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Scientific Reports

Scaling of Geometric Quantum Discord Close to a Topological Phase Transition

Chuan-Jia Shan, W. W. Cheng, Ji-Bing Liu, Yongshan Cheng, Tang-Kun Liu

Published Mar 26, 2014• 30 citations
Publisher

Abstract

Quantum phase transition is one of the most interesting aspects in quantum many-body systems. Recently, geometric quantum discord has been introduced to signature the critical behavior of various quantum systems. However, it is well-known that topological quantum phase transition can not be described by the conventional Landau's symmetry breaking theory, and thus it is unknown that whether previous study can be applicable in this case. Here, we study the topological quantum phase transition in Kitaev's 1D p-wave spinless quantum wire model in terms of its ground state geometric quantum discord. The derivative of geometric quantum discord is nonanalytic at the critical point, in both zero temperature and finite temperature cases. The scaling behavior and the universality are verified numerically. Therefore, our results clearly show that all the key ingredients of the topological phase transition can be captured by the nearest neighbor and long-range geometric quantum discord.

DOI
10.1038/srep04473

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Quantum phase transition is one of the most interesting aspects in quantum many-body systems. Recently, geometric quantum discord has been introduced to signature the critical behavior of various quantum systems. However, it is well-known that topological quantum phase transition can not be described by the conventional Landau's symmetry breaking theory, and thus it is unknown that whether previous study can be applicable in this case. Here, we study the topological quantum phase transition in Kitaev's 1D p-wave spinless quantum wire model in terms of its ground state geometric quantum discord. The derivative of geometric quantum discord is nonanalytic at the critical point, in both zero temperature and finite temperature cases. The scaling behavior and the universality are verified numerically. Therefore, our results clearly show that all the key ingredients of the topological phase transition can be captured by the nearest neighbor and long-range geometric quantum discord.
Quantum phase transition is one of the most interesting aspects in quantum many-body systems. Recently, geometric quantum discord has been introduced to signature the critical behavior of various quantum systems. However, it is well-known that topological quantum phase transition can not be described by the conventional Landau’s symmetry breaking theory, and thus it is unknown that whether previous study can be applicable in this case. Here, we study the topological quantum phase transition in Kitaev’s 1D p-wave spinless quantum wire model in terms of its ground state geometric quantum discord. The derivative of geometric quantum discord is nonanalytic at the critical point, in both zero temperature and finite temperature cases. The scaling behavior and the universality are verified numerically. Therefore, our results clearly show that all the key ingredients of the topological phase transition can be captured by the nearest neighbor and long-range geometric quantum discord.
We present a unified study of the topological quantum phase transition in Kitaev's 1D p-wave spinless quantum wire model in terms of its ground state geometric phase (GP). We also analyze zero-temperature and finite-temperature scaling parameters, extracted from the GP near the critical point. The derivative of the ground-state GP is nonanalytic at the phase boundary. A finite-size scaling and finite-temperature scaling analysis are carried out and, furthermore, the scaling behavior and universality are verified numerically.
The geometry of quantum states can be an indicator of criticality, yet it remains less explored under non-Hermitian topological conditions. In this work, we unveil diverse scalings of the quantum geometry over the ground-state manifold close to different topological phase transitions in a non-Hermitian long-range extension of the Kitaev chain. The derivative of the geometric phase, as well as its scaling behavior, shows that systems with different long-range couplings can belong to a distinct critical class. Near certain criticalities, we further find that the Wannier state correlation function associated with the extended Berry connection of the ground state exhibits spatially anomalous behaviors. Finally, we analyze the scaling of the quantum geometric tensor near phase transitions across exceptional points, shedding light on the emergence of a distinct critical class.
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.
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.
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.