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arXiv:0912.3874 · Physical Review A

Quantum correlations in topological quantum phase transitions

Yi-Xin Chen, Sheng-Wen Li

Published Mar 25, 2010• 106 citations
arXivHTMLPDF

Abstract

We study the quantum correlations in a two-dimensional system that possesses a topological quantum phase transition. The quantumness of two-body correlations is measured by quantum discord. We calculate both the correlation of two local spins and that between an arbitrary spin and the rest of the lattice. It is notable that local spins are classically correlated, while the quantum correlation is hidden in the global lattice. This is different from other systems which are not topologically ordered. Moreover, the mutual information and global quantum discord show critical behavior in the topological quantum phase transition.

DOI
10.1103/physreva.81.032120

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We study the quantum correlations in a two-dimensional system that possesses a topological quantum phase transition. The quantumness of two-body correlations is measured by quantum discord. We calculate both the correlation of two local spins and that between an arbitrary spin and the rest of the lattice. It is notable that local spins are classically correlated, while the quantum correlation is hidden in the global lattice. This is different from other systems which are not topologically ordered. Moreover, the mutual information and global quantum discord show critical behavior in the topological quantum phase transition.
We discuss a clusterlike one-dimensional system with triplet interaction. We study the topological properties of this system. We find that the degeneracy depends on the topology of the system and is well protected against external local perturbations. All these facts show that the system is topologically ordered. We also find a string order parameter to characterize the quantum phase transition. Besides, we investigate two-site correlations including entanglement, quantum discord, and mutual information. We study the different divergence behaviors of the correlations. The quantum correlation decays exponentially in both topological and magnetic phases, and diverges in reversed power law at the critical point. And we find that in topological order systems, the global difference of topology induced by dimension can be reflected in local quantum correlations.
Quantum phase transitions of the transverse Ising and antiferromagnetic XXZXXZXXZ spin S=1/2S=1/2S=1/2 chains are studied using quantum discord. Quantum discord allows the measure of quantum correlations present in many-body quantum systems. It is shown that the amount of quantum correlations increases close to the critical points. The observations are in agreement with the information provided by the concurrence, which measures the entanglement of the many-body system.
Quantum and classical pairwise correlations in two typical collective spin systems (i.e., the Dicke model and the Lipkin-Meshkov-Glick model) are discussed. These correlations in the thermodynamical limit are obtained analytically and in a finite-size system are calculated numerically. Large-size scaling behavior for the quantum discord itself is observed, which has never been reported in another critical system. A logarithmic diverging behavior for the first derivative of the quantum discord is also found in both models, which might be universal in the second-order quantum phase transition. It is suggested that the pronounced maximum or minimum of first derivative of quantum discord signifies the critical point. Comparisons between the quantum discord and the scaled concurrence are performed. It is shown that the quantum discord is very small in one phase and robust in the other phase, while the scaled concurrence shows maximum at the critical point and decays rapidly when away from the the critical point.
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Abstract We investigate the ground-state quantum correlations in the spin-1/2 XX chain with anisotropic four-spin interaction (AFSI), employing an exact analytical approach via fermionization. The phase diagram of the system hosts three distinct quantum critical lines that separate non-trivial topological phases characterized by winding numbers ν = ±1 and ν = ±3. To probe the system’s critical behavior and topological nature, we analyze two key quantum correlation measures: concurrence and quantum discord between nearest-neighbor spin pairs. Our results reveal that while concurrence is limited in detecting all critical lines particularly in phases with higher winding numbers, quantum discord successfully identifies all quantum phase transitions, either through cusps or discontinuities in its first derivative. Furthermore, quantum discord assumes larger values in topological phases with lower winding numbers, suggesting that the structure and localization of quantum correlations are influenced by topological order. These findings underscore the effectiveness of quantum discord as a robust diagnostic tool for both criticality and topology in many-body quantum systems. Our results offer valuable insight for advancing correlation-based techniques in quantum information science and highlight the potential role of topological spin chains in future quantum technologies.
Non-classical correlations arise in various quantum mechanical systems. Characterization and quantification of these correlations is an important and active branch of research in the field of quantum information theory. Investigation of non-classical correlations in condensed matter systems gives important insights about the characteristics of these systems. In particular, systems possessing a quantum critical point in their phase diagrams have attracted much attention due to the peculiar behavior of correlations near these points. In this thesis, we have investigated two distinct quantum spin models from the perspective of correlations and, we have discussed the correlation content of an important subclass of bipartite states. We start by an analytical calculation of the quantum discord for a system composed of spin-j and spin-1/2 subsystems possessing rotational symmetry. We have compared our results with the quantum discord of states having similar symmetries and seen that in rotationally invariant states the amount of quantum discord is much higher. Moreover, using the well known entanglement properties of these states, we have compared their quantum discord with entanglement and seen that quantum discord is higher than the entanglement. Next, we have investigated the thermal quantum correlations and entanglement in spin-1 Bose-Hubbard model with two and three particles. We have demonstrated that the energy level crossings in the ground state of the system are signalled by both the behavior of thermal quantum correlations and entanglement. Finally, we have investigated various thermal quantum and total correlations in the anisotropic XY spin-chain with transverse magnetic field. We have shown that the ability of the considered measures to estimate the critical points of this system at finite temperature strongly depends on the anisotropy parameter of the Hamiltonian. Furthermore, we have studied the effect of temperature on long-range correlations of the XY chain.