Density matrix elements and entanglement entropy for the spin-1/2 XXZ chain at Δ = 1/2

Sato, Jun; Shiroishi, Masahiro

doi:10.1088/1751-8113/40/30/009

Cited by 20 publications

(24 citation statements)

References 40 publications

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“…As the value of ∆ decreases from 1 to 0, bound states of quasiparticles progressively dissolve into elementary excitations, until the free fermion limit is reached. In this process, a quantitative change in the spectrum occurs at the midpoint ∆ = 1/2 where the system develops additional nontrivial symmetries [27][28][29].…”

Section: System and Quantities Studiedmentioning

confidence: 99%

Time fluctuations in isolated quantum systems of interacting particles

et al. 2013

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Numerically, we study the time fluctuations of few-body observables after relaxation in isolated dynamical quantum systems of interacting particles. Our results suggest that they decay exponentially with system size in both regimes, integrable and chaotic. The integrable systems considered are solvable with the Bethe ansatz and have a highly nondegenerate spectrum. This is in contrast with integrable Hamiltonians mappable to noninteracting ones. We show that the coefficient of the exponential decay depends on the level of delocalization of the initial state with respect to the energy shell.

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Section: System and Quantities Studiedmentioning

confidence: 99%

Time fluctuations in isolated quantum systems of interacting particles

et al. 2013

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“…The entanglement entropy in the TD limit is S 1 = log 2, S 2 = 0.950749, S 3 = 1.09287, S 4 = 1.19076, S 5 = 1.26588, S 6 = 1.32701 (7) the same as in Ref. [9]. We are in position to study the finite-size effects.…”

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confidence: 84%

Entanglement, combinatorics and finite-size effects in spin chains

Nienhuis¹,

Campostrini²,

Calabrese³

2009

J. Stat. Mech.

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We carry out a systematic study of the exact block entanglement in XXZ spin-chain at ∆ = −1/2. We present, the first analytic expressions for reduced density matrices of n spins in a chain of length L (for n ≤ 6 and arbitrary but odd L) of a truly interacting model. The entanglement entropy, the moments of the reduced density matrix, and its spectrum are then easily derived. We explicitely construct the "entanglement Hamiltonian" as the logarithm of this matrix. Exploiting the degeneracy of the ground-state, we find the scaling behavior of entanglement of the zero-temperature mixed state.Introduction. Entanglement is a central concept in quantum information science and it is becoming a common tool to study and analyze extended quantum systems because of its use in detecting the scaling behavior close to a quantum critical point [1]. It is has been pointed out that this scaling behavior is connected with the efficiency of numerical methods as quantum and density matrix renormalization group (DMRG) [1].Let ρ be the density matrix of a system and let the Hilbert space be written as a direct product H = H A ⊗ H B . A's reduced density matrix is ρ A = Tr B ρ and the entanglement entropy is the corresponding Von Neumann entropy

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“…Finally, let us mention that, recently, analytic expressions for reduced density matrices, several correlation functions and the entanglement entropy of small blocks (up to 6 spins) have been found for the XXZ model with ∆ = 1/2 (see Refs. [66] and [67]). …”

Section: B the Xxz Modelmentioning

confidence: 99%

A short review on entanglement in quantum spin systems

Latorre¹,

Riera²

2009

J. Phys. A: Math. Theor.

210

202

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We review some of the recent progress on the study of entropy of entanglement in many-body quantum systems. Emphasis is placed on the scaling properties of entropy for one-dimensional multi-partite models at quantum phase transitions and, more generally, on the concept of area law. We also briefly describe the relation between entanglement and the presence of impurities, the idea of particle entanglement, the evolution of entanglement along renormalization group trajectories, the dynamical evolution of entanglement and the fate of entanglement along a quantum computation.

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Density matrix elements and entanglement entropy for the spin-1/2 XXZ chain at Δ = 1/2

Cited by 20 publications

References 40 publications

Time fluctuations in isolated quantum systems of interacting particles

Time fluctuations in isolated quantum systems of interacting particles

Entanglement, combinatorics and finite-size effects in spin chains

A short review on entanglement in quantum spin systems

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