Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0707.0473 · Physical Review A

Entanglement generation resonances in XY chains

R. Rossignoli, Christian Tomás Schmiegelow

Published Jan 18, 2007• 7 citations
arXivHTMLPDF

Abstract

We examine the maximum entanglement reached by an initially fully aligned state evolving in an $XY$ Heisenberg spin chain placed in a uniform transverse magnetic field. Both the global entanglement between one qubit and the rest of the chain and the pairwise entanglement between adjacent qubits is analyzed. It is shown that in both cases the maximum is not a monotonous decreasing function of the aligning field, exhibiting instead a resonant behavior for low anisotropies, with pronounced peaks (a total of $[n∕2]$ peaks in the global entanglement for an $n$-spin chain), whose width is proportional to the anisotropy and whose height remains finite in the limit of small anisotropy. It is also seen that the maximum pairwise entanglement is not a smooth function of the field even in small finite chains, where it may exhibit narrow peaks above strict plateaus. Explicit analytical results for small chains, as well as general exact results for finite $n$-spin chains obtained through the Jordan-Wigner mapping, are discussed.

DOI
10.1103/physreva.75.012320

Related papers

Generando entrelazamiento en cadenas XY - (Generating entanglement in XY chains)

Christian Tomás Schmiegelow

Se estudia en este trabajo la capacidad de generar entrelazamiento de una cadena de espines con acoplamiento de Heisenberg XY y un campo magnetico uniforme a partir de un estado inicial en el que los espines estan completamente alineados. Se encuentra que la capacidad de generar estados entrelazados no muestra un comportamiento monotono con el campo presentando, en cambio, plateaus y resonancias. Tambien se muestra que, a pesar de que la anisotropia es necesaria para que se generen estados entrelazados, una mayor anisotropia no implica necesariamente mejores condiciones para generar entrelazamiento que sirva para usarse en una computadora cuantica. Inclusive, se observa que, se genera una cantidad finita de entrelazamiento en el limite de pequena anisotropia. (The maximum entanglement reached by an initially fully aligned state evolving in a XY Heisenberg spin chain placed in a uniform transverse magnetic field is studied. It is shown that the capacity to create entangled states (both of one qubit with the rest of the chain and pairwise between two adjacent qubits) is not a monotonous function of the magnetic field: it presents plateaus and resonances. It is also shown that, though anisotropy in the interaction is necessary for entanglement generation, the best conditions for generating entanglement that may be suitable for use in quantum computation is not that of biggest anisotropy. Moreover finite amounts of entanglement are generated in the small anisotropy limit.)

arXiv:quant-ph/0611258•Nov 27, 2006•0 citations

Entanglement between distant qubits in cyclic XX chains

N. Canosa, R. Rossignoli

We evaluate the exact concurrence between any two spins in a cyclic $XX$ chain of $n$ spins placed in a uniform transverse magnetic field, at both zero and finite temperature, by means of the Jordan-Wigner transformation plus a number-parity-projected statistics. It is shown that, while at $T=0$ there is always entanglement between any two spins in a narrow field interval before the transition to the aligned state, at low but nonzero temperatures the entanglement remains nonzero for arbitrarily high fields, for any pair separation $L$, although its magnitude decreases exponentially with increasing field. It is also demonstrated that the associated limit temperatures approach a constant nonzero value in this limit, which decreases as ${L}^{\ensuremath{-}2}$ for $L⪡n$, but exhibit special finite-size effects for distant qubits $(L\ensuremath{\approx}n∕2)$. Related aspects such as the different behavior of even and odd antiferromagnetic chains, the existence of $n$ ground-state transitions, and the thermodynamic limit $n\ensuremath{\rightarrow}\ensuremath{\infty}$ are also discussed.

arXiv:0906.0801•Physical Review A•Mar 30, 2007•17 citations

Ground State Entanglement in Spin Systems

Hironori Yano, Hidetoshi Nishimori

We study the entanglement between arbitrary two spins in the XY and the antiferromagnetic Heisenberg spin chains in a uniform magnetic field.The entanglement of pairwise qubits in these models is obtained as a function of magnetic field by exact and numerical calculations.We find that the behavior of entanglement in the isotropic XY model is qualitatively the same as that in the Heisenberg model.Properties of entanglement length are also discussed.

Progress of Theoretical Physics Supplement•Jan 1, 2005•8 citations

Entanglement in a time-dependent coupled XY spin chain in an external magnetic field

Gehad Sadiek, Bedoor Alkurtass, Omar Marzook Al-Dossary

We consider an infinite one-dimensional anisotropic $\mathit{XY}$ spin chain with a nearest-neighbor time-dependent Heisenberg coupling $J(t)$ between the spins in presence of a time-dependent magnetic field $h(t)$. We discuss a general solution for the system and present an exact solution for particular choice of $J$ and $h$ of practical interest. We investigate the dynamics of entanglement for different degrees of anisotropy of the system and at both zero and finite temperatures. We find that the time evolution of entanglement in the system shows nonergodic and critical behavior at zero and finite temperatures and different degrees of anisotropy. The asymptotic behavior of entanglement at the infinite time limit at zero temperature and constant $J$ and $h$ depends only the parameter $\ensuremath{\lambda}=J/h$ rather than the individual values of $J$ and $h$ for all degrees of anisotropy but changes for nonzero temperature. Furthermore, the asymptotic behavior is very sensitive to the initial values of $J$ and $h$ and for particular choices we may create finite asymptotic entanglement regardless of the final values of $J$ and $h$. The persistence of quantum effects in the system as it evolves and as the temperature is raised is studied by monitoring the entanglement. We find that the quantum effects dominate within certain regions of the $\mathit{kT}$-$\ensuremath{\lambda}$ space that vary significantly depending on the degree of the anisotropy of the system. Particularly, the quantum effects in the Ising model case persist in the vicinity of both its critical phase transition point and zero temperature as it evolves in time. Moreover, the interplay between the different system parameters to tune and control the entanglement evolution is explored.

arXiv:1009.0648•Physical Review A•Nov 30, 2010•31 citations

Global entanglement in XXZ chains

N. Canosa, R. Rossignoli

We examine the thermal entanglement of $XXZ$-type Heisenberg chains in the presence of a uniform magnetic field along the $z$ axes through the evaluation of the negativity associated with bipartitions of the whole system and subsystems. Limit temperatures for nonzero global negativities are shown to depend on the asymmetry $\ensuremath{\Delta}$, but not on the uniform field, and can be much higher than those limiting pairwise entanglement. It is also shown that global bipartite entanglement may exist for $T>0$ even for $\ensuremath{\Delta}\ensuremath{\geqslant}1$, i.e., when the system is fully aligned (and hence separable) at $T=0$, and that the bipartition leading to the highest limit temperature depends on $\ensuremath{\Delta}$.

arXiv:1112.1279•Physical Review A•Feb 28, 2006•38 citations

Pair entanglement in dimerized spin- s chains

A. Boette, R. Rossignoli, N. Canosa +1 more

We examine the pair entanglement in the ground state of finite dimerized spin-$s$ chains interacting through anisotropic $XY$ couplings immersed in a transverse magnetic field by means of a self-consistent pair mean-field approximation. The approach, which makes no a priori assumptions on the pair states, predicts, for sufficiently low coupling between pairs, $2s$ distinct dimerized phases for increasing fields below the pair factorizing field, separated by spin-parity-breaking phases. The dimerized phases lead to approximate magnetization and pair entanglement plateaus, while the parity-breaking phases are characterized by weak pair entanglement but non-negligible entanglement of the pair with the rest of the system. These predictions are confirmed by the exact results obtained in finite $s=1$ and $s=3/2$ chains. It is also shown that for increasing values of the spin $s$, the entanglement of an isolated pair, as measured by the negativity, rapidly saturates in the anisotropic $XY$ case but increases as ${s}^{1/2}$ in the $XX$ case, reflecting a distinct single-spin entanglement spectrum.

arXiv:1610.00056•Physical review. B./Physical review. B•Dec 5, 2016•3 citations
We examine the maximum entanglement reached by an initially fully aligned state evolving in an XYXYXY Heisenberg spin chain placed in a uniform transverse magnetic field. Both the global entanglement between one qubit and the rest of the chain and the pairwise entanglement between adjacent qubits is analyzed. It is shown that in both cases the maximum is not a monotonous decreasing function of the aligning field, exhibiting instead a resonant behavior for low anisotropies, with pronounced peaks (a total of [n∕2][n∕2][n∕2] peaks in the global entanglement for an nnn-spin chain), whose width is proportional to the anisotropy and whose height remains finite in the limit of small anisotropy. It is also seen that the maximum pairwise entanglement is not a smooth function of the field even in small finite chains, where it may exhibit narrow peaks above strict plateaus. Explicit analytical results for small chains, as well as general exact results for finite nnn-spin chains obtained through the Jordan-Wigner mapping, are discussed.
Se estudia en este trabajo la capacidad de generar entrelazamiento de una cadena de espines con acoplamiento de Heisenberg XY y un campo magnetico uniforme a partir de un estado inicial en el que los espines estan completamente alineados. Se encuentra que la capacidad de generar estados entrelazados no muestra un comportamiento monotono con el campo presentando, en cambio, plateaus y resonancias. Tambien se muestra que, a pesar de que la anisotropia es necesaria para que se generen estados entrelazados, una mayor anisotropia no implica necesariamente mejores condiciones para generar entrelazamiento que sirva para usarse en una computadora cuantica. Inclusive, se observa que, se genera una cantidad finita de entrelazamiento en el limite de pequena anisotropia. (The maximum entanglement reached by an initially fully aligned state evolving in a XY Heisenberg spin chain placed in a uniform transverse magnetic field is studied. It is shown that the capacity to create entangled states (both of one qubit with the rest of the chain and pairwise between two adjacent qubits) is not a monotonous function of the magnetic field: it presents plateaus and resonances. It is also shown that, though anisotropy in the interaction is necessary for entanglement generation, the best conditions for generating entanglement that may be suitable for use in quantum computation is not that of biggest anisotropy. Moreover finite amounts of entanglement are generated in the small anisotropy limit.)
We evaluate the exact concurrence between any two spins in a cyclic XXXXXX chain of nnn spins placed in a uniform transverse magnetic field, at both zero and finite temperature, by means of the Jordan-Wigner transformation plus a number-parity-projected statistics. It is shown that, while at T=0T=0T=0 there is always entanglement between any two spins in a narrow field interval before the transition to the aligned state, at low but nonzero temperatures the entanglement remains nonzero for arbitrarily high fields, for any pair separation LLL, although its magnitude decreases exponentially with increasing field. It is also demonstrated that the associated limit temperatures approach a constant nonzero value in this limit, which decreases as ${L}^{\ensuremath{-}2}$ for L⪡nL⪡nL⪡n, but exhibit special finite-size effects for distant qubits $(L\ensuremath{\approx}n∕2)$. Related aspects such as the different behavior of even and odd antiferromagnetic chains, the existence of nnn ground-state transitions, and the thermodynamic limit $n\ensuremath{\rightarrow}\ensuremath{\infty}$ are also discussed.
We consider an infinite one-dimensional anisotropic XY\mathit{XY}XY spin chain with a nearest-neighbor time-dependent Heisenberg coupling J(t)J(t)J(t) between the spins in presence of a time-dependent magnetic field h(t)h(t)h(t). We discuss a general solution for the system and present an exact solution for particular choice of JJJ and hhh of practical interest. We investigate the dynamics of entanglement for different degrees of anisotropy of the system and at both zero and finite temperatures. We find that the time evolution of entanglement in the system shows nonergodic and critical behavior at zero and finite temperatures and different degrees of anisotropy. The asymptotic behavior of entanglement at the infinite time limit at zero temperature and constant JJJ and hhh depends only the parameter $\ensuremath{\lambda}=J/h$ rather than the individual values of JJJ and hhh for all degrees of anisotropy but changes for nonzero temperature. Furthermore, the asymptotic behavior is very sensitive to the initial values of JJJ and hhh and for particular choices we may create finite asymptotic entanglement regardless of the final values of JJJ and hhh. The persistence of quantum effects in the system as it evolves and as the temperature is raised is studied by monitoring the entanglement. We find that the quantum effects dominate within certain regions of the kT\mathit{kT}kT-$\ensuremath{\lambda}$ space that vary significantly depending on the degree of the anisotropy of the system. Particularly, the quantum effects in the Ising model case persist in the vicinity of both its critical phase transition point and zero temperature as it evolves in time. Moreover, the interplay between the different system parameters to tune and control the entanglement evolution is explored.
We examine the thermal entanglement of XXZXXZXXZ-type Heisenberg chains in the presence of a uniform magnetic field along the zzz axes through the evaluation of the negativity associated with bipartitions of the whole system and subsystems. Limit temperatures for nonzero global negativities are shown to depend on the asymmetry $\ensuremath{\Delta}$, but not on the uniform field, and can be much higher than those limiting pairwise entanglement. It is also shown that global bipartite entanglement may exist for T>0T>0T>0 even for $\ensuremath{\Delta}\ensuremath{\geqslant}1$, i.e., when the system is fully aligned (and hence separable) at T=0T=0T=0, and that the bipartition leading to the highest limit temperature depends on $\ensuremath{\Delta}$.
We examine the pair entanglement in the ground state of finite dimerized spin-sss chains interacting through anisotropic XYXYXY couplings immersed in a transverse magnetic field by means of a self-consistent pair mean-field approximation. The approach, which makes no a priori assumptions on the pair states, predicts, for sufficiently low coupling between pairs, 2s2s2s distinct dimerized phases for increasing fields below the pair factorizing field, separated by spin-parity-breaking phases. The dimerized phases lead to approximate magnetization and pair entanglement plateaus, while the parity-breaking phases are characterized by weak pair entanglement but non-negligible entanglement of the pair with the rest of the system. These predictions are confirmed by the exact results obtained in finite s=1s=1s=1 and s=3/2s=3/2s=3/2 chains. It is also shown that for increasing values of the spin sss, the entanglement of an isolated pair, as measured by the negativity, rapidly saturates in the anisotropic XYXYXY case but increases as s1/2{s}^{1/2}s1/2 in the XXXXXX case, reflecting a distinct single-spin entanglement spectrum.