We study the ground state quantum phase transition by means of entanglement in the one-dimensional asymmetric Hubbard model with open boundary conditions. The local entanglement between the middle two sites and the rest of the system, and the block entanglement between the left and right portions of the system, are calculated using the density-matrix renormalization group (DMRG) method. We find that the entanglement shows interesting scaling and singular behavior around the phase transition line.We study the ground state quantum phase transition by means of entanglement in the one-dimensional asymmetric Hubbard model with open boundary conditions. The local entanglement between the middle two sites and the rest of the system, and the block entanglement between the left and right portions of the system, are calculated using the density-matrix renormalization group (DMRG) method. We find that the entanglement shows interesting scaling and singular behavior around the phase transition line.

arXiv:0805.2021Journal of Physics Condensed MatterAug 1, 200810 citations

Density matrix renormalization on random graphs and the quantum spin-glass transition

Javier Rodríguez-Laguna

The density matrix renormalization group (DMRG) has been extended to study quantum phase transitions on random graphs of fixed connectivity. As a relevant example, we have analysed the random Ising model in a transverse field. If the couplings are random, the number of retained states remains reasonably low even for large sizes. The resulting quantum spin-glass transition has been traced down for a few disorder realizations, through the careful measurement of the entanglement entropy and some selected observables: spatial correlations, energy gap and spin-glass susceptibility, among others.The density matrix renormalization group (DMRG) has been extended to study quantum phase transitions on random graphs of fixed connectivity. As a relevant example, we have analysed the random Ising model in a transverse field. If the couplings are random, the number of retained states remains reasonably low even for large sizes. The resulting quantum spin-glass transition has been traced down for a few disorder realizations, through the careful measurement of the entanglement entropy and some selected observables: spatial correlations, energy gap and spin-glass susceptibility, among others.

arXiv:cond-mat/0610661Journal of Physics A Mathematical and TheoreticalSep 18, 20076 citations

Entanglement and quantum phase transitions

Hai‐Qing Lin, Shi-Jian Gu, Guang-Shan Tian

Bulletin of the American Physical SocietyMar 21, 20050 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.

arXiv:quant-ph/0505168May 23, 20050 citations

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.