arXiv:cond-mat/0305573 · Physical Review A

Entanglement in a second-order quantum phase transition

Julien Vidal, Guillaume Palacios, Rémy Mosseri

Published Feb 18, 2004• 296 citations

Abstract

We consider a system of mutually interacting spins 1/2 embedded in a transverse magnetic field which undergoes a second-order quantum phase transition. We analyze the entanglement properties and the spin squeezing of the ground state and show that, contrarily to the one-dimensional case, a cusplike singularity appears at the critical point ${\ensuremath{\lambda}}_{c}$ in the thermodynamical limit. We also show that there exists a value ${\ensuremath{\lambda}}_{0}>~{\ensuremath{\lambda}}_{c}$ above which the ground state is not spin squeezed despite a nonvanishing concurrence.

DOI: 10.1103/physreva.69.022107

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arXiv:cond-mat/0305573 · Physical Review A

Entanglement in a second-order quantum phase transition

Julien Vidal, Guillaume Palacios, Rémy Mosseri

Published Feb 18, 2004• 296 citations

arXiv HTML PDF

Abstract

{\ensuremath{\lambda}}_{c}

in the thermodynamical limit. We also show that there exists a value

{\ensuremath{\lambda}}_{0}>~{\ensuremath{\lambda}}_{c}

above which the ground state is not spin squeezed despite a nonvanishing concurrence.

DOI: 10.1103/physreva.69.022107

Related papers

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Julien Vidal, Rémy Mosseri, J. Dukelsky

arXiv:cond-mat/0312130Physical Review AMay 12, 2004154 citations

Singular behavior of an entangled state for a one-dimensional quantum spin system

Kawaguchi, Akira, Kaoru Shimizu

We studied the entangled state for a one-dimensional $S=1/2$ antiferromagnetic quantum spin chain in a transverse field. We calculate the ground state using the density matrix renormalization group and discuss how the entangled state changes around a quantum phase transition (QPT) point. By analyzing concurrence $C(ρ)$ for two-qubit density matrix $ρ$ after the Lewenstein-Sanpera decomposition, $ρ=Λρ_s + (1-Λ) ρ_e $, where $ρ_s$ is a separable density matrix and $ρ_e$ is a pure entangled state obtained by a linear combination of Bell states, we find singular behaviors both in $C(ρ_e)$ and $1-Λ$ at the QPT point. $C(ρ_e)$ includes the effects of quantum fluctuations, which manifest the competition between the antiferromagnetic spin fluctuation and the effect of transverse field in the transverse Ising model. The quantum fluctuation shows the singular maximum at the QPT point as expected from the general picture of phase transition. In contrast, $1-Λ$ reveals the singular minimum at QPT point.We studied the entangled state for a one-dimensional $S=1/2$ antiferromagnetic quantum spin chain in a transverse field. We calculate the ground state using the density matrix renormalization group and discuss how the entangled state changes around a quantum phase transition (QPT) point. By analyzing concurrence $C(ρ)$ for two-qubit density matrix $ρ$ after the Lewenstein-Sanpera decomposition, $ρ=Λρ_s + (1-Λ) ρ_e $, where $ρ_s$ is a separable density matrix and $ρ_e$ is a pure entangled state obtained by a linear combination of Bell states, we find singular behaviors both in $C(ρ_e)$ and $1-Λ$ at the QPT point. $C(ρ_e)$ includes the effects of quantum fluctuations, which manifest the competition between the antiferromagnetic spin fluctuation and the effect of transverse field in the transverse Ising model. The quantum fluctuation shows the singular maximum at the QPT point as expected from the general picture of phase transition. In contrast, $1-Λ$ reveals the singular minimum at QPT point.

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{\ensuremath{\lambda}}_{c}

in the thermodynamical limit. We also show that there exists a value

{\ensuremath{\lambda}}_{0}>~{\ensuremath{\lambda}}_{c}

above which the ground state is not spin squeezed despite a nonvanishing concurrence.

We studied the entangled state for a one-dimensional

S=1/2

antiferromagnetic quantum spin chain in a transverse field. We calculate the ground state using the density matrix renormalization group and discuss how the entangled state changes around a quantum phase transition (QPT) point. By analyzing concurrence

C(ρ)

for two-qubit density matrix

ρ

after the Lewenstein-Sanpera decomposition, $ρ=Λρ_s + (1-Λ) ρ_e $, where

ρ_s

is a separable density matrix and

ρ_e

is a pure entangled state obtained by a linear combination of Bell states, we find singular behaviors both in

C(ρ_e)

and

1-Λ

at the QPT point.

C(ρ_e)

includes the effects of quantum fluctuations, which manifest the competition between the antiferromagnetic spin fluctuation and the effect of transverse field in the transverse Ising model. The quantum fluctuation shows the singular maximum at the QPT point as expected from the general picture of phase transition. In contrast,

1-Λ

reveals the singular minimum at QPT point.