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Europhysics Letters (EPL)

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

Z.-Y. Sun, Lu Li, Neng Li, K.L. Yao, J. Liu, Bo Luo, G.-H. Du, Hong-Nian Li

Published Jul 20, 2011• 14 citations
Publisher

Abstract

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.

DOI
10.1209/0295-5075/95/30008

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We compute the quantum correlation [quantum discord (QD)] and the entanglement (EOF) between nearest-neighbor qubits (spin-1/2) in an infinite chain described by the Heisenberg model (XXZ Hamiltonian) at finite temperatures. The chain is in the thermodynamic limit and thermalized with a reservoir at temperature T (canonical ensemble). We show that QD, in contrast to EOF and other thermodynamic quantities, spotlight the critical points associated with quantum phase transitions (QPT) for this model even at finite T. This remarkable property of QD may have important implications for experimental characterization of QPTs when one is unable to reach temperatures below which a QPT can be seen.
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We investigate how quantum correlations [quantum discord (QD)] of a two-qubit one-dimensional XYZ\mathit{XYZ}XYZ Heisenberg chain in thermal equilibrium depend on the temperature TTT of the bath and also on an external magnetic field BBB. We show that the behavior of thermal QD differs in many unexpected ways from thermal entanglement. For example, we show situations where QD increases with TTT when entanglement decreases, cases where QD increases with TTT even in regions with zero entanglement, and that QD signals a quantum phase transition even at finite TTT. We also show that by properly tuning BBB or the interaction between the qubits we get nonzero QD for any TTT and we present an effect not seen for entanglement, the ``regrowth'' of thermal QD.
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 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 quantum statistical mechanics, finite-temperature phase transitions are typically governed by classical field theories. In this context, the role of quantum correlations is unclear: recent contributions have shown how entanglement is typically very short-ranged, and thus uninformative about long-ranged critical correlations. In this work, we show the existence of finite-temperature phase transitions where a broader form of quantum correlation than entanglement, the entropic quantum discord, can display genuine signatures of critical behavior. We consider integrable bosonic field theories in both two- and three-dimensional lattices, and show how the two-mode Gaussian discord decays algebraically with the distance even in cases where the entanglement negativity vanishes beyond nearest-neighbor separations. Systematically approaching the zero-temperature limit allows us to connect discord to entanglement, drawing a generic picture of quantum correlations and critical behavior that naturally describes the transition between entangled and discordant quantum matter.