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:1304.7362 · physica status solidi (b)

Odd-even effect of quantum discord in the spin-1/2 Heisenberg two-leg ladder with ring exchange

Hailin Huang, Zhao‐Yu Sun, B. Wang

Published Jun 26, 2013• 3 citations
arXivHTMLPDF

Abstract

The singularity of quantum correlation has been widely regarded as a valuable indicator for quantum phase transition (QPT) in low-dimensional quantum systems. In this paper, in a two-leg spin ladder with ring exchange, the critical points of the system cannot be detected by analyzing the singularity of the quantum discord (a kind of quantum correlation). Instead, the discord exhibits a novel odd–even effect in the symmetry-breaking (SB) regions, which can be used to detect the two critical points between the SB regions and the non-SB regions. The underlying mechanism of the odd–even effect is explained.

DOI
10.1002/pssb.201349047

Related papers

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

Quantum discord in matrix product systems

Zhao‐Yu Sun, Liang Li, K.L. Yao +5 more

We consider a class of quantum systems with spin-flip symmetry and derive the quantum correlation measured by the quantum discord (QD). As an illustration, we investigate the QD in a three-body interaction model and an XYZ interaction model, whose ground states can be expressed as matrix product states, and the QD is exactly soluble. We show that the QD behaves differently than the quantum entanglement (QE) in many ways; for example, they may show opposite monotonicity and completely different finite-size effects. Furthermore, we compare the capability of the QD and the QE to detect quantum phase transitions (QPTs) and find that the QD is more reliable than the QE for signaling QPTs in these models: In the three-body interaction model, the QE is singular at the quantum critical point, however, it exhibits an additional singularity in the noncritical region, while the analyticity of the QD can be used to identify the quantum critical point perfectly; and in the XYZ interaction model, the QE vanishes in the thermodynamic limit, thus losing its ability to detect QPTs, while the QD still functions very well.

Physical Review A•Sep 10, 2010•30 citations

Pairing Correlation in the Three-Leg Hubbard Ladder – Renormalization Group and Quantum Monte Carlo Studies

T. Kimura, Kazuhiko Kuroki, Hideo Aoki

In order to shed light whether the `even-odd conjecture' (even numbers of legs will superconduct accompanied by a spin gap while odd ones do not) for correlated electrons in ladder systems, the pairing correlation is studied for the Hubbard model on a two- and three-leg ladders. We have employed both the weak-coupling renormalization group and the quantum Monte Carlo (QMC) method for strong interactions. For the two-leg Hubbard ladder, a systematic QMC (with a controlled level spacings) has detected an enhanced pairing correlation, which is consistent with the weak-coupling prediction. We also calculate the correlation functions in the three-leg Hubbard ladder and show that the weak-coupling study predicts the dominant superconductivity, which refutes the naive even-odd conjecture. A crucial point is a spin gap for only some of the multiple spin modes is enough to make the ladder superconduct with a pairing symmetry (d-like here) compatible with the gapped mode. A QMC study for the three-leg ladder endorses the enhanced pairing correlation.

arXiv:cond-mat/9706289•Journal of the Physical Society of Japan•Apr 15, 1998•16 citations

Phases of the generalized two-leg spin ladder: A view from the SU(4) symmetry

P. Lecheminant, Kiyohito Totsuka

The zero-temperature phases of a generalized two-leg spin ladder with four-spin exchanges are discussed by means of a low-energy field theory approach starting from an SU(4) quantum critical point. The latter fixed point is shown to be a rich multicritical point that unifies different competing dimerized orders and a scalar chirality phase that breaks spontaneously the time-reversal symmetry. The quantum phase transition between these phases is dominated by spin-singlet fluctuations and belongs to the Luttinger universality class due to the existence of a $\mathrm{U}(1)$ self-duality symmetry.

arXiv:cond-mat/0405275•Physical Review B•Jan 27, 2005•23 citations

Quantum discord and quantum phase transition in spin-1/2 frustrated Heisenberg chain

Chu-Hui Fan, Heng-Na Xiong, Yixiao Huang +1 more

By using the concept of the quantum discord (QD), we study the spin-1/2 antiferromagnetic Heisenberg chain with next-nearest-neighbor interaction. Due to the $SU(2)$ symmetry and $Z_{2}$ symmetry in this system, we obtain the analytical result of the QD and its geometric measure (GMQD), which is determined by the two-site correlators. For the 4-site and 6-site cases, the connection between GMQD (QD) and the eigenenergies was revealed. From the analytical and numerical results, we find GMQD (QD) is an effective tool in detecting the both the first-order and the infinite-order quantum-phase-transition points for the finite-size systems. Moreover, by using the entanglement excitation energy and a universal frustration measure we consider the frustration properties of the system and find a nonlinear dependence of the GMQD on the frustration.

arXiv:1301.6482•Quantum Information and Computation•May 1, 2013•6 citations

Quantum correlation and phase transitions in a two-dimensional doubly decorated Ising-Heisenberg model

Z.-Y. Sun, Lu Li, Neng Li +5 more

We investigate the pairwise quantum correlation, characterized by quantum entanglement (QE) and quantum discord (QD), of a two-dimensional Ising-Heisenberg model on a planar doubly decorated lattice. At zero temperature, the concurrence (a measurement of pairwise entanglement) and the QD are related to the correlation function q xx and the staggered magnetization δ S z , respectively, and both of them indicate the quantum phase transition (QPT) of the system. However, in a finite-temperature phase transition, all the pairwise entanglement vanishes thus it fails to detect the critical temperature T C , while the derivative of QD diverges at T C . This shows clearly that QD can capture the signal of phase transition in a separable state, thus it has a broader scope of application than QE in detecting phase transitions.

Europhysics Letters (EPL)•Jul 20, 2011•14 citations
The singularity of quantum correlation has been widely regarded as a valuable indicator for quantum phase transition (QPT) in low-dimensional quantum systems. In this paper, in a two-leg spin ladder with ring exchange, the critical points of the system cannot be detected by analyzing the singularity of the quantum discord (a kind of quantum correlation). Instead, the discord exhibits a novel odd–even effect in the symmetry-breaking (SB) regions, which can be used to detect the two critical points between the SB regions and the non-SB regions. The underlying mechanism of the odd–even effect is explained.
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 consider a class of quantum systems with spin-flip symmetry and derive the quantum correlation measured by the quantum discord (QD). As an illustration, we investigate the QD in a three-body interaction model and an XYZ interaction model, whose ground states can be expressed as matrix product states, and the QD is exactly soluble. We show that the QD behaves differently than the quantum entanglement (QE) in many ways; for example, they may show opposite monotonicity and completely different finite-size effects. Furthermore, we compare the capability of the QD and the QE to detect quantum phase transitions (QPTs) and find that the QD is more reliable than the QE for signaling QPTs in these models: In the three-body interaction model, the QE is singular at the quantum critical point, however, it exhibits an additional singularity in the noncritical region, while the analyticity of the QD can be used to identify the quantum critical point perfectly; and in the XYZ interaction model, the QE vanishes in the thermodynamic limit, thus losing its ability to detect QPTs, while the QD still functions very well.
In order to shed light whether the `even-odd conjecture' (even numbers of legs will superconduct accompanied by a spin gap while odd ones do not) for correlated electrons in ladder systems, the pairing correlation is studied for the Hubbard model on a two- and three-leg ladders. We have employed both the weak-coupling renormalization group and the quantum Monte Carlo (QMC) method for strong interactions. For the two-leg Hubbard ladder, a systematic QMC (with a controlled level spacings) has detected an enhanced pairing correlation, which is consistent with the weak-coupling prediction. We also calculate the correlation functions in the three-leg Hubbard ladder and show that the weak-coupling study predicts the dominant superconductivity, which refutes the naive even-odd conjecture. A crucial point is a spin gap for only some of the multiple spin modes is enough to make the ladder superconduct with a pairing symmetry (d-like here) compatible with the gapped mode. A QMC study for the three-leg ladder endorses the enhanced pairing correlation.
The zero-temperature phases of a generalized two-leg spin ladder with four-spin exchanges are discussed by means of a low-energy field theory approach starting from an SU(4) quantum critical point. The latter fixed point is shown to be a rich multicritical point that unifies different competing dimerized orders and a scalar chirality phase that breaks spontaneously the time-reversal symmetry. The quantum phase transition between these phases is dominated by spin-singlet fluctuations and belongs to the Luttinger universality class due to the existence of a U(1)\mathrm{U}(1)U(1) self-duality symmetry.
By using the concept of the quantum discord (QD), we study the spin-1/2 antiferromagnetic Heisenberg chain with next-nearest-neighbor interaction. Due to the SU(2)SU(2)SU(2) symmetry and Z2Z_{2}Z2​ symmetry in this system, we obtain the analytical result of the QD and its geometric measure (GMQD), which is determined by the two-site correlators. For the 4-site and 6-site cases, the connection between GMQD (QD) and the eigenenergies was revealed. From the analytical and numerical results, we find GMQD (QD) is an effective tool in detecting the both the first-order and the infinite-order quantum-phase-transition points for the finite-size systems. Moreover, by using the entanglement excitation energy and a universal frustration measure we consider the frustration properties of the system and find a nonlinear dependence of the GMQD on the frustration.
We investigate the pairwise quantum correlation, characterized by quantum entanglement (QE) and quantum discord (QD), of a two-dimensional Ising-Heisenberg model on a planar doubly decorated lattice. At zero temperature, the concurrence (a measurement of pairwise entanglement) and the QD are related to the correlation function q xx and the staggered magnetization δ S z , respectively, and both of them indicate the quantum phase transition (QPT) of the system. However, in a finite-temperature phase transition, all the pairwise entanglement vanishes thus it fails to detect the critical temperature T C , while the derivative of QD diverges at T C . This shows clearly that QD can capture the signal of phase transition in a separable state, thus it has a broader scope of application than QE in detecting phase transitions.