Thermal concurrence mixing in a one-dimensional Ising model

Gunlycke, Daniel; Kendon, Viv; Vedral, Vlatko; Bose, Sougato

doi:10.1103/physreva.64.042302

Cited by 276 publications

(236 citation statements)

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“…It is known that Werner states [12] can be generated in a one dimensional XY model [13] and that temper-ature and magnetic field can increase the entanglement of the systems as shown for the Ising and Heisenberg models [14,15]. Finally we mention the study on the role of the entanglement in the density matrix renormalization group flow and the introduction of entanglementpreserving renormalization schemes [16].…”

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confidence: 91%

Scaling of entanglement close to a quantum phase transition

Osterloh¹,

Amico

Falci

et al. 2002

Nature

1,847

2,051

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In this Letter we discuss the entanglement near a quantum phase transition by analyzing the properties of the concurrence for a class of exactly solvable models in one dimension. We find that entanglement can be classified in the framework of scaling theory. Further, we reveal a profound difference between classical correlations and the non-local quantum correlation, entanglement: the correlation length diverges at the phase transition, whereas entanglement in general remains short ranged.Classical phase transitions occur when a physical system reaches a state below a critical temperature characterized by a macroscopic order [1]. Quantum phase transitions occur at absolute zero; they are induced by the change of an external parameter or coupling constant [2], and are driven by fluctuations. Examples include transitions in quantum Hall systems [3], localization in Si-MOSFETs (metal oxide silicon field-effect transistors; Ref. [4]) and the superconductor-insulator transition in two-dimensional systems [5,6]. Both classical and quantum critical points are governed by a diverging correlation length, although quantum systems possess additional correlations that do not have a classical counterpart. This phenomenon, known as entanglement [7], is the resource that enables quantum computation and communication [8]. The role of the entanglement at a phase transition is not captured by statistical mechanics -a complete classification of the critical many-body state requires the introduction of concepts from quantum information theory [9]. Here we connect the theory of critical phenomena with quantum information by exploring the entangling resources of a system close to its quantum critical point. We demonstrate, for a class of one-dimensional magnetic systems, that entanglement shows scaling behaviour in the vicinity of the transition point.There are various questions that emerge in the study of this problem. Since the ground state wave-function undergoes qualitative changes at a quantum phase transition, it is important to understand how its genuine quantum aspects evolve throughout the transition. Will entanglement between distant subsystems be extended over macroscopic regions, as correlations are? Will it carry distinct features of the transition itself and show scaling behaviour? Answering these questions is important for a deeper understanding of quantum phase transitions and also from the perspective of quantum information theory. So results that bridge these two areas of research are of great relevance. We study a set of localized spins coupled through exchange interaction and subject to an external magnetic field (we consider only spin-1/2 particles), a model central both to condensed matter and information theory and subject to intense study [10]. FIG. 1. The change in the ground state wave-function in the critical region is analyzed considering ∂ λ C(1) as a function of the reduced coupling strength λ. The curves correspond to different lattice sizes N = 11, 41, 101, 251, 401, ∞. We choose N odd to avoid the sub...

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mentioning

confidence: 91%

Scaling of entanglement close to a quantum phase transition

Osterloh¹,

Amico

Falci

et al. 2002

Nature

1,847

2,051

View full text Add to dashboard Cite

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“…[3,5], and related itinerant fermion systems [6]. There has been a conjecture that for complex quantum systems, entanglement will be an indicator of quantum phase transitions [7,8].…”

Section: Introductionmentioning

confidence: 99%

Entanglement sharing in one-particle states

Lakshminarayan

Subrahmanyam

2003

Phys. Rev. A

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Entanglement sharing among sites of one-particle states is considered using the measure of concurrence. These are the simplest in an hierarchy of number-specific states of many qubits and corresponds to "one-magnon" states of spins. We study the effects of onsite potentials that are both integrable and nonintegrable. In the integrable case we point to a metal-insulator transition that reflects on the way entanglement is shared. In the nonintegrable case the average entanglement content increases and saturates along with a transition to classical chaos. Such quantum chaotic states are shown to have universal concurrence distributions that are modified Bessel functions derivable within random matrix theory. Time-reversal breaking and time evolving states are shown to possess significantly higher entanglement sharing capacity that eigenstates of time-reversal symmetric systems. We use the ordinary Harper and kicked Harper Hamiltonians as model systems.

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“…A physical system may exhibit entanglement at a finite temperature [1,2,3,4,5]. The thermal entanglement always vanishes above a threshold temperature for systems with finite Hilbert space dimension [6].…”

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confidence: 99%

Thermal entanglement in ferrimagnetic chains

Wang

2006

Phys. Rev. A

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A formula to evaluate the entanglement in an one-dimensional ferrimagnetic system is derived. Based on the formula, we find that the thermal entanglement in a small size spin-1/2 and spins ferrimagnetic chain is rather robust against temperature, and the threshold temperature may be arbitrarily high when s is sufficiently large. This intriguing result answers unambiguously a fundamental question: "can entanglement and quantum behavior in physical systems survive at arbitrary high temperatures?" PACS numbers: 03.65.Ud, 75.10.Jm A physical system may exhibit entanglement at a finite temperature [1,2,3,4,5]. The thermal entanglement always vanishes above a threshold temperature for systems with finite Hilbert space dimension [6]. Recently, Ferreira et al. raised a fundamental question: can entanglement and quantum behavior in physical systems survive at arbitrary high temperatures? [7] They found that the entanglement between a cavity mode and a movable mirror does occur for any finite temperature. This result sheds a new light on the question and help to understand macroscopic properties of solids.In this report, we derive a formula to evaluate the entanglement in an one-dimensional ferrimagnetic system. Intriguingly, we find that the entanglement is rather robust against temperature in this kind of system, with the Hamiltonianwhere s n and S n are spin-1/2 and spin-s operators, respectively. The antiferromagnetic exchange interactions exist only between nearest neighbors, and they are of the same strength which is set to unity (J = 1). Physically, the system contains two kinds of spins, spin 1 2 and s, alternating on a ring (or a chain with the periodic boundary condition).Let us now study the entanglement of states of the system at thermal equilibrium described by the density operator ρ(T ) = exp(−βH)/Z, where β = 1/k B T , k B is the Boltzmann's constant, which is assume to be 1, and Z = Tr{exp(−βH)} is the partition function. The entanglement in the thermal state is referred to as the thermal entanglement.To study quantum entanglement in the ferrimagnetic system, we need a good entanglement measure. One possible way is to use the negativity [8] based on the partial transpose method [9]. In the cases of two spin halves and the (1/2,1) mixed spins, a positive partial transpose (PPT) (or the non-zero negativity) is necessary and sufficient for separability (entanglement). Although the present ferrimagnetic system is a kind of (1/2,s) system, fortunately, it was shown that due to the SU(2) symmetry in the model Hamiltonian (1), the non-zero negativity is still a necessary and sufficient condition for entanglement between a spin half and spin s [10]. This result allows us to exactly investigate entanglement features of our mixed spin systems.The negativity of a state ρ is defined aswhere µ i is the negative eigenvalue of ρ T2 , and T 2 denotes the partial transpose with respect to the second system. The negativity N is related to the trace norm of ρ T2 viawhere the trace norm of ρ T2 is equal to the sum of the abso...

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Thermal concurrence mixing in a one-dimensional Ising model

Cited by 276 publications

References 16 publications

Scaling of entanglement close to a quantum phase transition

Scaling of entanglement close to a quantum phase transition

Entanglement sharing in one-particle states

Thermal entanglement in ferrimagnetic chains

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