Dynamics of entanglement in one-dimensional spin systems

Amico, Luigi; Osterloh, Andreas; Plastina, Francesco; Fazio, Rosario; Palma, G. Massimo

doi:10.1103/physreva.69.022304

Cited by 290 publications

(307 citation statements)

References 47 publications

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“…Despite being mapped into a non-interacting system, the model in the infinite N limit has a rich phase diagram featuring a quantum phase transition [26] at h = 1 and, as far as the entanglement properties are concerned, the divergence of the entanglement range when approaching the curve h 2 + γ 2 = 1, where pairwise entanglement vanishes [27][28][29]. Moreover, its peculiar non equilibrium dynamics has been studied in the framework of dynamical entanglement sharing [30], with periodic boundary conditions assumed. For diagonalizing this Hamiltonian one first maps spin operators σ ± = (σ x ± iσ y )/2 to fermionic operators through the Jordan-Wigner transformation c l =…”

Section: Free Fermionic Systems: Xy Hamiltonianmentioning

confidence: 99%

Initializing an unmodulated spin chain to operate as a high-quality quantum data bus

et al. 2011

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We study the quality of state and entanglement transmission through quantum channels described by spin chains varying both the system parameters and the initial state of the channel. We consider a vast class of one-dimensional many-body models which contains some of the most relevant experimental realizations of quantum data-buses. In particular, we consider spin-1/2 XY and XXZ model with open boundary conditions. Our results show a significant difference between free-fermionic (non-interacting) systems (XY) and interacting ones (XXZ), where in the former case initialization can be exploited for improving the entanglement distribution, while in the latter case it also determines the quality of state transmission. In fact, we find that in non interacting systems the exchange with fermions in the initial state of the chain always has a destructive effect, and we prove that it can be completely removed in the isotropic XX model by initializing the chain in a ferromagnetic state. On the other hand, in interacting systems constructive effects can arise by scattering between hopping fermions and a proper initialization procedure. Remarkably our results are the first example in which state and entanglement transmission show maxima at different points as the interactions and initializations of spin chain channels are varied.

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Section: Free Fermionic Systems: Xy Hamiltonianmentioning

confidence: 99%

Initializing an unmodulated spin chain to operate as a high-quality quantum data bus

et al. 2011

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“…We start our analysis by considering again the XY spin bath: the concurrence C(k) in terms of one-point and two-point spin-correlation functions can be analytically evaluated [41,42]. As long as γ = 0, this system belongs to the Ising universality class, for which it has been shown that the concurrence between two spins vanishes unless the two sites are at most next-to-nearest neighbor [36,37].…”

Section: Decoherence and Entanglementmentioning

confidence: 99%

Decoherence induced by interacting quantum spin baths

et al. 2007

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We study decoherence induced on a two-level system coupled to a one-dimensional quantum spin chain. We consider the cases where the dynamics of the chain is determined by the Ising, XY , or Heisenberg exchange Hamiltonian. This model of quantum baths can be of fundamental importance for the understanding of decoherence in open quantum systems, since it can be experimentally engineered by using atoms in optical lattices. As an example, here we show how to implement a pure dephasing model for a qubit system coupled to an interacting spin bath. We provide results that go beyond the case of a central spin coupled uniformly to all the spins of the bath, in particular showing what happens when the bath enters different phases, or becomes critical; we also study the dependence of the coherence loss on the number of bath spins to which the system is coupled and we describe a coupling-independent regime in which decoherence exhibits universal features, irrespective of the system-environment coupling strength. Finally, we establish a relation between decoherence and entanglement inside the bath. For the Ising and the XY models we are able to give an exact expression for the decay of coherences, while for the Heisenberg bath we resort to the numerical time-dependent Density Matrix Renormalization Group.

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“…These manifest themselves as qualitative changes in the decay of correlations: algebraic in the proximity of a critical point and exponential decay away from it. Entanglement plays a fundamental role in the quantum phase transitions that occur in interacting lattice systems at zero temperature [2,3,4,5,6]. Under these conditions the system is in the ground state, which is also a pure state, and any correlations must be a consequence of the fact the ground state is entangled.…”

Section: Introductionmentioning

confidence: 99%

Random Matrix Theory and Entanglement in Quantum Spin Chains

Keating

Mezzadri

2004

Commun. Math. Phys.

126

253

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We compute the entropy of entanglement in the ground states of a general class of quantum spin-chain Hamiltonians -those that are related to quadratic forms of Fermi operators -between the first N spins and the rest of the system in the limit of infinite total chain length. We show that the entropy can be expressed in terms of averages over the classical compact groups and establish an explicit correspondence between the symmetries of a given Hamiltonian and those characterizing the Haar measure of the associated group. These averages are either Toeplitz determinants or determinants of combinations of Toeplitz and Hankel matrices. Recent generalizations of the Fisher-Hartwig conjecture are used to compute the leading order asymptotics of the entropy as N → ∞. This is shown to grow logarithmically with N . The constant of proportionality is determined explicitly, as is the next (constant) term in the asymptotic expansion. The logarithmic growth of the entropy was previously predicted on the basis of numerical computations and conformal-field-theoretic calculations. In these calculations the constant of proportionality was determined in terms of the central charge of the Virasoro algebra. Our results therefore lead to an explicit formula for this charge. We also show that the entropy is related to solutions of ordinary differential equations of Painlevé type. In some cases these solutions can be evaluated to all orders using recurrence relations.

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Dynamics of entanglement in one-dimensional spin systems

Cited by 290 publications

References 47 publications

Initializing an unmodulated spin chain to operate as a high-quality quantum data bus

Initializing an unmodulated spin chain to operate as a high-quality quantum data bus

Decoherence induced by interacting quantum spin baths

Random Matrix Theory and Entanglement in Quantum Spin Chains

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