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:1112.0361 · International Journal of Modern Physics B

QUANTUM DISCORD IN A SPIN SYSTEM WITH SYMMETRY BREAKING

Bruno Tomasello, Davide Rossini, Alioscia Hamma, Luigi Amico A

Published Sep 18, 2012• 18 citations
arXivHTMLPDF

Abstract

We analyze the quantum discordQ throughout the low temperature phase diagram of the quantum XY model in transverse field. We first focus on the T = 0 order–disorder quantum phase transition QPT both in the symmetric ground state and in the symmetry broken one. Beside it, we highlight how Q displays clear anomalies also at a noncritical value of the control parameter inside the ordered phase, where the ground state is completely factorized. We evidence how the phenomenon is in fact of collective nature and displays universal features. We also study Q at finite temperature. We show that, close to the QPT, Q exhibits quantum-classical crossover of the system with universal scaling behavior. We evidence a nontrivial pattern of thermal correlations resulting from the factorization phenomenon.

DOI
10.1142/s0217979212430023

Related papers

Ground-state factorization and correlations with broken symmetry

Bruno Tomasello, Davide Rossini, Alioscia Hamma +1 more

We show how the phenomenon of factorization in a quantum many-body system is of collective nature. To this aim we study the quantum discord Q in the one-dimensional XY model in a transverse field. We analyze the behavior of Q at both the critical point and at the non-critical factorizing field. The factorization is found to be governed by an exponential scaling law for Q . We also address the thermal effects fanning out from the anomalies occurring at zero temperature. Close to the quantum phase transition, Q exhibits a finite-temperature crossover with universal scaling behavior, while the factorization phenomenon results in a non-trivial pattern of correlations present at low temperature.

arXiv:1012.4270•Europhysics Letters (EPL)•Sep 23, 2011•63 citations

QUANTUM DISCORD IN THE GROUND STATE OF SPIN CHAINS

M. S. Sarandy, THIAGO R. DE OLIVEIRA, Luigi Amico A

The ground state of a quantum spin chain is a natural playground for investigating correlations. Nevertheless, not all correlations are genuinely of quantum nature. Here we review the recent progress to quantify the "quantumness" of the correlations throughout the phase diagram of quantum spin systems. Focusing to one spatial dimension, we discuss the behavior of quantum discord (QD) close to quantum phase transitions (QPT). In contrast to the two-spin entanglement, pairwise discord is effectively long-ranged in critical regimes. Besides the features of QPT, QD is especially feasible to explore the factorization phenomenon, giving rise to nontrivial ground classical states in quantum systems. The effects of spontaneous symmetry breaking are also discussed as well as the identification of quantum critical points through correlation witnesses.

arXiv:1208.4817•International Journal of Modern Physics B•Nov 1, 2012•48 citations

INTERPLAY BETWEEN QUANTUM PHASE TRANSITIONS AND THE BEHAVIOR OF QUANTUM CORRELATIONS AT FINITE TEMPERATURES

T. Werlang, G. A. P. RIBEIRO, GUSTAVO RIGOLIN

We review the main results and ideas showing that quantum correlations at finite temperatures (T), in particular quantum discord, are useful tools in characterizing quantum phase transitions (QPT) that only occur, in principle, at the unattainable absolute zero temperature. We first review some interesting results about the behavior of thermal quantum discord for small spin-1/2 chains and show that they already give us important hints of the infinite chain behavior. We then study in detail and in the thermodynamic limit (infinite chains) the thermal quantum correlations for the XXZ and XY models, where one can clearly appreciate that the behavior of thermal quantum discord at finite T is a useful tool to spotlight the critical point of a QPT.

arXiv:1205.1046•International Journal of Modern Physics B•Oct 2, 2012•28 citations

Quantum Correlation in One Dimensional Spin Model

Sarnava Datta

We investigate the behaviour of quantum correlations (entanglement and quantum discord) for homogeneous XY model at absolute zero and at finite temperature. Study of this correlation measures of quenched disordered quantum spin models like the XY spin glass and random-field XY models is also reviewed. We show that quenched averaged quantum correlations can showcase the order-from-disorder phenomenon for finite-size systems and also when the system is in the thermodynamic limit. Though we find some regions with positive enhancement score. This order from disorder phenomena is more prominent when the system is in the finite temparature with some definite values of external parameter. We also look into correlation length. Correlation functions of ground states typically decay exponentially with the distance for quantum spin systems. In such systems, entanglement does not survive when |i-j| ≳ 3. However, quantum discord survives long lattice distances as it is not monogamous for this system. We investigate the effects of quenched disorder on quantum correlation lengths of quenched averaged entanglement and quantum discord, in the anisotropic XY spin glass chains. We realize that there is practically neither diminution nor growth in entanglement length while quantum discord length increases significantly with the introduction of quenched disorder except near factorization point. Apart from that, we also investigate the scaling behaviour of quantum entanglement and quantum discord. We find that though entanglement follows finite size scaling close to quantum phase transition, scaling can't be done for quantum discord.

•Apr 1, 2017•0 citations

Thermal quantum and classical correlations and entanglement in the XY spin model with three-spin interaction

Yanchao Li, Hai‐Qing Lin

Pairwise quantum discord (QD) and classical correlation (CC) are studied in the $\mathit{XY}$ spin chain with three-spin interaction. We analyze their capability in detecting quantum phase transitions (QPTs) at both zero and finite temperatures and find that the pairwise QD of two neighboring spins is more reliable than that of any other distances in identifying QPTs. Both the QD and CC detect quantum critical points associated with first- and higher-order QPTs caused by field and three-spin interactions at finite temperatures. In addition, we find a different finite-size scaling behavior for QD from previous reports for the transverse field Ising case and show some interesting phenomena of QD and entanglement of formation for finite temperatures.

Physical Review A•May 24, 2011•130 citations

Quantum Correlations in Infinite XY Spin-1/2 Chains and Quantum Phase Transition

Xiaodong Tan, Shou-Sheng Huang, Bai-Qi Jin

We examine the ability of quantum discord (QD) and entanglements (concurrence, EoF and negativity) to detect the critical points associated to quantum phase transitions (QPTs) for XY models, i.e., the isotropic XY model with three-spin interactions at zero temperature, and the anisotropic XY model in a transverse magnetic field h at finite temperatures. For the case of zero temperature, we found that both entanglements and QD can spotlight the critical points of QPTs for these two models. Moreover, QD versus distance M exhibits the long-range behavior of quantum correlation for the anisotropic XY model, while entanglement is short-ranged. For the case of finite temperatures, we found that negativity has the same behaviors with concurrence at or near transition points. Moreover, QD for the anisotropic XY model can increase with temperature even in the absence of a magnetic field.

Communications in Theoretical Physics•Feb 1, 2013•9 citations
We analyze the quantum discordQ throughout the low temperature phase diagram of the quantum XY model in transverse field. We first focus on the T = 0 order–disorder quantum phase transition QPT both in the symmetric ground state and in the symmetry broken one. Beside it, we highlight how Q displays clear anomalies also at a noncritical value of the control parameter inside the ordered phase, where the ground state is completely factorized. We evidence how the phenomenon is in fact of collective nature and displays universal features. We also study Q at finite temperature. We show that, close to the QPT, Q exhibits quantum-classical crossover of the system with universal scaling behavior. We evidence a nontrivial pattern of thermal correlations resulting from the factorization phenomenon.
We show how the phenomenon of factorization in a quantum many-body system is of collective nature. To this aim we study the quantum discord Q in the one-dimensional XY model in a transverse field. We analyze the behavior of Q at both the critical point and at the non-critical factorizing field. The factorization is found to be governed by an exponential scaling law for Q . We also address the thermal effects fanning out from the anomalies occurring at zero temperature. Close to the quantum phase transition, Q exhibits a finite-temperature crossover with universal scaling behavior, while the factorization phenomenon results in a non-trivial pattern of correlations present at low temperature.
The ground state of a quantum spin chain is a natural playground for investigating correlations. Nevertheless, not all correlations are genuinely of quantum nature. Here we review the recent progress to quantify the "quantumness" of the correlations throughout the phase diagram of quantum spin systems. Focusing to one spatial dimension, we discuss the behavior of quantum discord (QD) close to quantum phase transitions (QPT). In contrast to the two-spin entanglement, pairwise discord is effectively long-ranged in critical regimes. Besides the features of QPT, QD is especially feasible to explore the factorization phenomenon, giving rise to nontrivial ground classical states in quantum systems. The effects of spontaneous symmetry breaking are also discussed as well as the identification of quantum critical points through correlation witnesses.
We review the main results and ideas showing that quantum correlations at finite temperatures (T), in particular quantum discord, are useful tools in characterizing quantum phase transitions (QPT) that only occur, in principle, at the unattainable absolute zero temperature. We first review some interesting results about the behavior of thermal quantum discord for small spin-1/2 chains and show that they already give us important hints of the infinite chain behavior. We then study in detail and in the thermodynamic limit (infinite chains) the thermal quantum correlations for the XXZ and XY models, where one can clearly appreciate that the behavior of thermal quantum discord at finite T is a useful tool to spotlight the critical point of a QPT.
We investigate the behaviour of quantum correlations (entanglement and quantum discord) for homogeneous XY model at absolute zero and at finite temperature. Study of this correlation measures of quenched disordered quantum spin models like the XY spin glass and random-field XY models is also reviewed. We show that quenched averaged quantum correlations can showcase the order-from-disorder phenomenon for finite-size systems and also when the system is in the thermodynamic limit. Though we find some regions with positive enhancement score. This order from disorder phenomena is more prominent when the system is in the finite temparature with some definite values of external parameter. We also look into correlation length. Correlation functions of ground states typically decay exponentially with the distance for quantum spin systems. In such systems, entanglement does not survive when |i-j| ≳ 3. However, quantum discord survives long lattice distances as it is not monogamous for this system. We investigate the effects of quenched disorder on quantum correlation lengths of quenched averaged entanglement and quantum discord, in the anisotropic XY spin glass chains. We realize that there is practically neither diminution nor growth in entanglement length while quantum discord length increases significantly with the introduction of quenched disorder except near factorization point. Apart from that, we also investigate the scaling behaviour of quantum entanglement and quantum discord. We find that though entanglement follows finite size scaling close to quantum phase transition, scaling can't be done for quantum discord.
Pairwise quantum discord (QD) and classical correlation (CC) are studied in the XY\mathit{XY}XY spin chain with three-spin interaction. We analyze their capability in detecting quantum phase transitions (QPTs) at both zero and finite temperatures and find that the pairwise QD of two neighboring spins is more reliable than that of any other distances in identifying QPTs. Both the QD and CC detect quantum critical points associated with first- and higher-order QPTs caused by field and three-spin interactions at finite temperatures. In addition, we find a different finite-size scaling behavior for QD from previous reports for the transverse field Ising case and show some interesting phenomena of QD and entanglement of formation for finite temperatures.
We examine the ability of quantum discord (QD) and entanglements (concurrence, EoF and negativity) to detect the critical points associated to quantum phase transitions (QPTs) for XY models, i.e., the isotropic XY model with three-spin interactions at zero temperature, and the anisotropic XY model in a transverse magnetic field h at finite temperatures. For the case of zero temperature, we found that both entanglements and QD can spotlight the critical points of QPTs for these two models. Moreover, QD versus distance M exhibits the long-range behavior of quantum correlation for the anisotropic XY model, while entanglement is short-ranged. For the case of finite temperatures, we found that negativity has the same behaviors with concurrence at or near transition points. Moreover, QD for the anisotropic XY model can increase with temperature even in the absence of a magnetic field.