Topological Estimator of Block Entanglement for Heisenberg Antiferromagnets

Chhajlany, Ravindra W.; Tomczak, P.; Wójcik, Antoni

doi:10.1103/physrevlett.99.167204

Cited by 32 publications

(51 citation statements)

References 43 publications

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“…On the other hand the SU(2) singlet basis is not orthogonal. However it might happen that in the basis of SU(2) singlets, the coefficients appearing in the wavefunction are non-negative real numbers which through a proper normalisation can be interpreted as probabilities [7,8]. One can then consider the problem of shared information in the wavefunction as if it were the PDF of a stationary state of a stochastic process.…”

Section: Estimators Of Shared Information For Dyck Paths Configurationsmentioning

confidence: 99%

“…This estimator was introduced independently by Chhajiany et al [7] and Alet et al [8] in the context of SU(2) symmetric spin 1/2 quantum chains, and further studied by Jacobsen and Saleur [19]. The aim was to measure the average number of link (SU(2) singlets) crossings at a given site of the quantum chain.…”

Section: Estimators Of Shared Information For Dyck Paths Configurationsmentioning

confidence: 99%

“…An example is the ground-state wavefunction of the spin 1/2 SU(2) symmetric Hamiltonian if one uses the valence bond (SU(2) singlets) basis [7,8].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Estimators Of Shared Information For Dyck Paths Configurationsmentioning

confidence: 99%

Section: Estimators Of Shared Information For Dyck Paths Configurationsmentioning

confidence: 99%

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Shared information in stationary states at criticality

Alcaraz¹,

Rittenberg²

2010

J. Stat. Mech.

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“…One such quantity is the valence bond (VB) entanglement entropy for SU(2) quantum spin systems [134,135], which generalizes the idea, first used in the context of random spin chains [79,92,93], that for a pure valence bond state whose wave function is a product of disjoint singlet bonds between two spin-1/2s the entanglement entropy of a subsystem is essentially the number of singlet bonds that cross the boundary between the subsystem and the remainder of the system, with each singlet |Ψ s = (|↑ A ↓ B − |↓ A ↑ B )/ √ 2 contributing ln 2 to the entanglement entropy. For more general wave functions which are superpositions of pure VB states the number of such crossings can be averaged to obtain a well-defined (with certain restrictions [134]) measure of entanglement.…”

Section: Concluding Remarks On Bipartite Fluctuations a Comparismentioning

confidence: 99%

Bipartite fluctuations as a probe of many-body entanglement

et al. 2012

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We investigate in detail the behavior of the bipartite fluctuations of particle numberN and spin S z in many-body quantum systems, focusing on systems where such U(1) charges are both conserved and fluctuate within subsystems due to exchange of charges between subsystems. We propose that the bipartite fluctuations are an effective tool for studying many-body physics, particularly its entanglement properties, in the same way that noise and Full Counting Statistics have been used in mesoscopic transport and cold atomic gases. For systems that can be mapped to a problem of non-interacting fermions we show that the fluctuations and higher-order cumulants fully encode the information needed to determine the entanglement entropy as well as the full entanglement spectrum through the Rényi entropies. In this connection we derive a simple formula that explicitly relates the eigenvalues of the reduced density matrix to the Rényi entropies of integer order for any finite density matrix. In other systems, particularly in one dimension, the fluctuations are in many ways similar but not equivalent to the entanglement entropy. Fluctuations are tractable analytically, computable numerically in both density matrix renormalization group and quantum Monte Carlo calculations, and in principle accessible in condensed matter and cold atom experiments. In the context of quantum point contacts, measurement of the second charge cumulant showing a logarithmic dependence on time would constitute a strong indication of many-body entanglement.

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“…In an interesting recent paper [10] (see also [11] for a related, independent work) it was suggested that, even when |Ω is not a single valence bond state but a superposition of such states, the average number of singlets N c (Ω) crossing the boundary of the subsystem (multiplied e.g. by ln 2 for spins 1/2) could still be used as a measure of the entanglement entropy with all the required qualitative properties.…”

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confidence: 99%

Exact Valence Bond Entanglement Entropy and Probability Distribution in theXXXSpin Chain and the Potts Model

Jacobsen

Saleur

2008

Phys. Rev. Lett.

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By relating the ground state of Temperley-Lieb hamiltonians to partition functions of 2D statistical mechanics systems on a half plane, and using a boundary Coulomb gas formalism, we obtain in closed form the valence bond entanglement entropy as well as the valence bond probability distribution in these ground states. We find in particular that for the XXX spin chain, the number Nc of valence bonds connecting a subsystem of size L to the outside goes, in the thermodynamic limit, as Nc (Ω) = 4 π 2 ln L, disproving a recent conjecture that this should be related with the von Neumann entropy, and thus equal to 1 3 ln 2 ln L. Our results generalize to the Q-state Potts model. Introduction. Entanglement is a central concept in quantum information processing, as well as in the study of quantum phase transitions. One of the widely used entanglement measures is the von Neumann entanglement entropy S vN , which quantifies entanglement of a pure quantum state in a bipartite system. To define S vN precisely, let ρ = |Ψ Ψ| be the density matrix of the system, where |Ψ is a pure quantum state. Given a complete set X of commuting observables, let X = A ∪ B be a bipartition thereof. Then S vN is defined as

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Topological Estimator of Block Entanglement for Heisenberg Antiferromagnets

Cited by 32 publications

References 43 publications

Shared information in stationary states at criticality

Shared information in stationary states at criticality

Bipartite fluctuations as a probe of many-body entanglement

Exact Valence Bond Entanglement Entropy and Probability Distribution in theXXXSpin Chain and the Potts Model

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