Entanglement and local extremes at an infinite-order quantum phase transition

Abstract

The characterization of an infinite-order quantum phase transition (QPT) by entanglement measures is analyzed. To this aim, we consider two closely related solvable spin-1/2 chains, namely, the Ashkin-Teller and the staggered XXZ models. These systems display a distinct pattern of eigenstates but exhibit the same thermodynamics, i.e. the same energy spectrum. By performing exact diagonalization, we investigate the behavior of pairwise and block entanglement in the ground state of both models. In contrast with the XXZ chain, we show that pairwise entanglement fails in the characterization of the infinite-order QPT in the Ashkin-Teller model, although it can be achieved by analyzing the distance of the pair state from the separability boundary. Concerning block entanglement, we show that both XXZ and Ashkin-Teller models exhibit identical von Neumann entropies as long as a suitable choice of blocks is performed. Entanglement entropy is then shown to be able to identify the quantum phase diagram, even though its local extremes (either maximum or minimum) may also appear in the absence of any infinite-order QPT.

8 pages, 10 figures. v3: references added, figures improved, and minor corrections. v2: minor corrections in figures 3 and 10

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• Spotlighting quantum critical points via quantum correlations at finite temperatures
• Long-range quantum discord in critical spin systems
• Correlation and nonlocality measures as indicators of quantum phase transitions in several critical systems
• Experimental Quantum Simulation of Entanglement in Many-body Systems
• Precise Determination of Quantum Critical Points by the Violation of the Entropic Area Law
• Interplay between quantum phase transitions and the behavior of quantum correlations at finite temperatures
• Witnessing nonclassical multipartite states
• Visualizing quantum phase transitions in the XXZ model via the quantum steering ellipsoid
• Correlation-induced coherence and its use in detecting quantum phase transitions
• Fidelity and entanglement entropy for infinite-order phase transitions
• Discrete and generalized phase space techniques in critical quantum spin chains
• Generalized Phase-Space Techniques to Explore Quantum Phase Transitions in Critical Quantum Spin Systems
• Cumulative measure of correlation for multipartite quantum states
• Phase diagram of an extended parafermion chain