arXiv:cond-mat/0511719 · Physical Review B

Enhancement of nearest-neighbor entanglement in one-dimensional disordered systems

Román López-Sandoval, Martı́n E. Garcia

Published Nov 15, 2006• 11 citations

Abstract

The pairwise quantum entanglement between sites in disordered electronic one-dimensional systems (rings) is studied. We focus on the effect of diagonal and off-diagonal disorder on the ground-state concurrence ${C}_{ij}$ between neighboring and not neighboring sites $i,j$ as a function of electron band filling. In the case of diagonal disorder, increasing the degree of disorder leads to a decrease of the concurrence with respect to the ordered case. However, off-diagonal disorder causes a surprisingly strong enhancement of nearest-neighbor entanglement. This remarkable effect occurs near half filling, where the concurrence becomes up to 15% larger than in the periodic system.

DOI: 10.1103/physrevb.74.174204

Related papers

Entanglement of the Heisenberg chain with the next-nearest-neighbor interaction

Shi-Jian Gu, Haibin Li, You‐Quan Li +1 more

arXiv:quant-ph/0403026Physical Review ANov 1, 200465 citations

Localized Entanglement in one-dimensional Anderson model

Li, H, Wang, X, Li, Y

Jan 1, 20049 citations

Boundary and impurity effects on the entanglement of Heisenberg chains

Xiaoguang Wang

arXiv:cond-mat/0312351Physical Review EJun 10, 200448 citations

Quantum entanglement in Heisenberg antiferromagnets

V. Subrahmanyam

arXiv:quant-ph/0309004Physical Review AFeb 20, 200434 citations

Effects of the Next-Nearest-Neighbor Interaction on the Entanglement of the Heisenberg XX Chain

Ming Hu

Chinese Physics CJan 1, 20060 citations

Electron-electron interaction effects on Peierls dimerization in a half-filled band

S. N. Dixit, S. Mazumdar

Physical review. B, Condensed matterFeb 15, 1984125 citations

arXiv:cond-mat/0511719 · Physical Review B

Enhancement of nearest-neighbor entanglement in one-dimensional disordered systems

Román López-Sandoval, Martı́n E. Garcia

Published Nov 15, 2006• 11 citations

arXiv HTML PDF

Abstract

{C}_{ij}

between neighboring and not neighboring sites

i,j

as a function of electron band filling. In the case of diagonal disorder, increasing the degree of disorder leads to a decrease of the concurrence with respect to the ordered case. However, off-diagonal disorder causes a surprisingly strong enhancement of nearest-neighbor entanglement. This remarkable effect occurs near half filling, where the concurrence becomes up to 15% larger than in the periodic system.

DOI: 10.1103/physrevb.74.174204

Related papers

Entanglement of the Heisenberg chain with the next-nearest-neighbor interaction

Shi-Jian Gu, Haibin Li, You‐Quan Li +1 more

The features of the concurrences between the nearest-neighbors and that of the next-nearest-neighbors for the one-dimensional Heisenberg model with next-nearest-neighbor coupling $J$ are studied as functions of temperature and $J$ . The two concurrences exhibit a different dependence on $J$ at the ground state, which could be interpreted from the point of view of the correlation functions. The threshold temperature at which the concurrence is zero and the temperature effect on the two concurrences for systems up to 12 sites are studied numerically.The features of the concurrences between the nearest-neighbors and that of the next-nearest-neighbors for the one-dimensional Heisenberg model with next-nearest-neighbor coupling $J$ are studied as functions of temperature and $J$. The two concurrences exhibit a different dependence on $J$ at the ground state, which could be interpreted from the point of view of the correlation functions. The threshold temperature at which the concurrence is zero and the temperature effect on the two concurrences for systems up to 12 sites are studied numerically.

arXiv:quant-ph/0403026Physical Review ANov 1, 200465 citations

Localized Entanglement in one-dimensional Anderson model

Li, H, Wang, X, Li, Y

The entanglement in one-dimensional Anderson model is studied. We show that the pairwise entanglement measured by the average concurrence has a direct relation to the localization length. The numerical study indicates that the disorder significantly reduces the average entanglement, and entanglement distribution clearly displays the entanglement localization. The maximal pairwise entanglement exhibits a maximum as the disorder strength increases,experiencing a transition from increase to decrease. The entanglement between the center of localization and other site decreases exponentially along the spatial direction. Finally,we study effects of disorder on dynamical properties of entanglement.The entanglement in one-dimensional Anderson model is studied. We show that the pairwise entanglement measured by the average concurrence has a direct relation to the localization length. The numerical study indicates that the disorder significantly reduces the average entanglement, and entanglement distribution clearly displays the entanglement localization. The maximal pairwise entanglement exhibits a maximum as the disorder strength increases,experiencing a transition from increase to decrease. The entanglement between the center of localization and other site decreases exponentially along the spatial direction. Finally,we study effects of disorder on dynamical properties of entanglement.

Jan 1, 20049 citations

Boundary and impurity effects on the entanglement of Heisenberg chains

Xiaoguang Wang

We study entanglement of a pair of qubits and the bipartite entanglement between the pair and the rest within open-ended Heisenberg XXX and XY models. The open boundary condition leads to strong oscillations of entanglements with a two-site period, and the two kinds of entanglements are 180 degrees out of phase with each other. The mean pairwise entanglement and ground-state energy per site in the XXX model are found to be proportional to each other. We study the effects of a single bulk impurity on entanglement, and find that there exist threshold values of the relative coupling strength between the impurity and its nearest neighbors, after which the impurity becomes pairwise entangled with its nearest neighbors.We study entanglement of a pair of qubits and the bipartite entanglement between the pair and the rest within open-ended Heisenberg XXX and XY models. The open boundary condition leads to strong oscillations of entanglements with a two-site period, and the two kinds of entanglements are 180 degrees out of phase with each other. The mean pairwise entanglement and ground-state energy per site in the XXX model are found to be proportional to each other. We study the effects of a single bulk impurity on entanglement, and find that there exist threshold values of the relative coupling strength between the impurity and its nearest neighbors, after which the impurity becomes pairwise entangled with its nearest neighbors.

arXiv:cond-mat/0312351Physical Review EJun 10, 200448 citations

Quantum entanglement in Heisenberg antiferromagnets

V. Subrahmanyam

Entanglement sharing among pairs of spins in Heisenberg antiferromagnets is investigated using the concurrence measure. For a nondegenerate $S=0$ ground state, a simple formula relates the concurrence to the diagonal correlation function. The concurrence length is seen to be extremely short. Various finite clusters are studied numerically, to see the trend in two dimensions. It is argued that the concurrences vanish between pairs of spins which are not nearest neighbors for the linear-chain and square-lattice antiferromagnet ground states. For the triangular lattice and Kagome' lattice, nearest-neighbor concurrences also vanish. The concurrences in the maximal-spin states are explicitly calculated, where the concurrence averaged over all pairs is larger than the $S=0$ states.Entanglement sharing among pairs of spins in Heisenberg antiferromagnets is investigated using the concurrence measure. For a nondegenerate $S=0$ ground state, a simple formula relates the concurrence to the diagonal correlation function. The concurrence length is seen to be extremely short. Various finite clusters are studied numerically, to see the trend in two dimensions. It is argued that the concurrences vanish between pairs of spins which are not nearest neighbors for the linear-chain and square-lattice antiferromagnet ground states. For the triangular lattice and Kagome' lattice, nearest-neighbor concurrences also vanish. The concurrences in the maximal-spin states are explicitly calculated, where the concurrence averaged over all pairs is larger than the $S=0$ states.

arXiv:quant-ph/0309004Physical Review AFeb 20, 200434 citations

Effects of the Next-Nearest-Neighbor Interaction on the Entanglement of the Heisenberg XX Chain

Ming Hu

The pairwise entanglement of the Heisenberg XX chain with next-nearest-neighbor (NNN) interactions was investigated by using the concurrence measure. The results show that for the nearest-neighbor sites, the entanglement may be improved or suppressed depending on the magnitudes of the NNN coupling constant J, while for the next-nearest-neighbor sites, it always increases with the increase of |J|. The critical temperature Tc decreases with the increase of J for the nearest-neighbor entanglement and increases with the increase of |J| for the next-nearest-neighbor entanglement, respectively. We also show that the general Heisenberg XX model still can be used to create the entangled W states of three and four qubits, and that the presence of NNN coupling has no effect on the creation of four-qubit W states, while it shifts the instant of time at which the three-qubit W states are created.The pairwise entanglement of the Heisenberg XX chain with next-nearest-neighbor (NNN) interactions was investigated by using the concurrence measure. The results show that for the nearest-neighbor sites, the entanglement may be improved or suppressed depending on the magnitudes of the NNN coupling constant J, while for the next-nearest-neighbor sites, it always increases with the increase of |J|. The critical temperature Tc decreases with the increase of J for the nearest-neighbor entanglement and increases with the increase of |J| for the next-nearest-neighbor entanglement, respectively. We also show that the general Heisenberg XX model still can be used to create the entangled W states of three and four qubits, and that the presence of NNN coupling has no effect on the creation of four-qubit W states, while it shifts the instant of time at which the three-qubit W states are created.

Chinese Physics CJan 1, 20060 citations

Electron-electron interaction effects on Peierls dimerization in a half-filled band

S. N. Dixit, S. Mazumdar

A novel real-space approach to dimerization in a half-filled band is developed to investigate effects of electron-electron interactions on the Peierls instability. Dimerization is shown to be a result of imperfect resonance between pairs of electron configurations related to each other by a mirror-plane symmetry passing through the longest diagonal of the infinite ring, and the kinetic- and potential-energy contributions to the barrier to resonance are identified separately. The effects of including the on-site, nearest-neighbor, and next-nearest-neighbor interactions are investigated, and in each case it is shown that the enhancement or reduction in dimerization can be predicted from elementary physical arguments. These predictions are then substantiated by exact numerical calculations on a ten-site ring, and finite-size effects are shown to be small. The principal results that are obtained are the following: (i) The on-site correlation $U$ strongly enhances the dimerization, the enhancement being strongest for $U\ensuremath{\sim}4{t}_{0}$, where $4{t}_{0}$ is the bandwidth of the uniform chain; (ii) the nearest-neighbor interaction ${V}_{1}$ further enhances the dimerization until ${V}_{1}\ensuremath{\lesssim}\frac{1}{2}U$, while ${V}_{1}>\frac{1}{2}U$ favors a uniform chain with a different broken-symmetry ground state, an on-site charge-density wave; (iii) for ${V}_{1}\ensuremath{\lesssim}\frac{1}{2}U$, the second-neighbor interaction ${V}_{2}$ reduces the dimerization slightly, although the dimerization is still stronger than that with an effective nearest-neighbor interaction ${V}_{1}\ensuremath{-}{V}_{2}$; (iv) for ${V}_{1}>\frac{1}{2}U$ , ${V}_{2}$ destroys the on-site charge-density wave and the ground state is strongly dimerized again. The complete Parisier-Parr-Pople (PPP) Hamiltonian is discussed, and it is pointed out that the above results, together with the excited-state orderings in the PPP Hamiltonian, strongly indicate that the ground state of the PPP Hamiltonian is the dimerized state. The excited-state orderings in finite polyenes, spin-density distributions in polyacetylene, and our theoretical results all indicate then that explicit inclusion of Coulomb interactions may be necessary for an accurate description of the ground and excited states in polyacetylene.A novel real-space approach to dimerization in a half-filled band is developed to investigate effects of electron-electron interactions on the Peierls instability. Dimerization is shown to be a result of imperfect resonance between pairs of electron configurations related to each other by a mirror-plane symmetry passing through the longest diagonal of the infinite ring, and the kinetic- and potential-energy contributions to the barrier to resonance are identified separately. The effects of including the on-site, nearest-neighbor, and next-nearest-neighbor interactions are investigated, and in each case it is shown that the enhancement or reduction in dimerization can be predicted from elementary physical arguments. These predictions are then substantiated by exact numerical calculations on a ten-site ring, and finite-size effects are shown to be small. The principal results that are obtained are the following: (i) The on-site correlation $U$ strongly enhances the dimerization, the enhancement being strongest for $U\ensuremath{\sim}4{t}_{0}$, where $4{t}_{0}$ is the bandwidth of the uniform chain; (ii) the nearest-neighbor interaction ${V}_{1}$ further enhances the dimerization until ${V}_{1}\ensuremath{\lesssim}\frac{1}{2}U$, while ${V}_{1}>\frac{1}{2}U$ favors a uniform chain with a different broken-symmetry ground state, an on-site charge-density wave; (iii) for ${V}_{1}\ensuremath{\lesssim}\frac{1}{2}U$, the second-neighbor interaction ${V}_{2}$ reduces the dimerization slightly, although the dimerization is still stronger than that with an effective nearest-neighbor interaction ${V}_{1}\ensuremath{-}{V}_{2}$; (iv) for ${V}_{1}>\frac{1}{2}U$, ${V}_{2}$ destroys the on-site charge-density wave and the ground state is strongly dimerized again. The complete Parisier-Parr-Pople (PPP) Hamiltonian is discussed, and it is pointed out that the above results, together with the excited-state orderings in the PPP Hamiltonian, strongly indicate that the ground state of the PPP Hamiltonian is the dimerized state. The excited-state orderings in finite polyenes, spin-density distributions in polyacetylene, and our theoretical results all indicate then that explicit inclusion of Coulomb interactions may be necessary for an accurate description of the ground and excited states in polyacetylene.

Physical review. B, Condensed matterFeb 15, 1984125 citations

{C}_{ij}

between neighboring and not neighboring sites

i,j

The features of the concurrences between the nearest-neighbors and that of the next-nearest-neighbors for the one-dimensional Heisenberg model with next-nearest-neighbor coupling

J

are studied as functions of temperature and

J

. The two concurrences exhibit a different dependence on

J

at the ground state, which could be interpreted from the point of view of the correlation functions. The threshold temperature at which the concurrence is zero and the temperature effect on the two concurrences for systems up to 12 sites are studied numerically.

Entanglement sharing among pairs of spins in Heisenberg antiferromagnets is investigated using the concurrence measure. For a nondegenerate

S=0

ground state, a simple formula relates the concurrence to the diagonal correlation function. The concurrence length is seen to be extremely short. Various finite clusters are studied numerically, to see the trend in two dimensions. It is argued that the concurrences vanish between pairs of spins which are not nearest neighbors for the linear-chain and square-lattice antiferromagnet ground states. For the triangular lattice and Kagome' lattice, nearest-neighbor concurrences also vanish. The concurrences in the maximal-spin states are explicitly calculated, where the concurrence averaged over all pairs is larger than the

S=0

states.

U

strongly enhances the dimerization, the enhancement being strongest for $U\ensuremath{\sim}4{t}_{0}$, where

4{t}_{0}

is the bandwidth of the uniform chain; (ii) the nearest-neighbor interaction

{V}_{1}

further enhances the dimerization until ${V}_{1}\ensuremath{\lesssim}\frac{1}{2}U$, while

{V}_{1}>\frac{1}{2}U

favors a uniform chain with a different broken-symmetry ground state, an on-site charge-density wave; (iii) for ${V}_{1}\ensuremath{\lesssim}\frac{1}{2}U$, the second-neighbor interaction

{V}_{2}

reduces the dimerization slightly, although the dimerization is still stronger than that with an effective nearest-neighbor interaction ${V}_{1}\ensuremath{-}{V}_{2}$; (iv) for

{V}_{1}>\frac{1}{2}U

{V}_{2}

destroys the on-site charge-density wave and the ground state is strongly dimerized again. The complete Parisier-Parr-Pople (PPP) Hamiltonian is discussed, and it is pointed out that the above results, together with the excited-state orderings in the PPP Hamiltonian, strongly indicate that the ground state of the PPP Hamiltonian is the dimerized state. The excited-state orderings in finite polyenes, spin-density distributions in polyacetylene, and our theoretical results all indicate then that explicit inclusion of Coulomb interactions may be necessary for an accurate description of the ground and excited states in polyacetylene.