum critical points

2011

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“…At this value of the loop weight the model is well known to be equivalent to bond percolation [14]. We note here that this model is also equivalent to the stochastic raise and peel model for which the stationary state entanglement entropy in the context of shared information was studied in [15]. The rigorous finite size results allow us to perform a detailed asymptotic analysis in L, of which the universal contribution can be compared to the CFT predictions.…”

Section: Introductionmentioning

confidence: 83%

“…For reflecting boundary conditions we were not able to obtain rigorous results from (15) and (16), except for some special values of the loop weight x, see Appendix A.3 and A.4. We can however analyse (15) and (16) with arbitrary numerical precision and have in this way been able to obtain closed form expressions for their exact asymptotics.…”

Section: Asymptotics For the Model On The Stripmentioning

confidence: 99%

Finite-size corrections for universal boundary entropy in bond percolation

2016

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We compute the boundary entropy for bond percolation on the square lattice in the presence of a boundary loop weight, and prove explicit and exact expressions on a strip and on a cylinder of size L. For the cylinder we provide a rigorous asymptotic analysis which allows for the computation of finitesize corrections to arbitrary order. For the strip we provide exact expressions that have been verified using high-precision numerical analysis. Our rigorous and exact results corroborate an argument based on conformal field theory, in particular concerning universal logarithmic corrections for the case of the strip due to the presence of corners in the geometry. We furthermore observe a crossover at a special value of the boundary loop weight.

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“…We see a nice collapse of the curves regardless p < p 1 or p > p 1 . We also show in the figure (circles) the predicted curve [10] for the standard u = 1 RPM: h(L) = γ ln[L sin(πx/L)/π] + β, with γ = √ 3/2π ≈ 0.2757 and β = 0.77. The coefficient γ can be derived exploiting the conformal invariance of the model [11,10].…”

Section: The Model With Equal Rates Of Adsorption and Desorptionmentioning

confidence: 99%

Quasi-stationary states in nonlocal stochastic growth models with infinitely many absorbing states

Jara

Alcaraz

2017

J. Stat. Mech.

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We study a two parameter (u, p) extension of the conformally invariant raise and peel model. The model also represents a nonlocal and biased-asymmetric exclusion process with local and nonlocal jumps of excluded volume particles in the lattice. The model exhibits an unusual and interesting critical phase where, in the bulk limit, there are an infinite number of absorbing states. In spite of these absorbing states the system stays, during a time that increases exponentially with the lattice size, in a critical quasi-stationary state. In this critical phase the critical exponents depend only on one of the parameters defining the model (u). The endpoint of this critical phase, where the system changes from an active to an inactive frozen phase, belongs to a distinct universality class. This new behavior, we believe, is due to the appearance of Jordan cells in the Hamiltonian describing the time evolution. The dimensions of these cells increase with the lattice size. In a special case (u = 0) where the model has no adsorptions we are able to calculate analytically the time evolution of some observables. A polynomial time dependence is obtained thanks to the appearance of Jordan cells structures in the Hamiltonian.

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Shared information in stationary states at criticality

Cited by 20 publications

References 25 publications

Entanglement spectrum of random-singlet quantum critical points

Entanglement spectrum of random-singlet quantum critical points

Finite-size corrections for universal boundary entropy in bond percolation

Quasi-stationary states in nonlocal stochastic growth models with infinitely many absorbing states

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