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:1610.00056 · Physical review. B./Physical review. B

Pair entanglement in dimerized spin- s chains

A. Boette, R. Rossignoli, N. Canosa, J. M. Matera

Published Dec 5, 2016• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.94.214403

Related papers

Generalized mean-field description of entanglement in dimerized spin systems

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

We discuss a generalized self-consistent mean-field (MF) treatment, based on the selection of an arbitrary subset of operators for representing the system density matrix, and its application to the problem of entanglement evaluation in composite quantum systems. As a specific example, we examine in detail a pair MF approach to the ground state (GS) of dimerized spin-$1/2$ systems with anisotropic ferromagnetic-type $XY$ and $XYZ$ couplings in a transverse field, including chains and arrays with first neighbor and also longer range couplings. The approach is fully analytic and able to capture the main features of the GS of these systems, in contrast with the conventional single-spin MF. Its phase diagram differs significantly from that of the latter, exhibiting $({S}_{z})$ parity breaking just in a finite field window if the coupling between pairs is sufficiently weak, together with a fully dimerized phase below this window and a partially aligned phase above it. It is then shown that through symmetry restoration, the approach is able to correctly predict not only the concurrence of a pair, but also its entanglement with the rest of the chain, which shows a pronounced peak in the parity breaking window. Perturbative corrections allow to reproduce more subtle observables like the entanglement between weakly coupled spins and the low lying energy spectrum. All predictions are tested against exact results for finite systems.

arXiv:1410.6007•Physical Review B•Feb 27, 2015•5 citations

Entanglement of finite cyclic chains at factorizing fields

R. Rossignoli, N. Canosa, J. M. Matera

We examine the entanglement of cyclic spin-1/2 chains with anisotropic $XYZ$ Heisenberg couplings of arbitrary range at transverse factorizing magnetic fields. At these fields the system exhibits a degenerate symmetry-breaking separable ground state (GS). It is shown, however, that the side limits of the GS pairwise entanglement at these fields are actually nonzero in finite chains, corresponding such fields to a GS spin-parity transition. These limits exhibit universal properties like being independent of the pair separation and interaction range, and are directly related to the magnetization jump. Illustrative exact results are shown for chains with (I) full range and (II) nearest-neighbor couplings. Global entanglement properties at such points are also discussed.

arXiv:1101.3908•Physical Review A•May 19, 2008•58 citations

Separability and entanglement in finite dimer-type chains in general transverse fields

N. Canosa, R. Rossignoli, J. M. Matera

We determine the conditions under which general dimer-type spin chains with $XYZ$ couplings of arbitrary range in a general transverse field will exhibit an exactly separable parity-breaking eigenstate. We also provide sufficient conditions which ensure that it will be a ground state. We then examine the exact side limits at separability of the entanglement between any two spins in a finite chain, showing that in the vicinity of separability, the system will loose all signatures of dimerization, with pairwise entanglement approaching infinite range and becoming independent of separation and interaction range. The possibility of a nonuniform exactly separable ground state induced by an alternating field is also shown. As illustration, we examine the behavior of the pairwise entanglement in a finite $XY$ dimer chain under a uniform as well as alternating field. Related aspects of the magnetization are also discussed.

arXiv:1008.4412•Physical Review B•Feb 11, 2010•25 citations

Factorization and entanglement in general XYZ spin arrays in nonuniform transverse fields

R. Rossignoli, N. Canosa, J. M. Matera

We determine the conditions for the existence of a pair of degenerate parity breaking separable eigenstates in general arrays of arbitrary spins connected through $XYZ$ couplings of arbitrary range and placed in a transverse field, not necessarily uniform. Sufficient conditions under which they are ground states are also provided. It is then shown that in finite chains, the associated definite parity states, which represent the actual ground state in the immediate vicinity of separability, can exhibit entanglement between any two spins regardless of the coupling range or separation, with the reduced state of any two subsystems equivalent to that of pair of qubits in an entangled mixed state. The corresponding concurrences and negativities are exactly determined. The same properties persist in the mixture of both definite parity states. These effects become specially relevant in systems close to the $XXZ$ limit. The possibility of field induced alternating separable solutions with controllable entanglement side limits is also discussed. Illustrative numerical results for the negativity between the first and the ${j}^{\text{th}}$ spin in an open spin $s$ chain for different values of $s$ and $j$ are as well provided.

arXiv:0910.0300•Physical Review A•Dec 10, 2009•40 citations

Quantum Phase Transition in Dimerized Spin-1/2 Chains

Aparajita Das, Sreeparna Bhadra, Sonali Saha

Quantum phase transition in dimerized antiferromagnetic Heisenberg spin chain has been studied. A staircase structure in the variation of concurrence within strongly coupled pairs with that of external magnetic field has been observed indicating multiple critical points. Emergence of entanglement due to external magnetic field or magnetic entanglement is observed for weakly coupled spin pairs in the same dimer chain. Though closed dimerized isotropic XXX Heisenberg chains with different dimer strengths were mainly explored, analogous studies on open chains as well as closed anisotropic (XX interaction) chains with tilted external magnetic field have also been studied.

arXiv:1503.08716•Mar 30, 2015•1 citation

Thermal entanglement in fully connected spin systems and its random-phase-approximation description

J. M. Matera, R. Rossignoli, N. Canosa

We examine the thermal pairwise entanglement in a symmetric system of $n$ spins fully connected through anisotropic $XYZ$-type couplings embedded in a transverse magnetic field. We consider both the exact evaluation together with that obtained with the static $\text{path}+\text{random}$ phase approximation (RPA) and the ensuing mean $\text{field}+\text{RPA}$. The latter is shown to provide an accurate analytic description of both the parallel and antiparallel thermal concurrence in large systems. We also analyze the limit temperature for pairwise entanglement, which is shown to increase for large fields and to decrease logarithmically with increasing $n$. Special finite-size effects are also discussed.

arXiv:1104.5694•Physical Review A•Jul 10, 2008•17 citations
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.
We discuss a generalized self-consistent mean-field (MF) treatment, based on the selection of an arbitrary subset of operators for representing the system density matrix, and its application to the problem of entanglement evaluation in composite quantum systems. As a specific example, we examine in detail a pair MF approach to the ground state (GS) of dimerized spin-1/21/21/2 systems with anisotropic ferromagnetic-type XYXYXY and XYZXYZXYZ couplings in a transverse field, including chains and arrays with first neighbor and also longer range couplings. The approach is fully analytic and able to capture the main features of the GS of these systems, in contrast with the conventional single-spin MF. Its phase diagram differs significantly from that of the latter, exhibiting (Sz)({S}_{z})(Sz​) parity breaking just in a finite field window if the coupling between pairs is sufficiently weak, together with a fully dimerized phase below this window and a partially aligned phase above it. It is then shown that through symmetry restoration, the approach is able to correctly predict not only the concurrence of a pair, but also its entanglement with the rest of the chain, which shows a pronounced peak in the parity breaking window. Perturbative corrections allow to reproduce more subtle observables like the entanglement between weakly coupled spins and the low lying energy spectrum. All predictions are tested against exact results for finite systems.
We examine the entanglement of cyclic spin-1/2 chains with anisotropic XYZXYZXYZ Heisenberg couplings of arbitrary range at transverse factorizing magnetic fields. At these fields the system exhibits a degenerate symmetry-breaking separable ground state (GS). It is shown, however, that the side limits of the GS pairwise entanglement at these fields are actually nonzero in finite chains, corresponding such fields to a GS spin-parity transition. These limits exhibit universal properties like being independent of the pair separation and interaction range, and are directly related to the magnetization jump. Illustrative exact results are shown for chains with (I) full range and (II) nearest-neighbor couplings. Global entanglement properties at such points are also discussed.
We determine the conditions under which general dimer-type spin chains with XYZXYZXYZ couplings of arbitrary range in a general transverse field will exhibit an exactly separable parity-breaking eigenstate. We also provide sufficient conditions which ensure that it will be a ground state. We then examine the exact side limits at separability of the entanglement between any two spins in a finite chain, showing that in the vicinity of separability, the system will loose all signatures of dimerization, with pairwise entanglement approaching infinite range and becoming independent of separation and interaction range. The possibility of a nonuniform exactly separable ground state induced by an alternating field is also shown. As illustration, we examine the behavior of the pairwise entanglement in a finite XYXYXY dimer chain under a uniform as well as alternating field. Related aspects of the magnetization are also discussed.
We determine the conditions for the existence of a pair of degenerate parity breaking separable eigenstates in general arrays of arbitrary spins connected through XYZXYZXYZ couplings of arbitrary range and placed in a transverse field, not necessarily uniform. Sufficient conditions under which they are ground states are also provided. It is then shown that in finite chains, the associated definite parity states, which represent the actual ground state in the immediate vicinity of separability, can exhibit entanglement between any two spins regardless of the coupling range or separation, with the reduced state of any two subsystems equivalent to that of pair of qubits in an entangled mixed state. The corresponding concurrences and negativities are exactly determined. The same properties persist in the mixture of both definite parity states. These effects become specially relevant in systems close to the XXZXXZXXZ limit. The possibility of field induced alternating separable solutions with controllable entanglement side limits is also discussed. Illustrative numerical results for the negativity between the first and the jth{j}^{\text{th}}jth spin in an open spin sss chain for different values of sss and jjj are as well provided.
Quantum phase transition in dimerized antiferromagnetic Heisenberg spin chain has been studied. A staircase structure in the variation of concurrence within strongly coupled pairs with that of external magnetic field has been observed indicating multiple critical points. Emergence of entanglement due to external magnetic field or magnetic entanglement is observed for weakly coupled spin pairs in the same dimer chain. Though closed dimerized isotropic XXX Heisenberg chains with different dimer strengths were mainly explored, analogous studies on open chains as well as closed anisotropic (XX interaction) chains with tilted external magnetic field have also been studied.
We examine the thermal pairwise entanglement in a symmetric system of nnn spins fully connected through anisotropic XYZXYZXYZ-type couplings embedded in a transverse magnetic field. We consider both the exact evaluation together with that obtained with the static path+random\text{path}+\text{random}path+random phase approximation (RPA) and the ensuing mean field+RPA\text{field}+\text{RPA}field+RPA. The latter is shown to provide an accurate analytic description of both the parallel and antiparallel thermal concurrence in large systems. We also analyze the limit temperature for pairwise entanglement, which is shown to increase for large fields and to decrease logarithmically with increasing nnn. Special finite-size effects are also discussed.