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arXiv:1206.4246

Classification of entanglement and quantum phase transition in XX model

Ting Zhang, Pinx-Xing Chen, Wei-Tao Liu, Cheng-Zu Li

Published Jun 19, 2012• 2 citations
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Abstract

We study the relation between entanglement and quantum phase transition (QPT) from a new perspective. Motivated by one's intuition: QPT is characterized by the change of the ground-state structure, while entangled states belong to different classes have different structures, we conjecture that QPT occurs as the class of ground-state entanglement changes and prove it in XX model. Despite the classification of multipartite entanglement is yet unresolved, we proposed a new method to judge whether two many-body states belong to the same entanglement class.

DOI
10.48550/arxiv.1206.4246

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We study the relation between entanglement and quantum phase transition (QPT) from a new perspective. Motivated by one's intuition: QPT is characterized by the change of the ground-state structure, while entangled states belong to different classes have different structures, we conjecture that QPT occurs as the class of ground-state entanglement changes and prove it in XX model. Despite the classification of multipartite entanglement is yet unresolved, we proposed a new method to judge whether two many-body states belong to the same entanglement class.
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Abstract With the aid of the quantum renormalization group (QRG) method, we study the multipartite entanglement and quantum phase transitions (QPTs) in the XXZ model with Dzyaloshinskii–Moriya (DM) interaction. The measures employed here are genuine multipartite entanglement (GME-concurrence) and global entanglement. The results show that both multipartite entanglement measures can accurately detect QPTs at the critical points after sufficient iteration steps. By the difference analysis, moreover, we derive an inequality such that the global entanglement is exactly an upper bound of the square GME-concurrence. Actually, this inequality is established whether or not the QRG method is carried out, which discloses some intrinsic features of long-scale multipartite entanglement. Based on the first derivative of GME-concurrence, the non-analytic phenomenon and scaling behaviors with different theoretical exponents are analyzed in detail, showing that the ground states of the XXZ model with DM interaction are asymmetrical.
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Quantum materials exhibit rich phenomenology when driven across quantum critical points. Conventional quantum phase transitions are characterized by the change of an order parameter and the emergence of a divergent correlation length. In this work we propose a new class of quantum phase transitions, termed Quantum Matter Causal Phase Transitions (QMCPT), where the underlying causal structure of the many‑body wavefunction reorganizes itself rather than merely the order parameter. We develop a theoretical framework that describes how a causal graph, built from the entanglement structure of the ground state, can undergo a topological change. The transition is marked by a discontinuity or singularity in the causal depth, a quantity that counts the minimal number of layers of local operations required to prepare the state from a product state. We derive scaling relations for the causal depth near criticality, establish its universal behaviour, and discuss possible experimental signatures in strongly correlated systems such as heavy‑fermion compounds and twisted bilayer graphene. The QMCPT framework offers a new classification of quantum phases and provides a bridge between quantum information theory and condensed matter physics, opening pathways for identifying new materials with quantum critical behaviour and potential Nobel‑level discoveries.
Gerardo Ortiz Department of Physics, Indiana University, Bloomington, Indiana 47405, U.S.A. Quantum matter often displays complex phase diagrams as a result of competing interactions, with orderings (states of matter) which are believed to be influenced by being in proximity to quantum critical points, e.g., high-Tc materials, heavy fermion compounds, and frustrated magnets. Each quantum phase is characterized by different behaviors of appropriate correlation functions, such as long-range order, or algebraic or exponential decay. Since entanglement is a property inherent in quantum states and is strongly related to quantum correlations, one would expect that the entanglement present in the ground state (GS) of the system changes substantially at a quantum phase transition (QPT), i.e., when there is a qualitative change in the behavior of the correlations between constituents. Obviously, the identification and quantification of those changes become issues of utmost relevance.
We derive a general relation between the nonanalyticities of the ground state energy and those of a subclass of the multipartite generalized global entanglement (GGE) measure defined by de Oliveira et al. [Phys. Rev. A 73, 010305(R) (2006)] for many-particle systems. We show that GGE signals both a critical point location and the order of a quantum phase transition (QPT). We also show that GGE allows us to study the relation between multipartite entanglement and QPTs, suggesting that multipartite but not bipartite entanglement is favored at the critical point. Finally, using GGE we were able, at a second-order QPT, to define a diverging entanglement length (EL) in terms of the usual correlation length. We exemplify this with the XY spin-1/2 chain and show that the EL is half the correlation length.