General relation between entanglement and fluctuations in one dimension

Song, Hongwen; Rachel, Stephan; Hur, Karyn Le

doi:10.1103/physrevb.82.012405

Cited by 134 publications

(159 citation statements)

References 38 publications

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“…4, for small lattices there are important differences between the Rényi interdependencies computed for l odd and l even at u = 1. A similar phenomenon was observed for the Rényi entropies but not for the von Neumann entanglement entropy, in the study of quantum chains [14,15,16]. Moreover, in [15] it was conjectured that for the XXZ model with an anisotropy −1 ≤ ∆ ≤ 1 and open boundaries, in the finite-size scaling limit, one has:…”

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confidence: 75%

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Shared information in stationary states at criticality

Alcaraz¹,

Rittenberg²

2010

J. Stat. Mech.

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We consider bipartitions of one-dimensional extended systems whose probability distribution functions describe stationary states of stochastic models. We define estimators of the shared information between the two subsystems. If the correlation length is finite, the estimators stay finite for large system sizes. If the correlation length diverges, so do the estimators. The definition of the estimators is inspired by information theory. We look at several models and compare the behavior of the estimators in the finite-size scaling limit. Analytical and numerical methods as well as Monte Carlo simulations are used. We show how the finite-size scaling functions change for various phase transitions, including the case where one has conformal invariance.

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confidence: 75%

“…[14,15,16] in gapless conformal invariant quantum chains, the Rényi entropies get different subleading contributions if one consider separately systems with l odd and l even. In Sec.…”

Section: Introductionmentioning

confidence: 99%

Shared information in stationary states at criticality

Alcaraz¹,

Rittenberg²

2010

J. Stat. Mech.

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“…Although being a simpler physical quantity, its scaling properties were shown to be similar to that of the entanglement entropy in a variety of 1D quantum systems 33 and, in the case of free fermions, also in arbitrary dimensions 34,35 . Therefore it is an interesting question whether this connection persists for the present impurity problem.…”

Section: Particle Number Fluctuationmentioning

confidence: 99%

Fano resonances and entanglement entropy

Eisler

Garmon

2010

Phys. Rev. B

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We study the entanglement in the ground state of a chain of free spinless fermions with a single side-coupled impurity. We find a logarithmic scaling for the entanglement entropy of a segment neighboring the impurity. The prefactor of the logarithm varies continuously and contains an impurity contribution described by a one-parameter function, while the contribution of the unmodified boundary enters additively. The coefficient is found explicitly by pointing out similarities with other models involving interface defects. The proposed formula gives excellent agreement with our numerical data. If the segment has an open boundary, one finds a rapidly oscillating subleading term in the entropy that persists in the limit of large block sizes. The particle number fluctuation inside the subsystem is also reported. It is analogous with the expression for the entropy scaling, however with a simpler functional form for the coefficient.

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“…In the fermionized picture, this corresponds to density fluctuations in a box, which was shown to scale identically to the entanglement in equilibrium [30]. After bosonization, it is given by…”

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confidence: 99%

Linear quantum quench in the Heisenberg XXZ chain: Time-dependent Luttinger-model description of a lattice system

2013

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We study variable-rate linear quenches in the anisotropic Heisenberg (XXZ) chain, starting at the XX point. This is equivalent to swithcing on a nearest neighbour interaction for hard-core bosons or an interaction quench for free fermions. The physical observables we investigate are: the energy pumped into the system during the quench, the spin-flip correlation function, and the bipartite fluctuations of the z component of the spin in a box. We find excellent agreement between exact numerics (infinite system time-evolving block decimation, iTEBD) and analytical results from bosonization, as a function of the quench time, spatial coordinate and interaction strength. This provides a stringent and much-needed test of Luttinger liquid theory in a non-equilibrium situation.PACS numbers: 71.10. Pm,75.10.Jm,05.70.Ln, While it is difficult to study genuine non-equilibrium dynamics in solid state systems due to the presence of many relaxation channels (phonons, impurities, interactions etc.), cold atoms in optical lattices provide an ideal laboratory for non-equilibrium investigations due to the high degree of control over various dissipation mechanisms. Cold-atom experiments in the past decade have explored a wide variety of non-equilibrium quantum dynamics in previously inaccessible regimes [1,2]. This has also led to an increasing amount of theoretical activity [2,3]. Key issues include thermalization as well as equilibration and their relation to integrability [2], pumping beyond the adiabatic limit or quantum fluctuation relations [4], and universal near-adiabatic dynamics in quantum critical systems [2,3]. Linear quenches occuring over a finite time can interpolate between the more familiar limits of an instantaneous quench and an adiabatic sweep. Very recently, a few experiments have examined the response of many-body experiments to such finitetime quenches [5,6]. It is thus of vital current interest to address the dynamics under linear sweeps of system parameters such as interaction strength.The response of a system to an external perturbation depends sensitively on its spatial dimension, as famously demonstrated in the experiment of Ref. [7]. There, one dimensional interacting bosons did not reach thermalization within the experimental timescale, while their higher dimensional realizations did. One dimensional systems are notoriously strongly correlated due to the limited phase space for scattering. The non-interacting ground state is immediately destroyed by interactions, forming a Luttinger liquid (LL) in many instances [8,9], and described by critical phenomena of collective modes with anomalous (non-integer) power-law dependence of correlation functions.Quantum quenches in Luttinger liquids have been addressed by several authors [10][11][12][13][14][15][16][17]. However, it is not clear to what extent the Luttinger liquid (LL) picture, which is a genuine low energy description, is applicable under non-equilibrium circumstances [17]. For an abrupt interaction change, certain observables revealed universal LL ...

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General relation between entanglement and fluctuations in one dimension

Cited by 134 publications

References 38 publications

Shared information in stationary states at criticality

Shared information in stationary states at criticality

Fano resonances and entanglement entropy

Linear quantum quench in the Heisenberg XXZ chain: Time-dependent Luttinger-model description of a lattice system

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