Entanglement in a second-order quantum phase transition (4 pages)

Howard Barnum, Rolando D. Somma, Gerardo Ortíz

Neill Lambert

Zhe Yang, Jian-Pin Wu, Peng Liu

We study mixed-state entanglement measures in Einstein-Born-Infeld (EBI) massive gravity theory, a model exhibiting both Hawking-Page phase transitions and effective metal-insulator transitions (MIT) at finite temperatures. Our comprehensive investigation reveals that the entanglement wedge cross-section (EWCS), a holographic probe of mixed-state entanglement structure, demonstrates distinctive properties in detecting phase transitions. For the effective MIT, we find that the higher-order terms of EWCS align closely with the crossover temperature, a feature not shared by holographic entanglement entropy (HEE). This sensitivity makes EWCS a complementary geometric tool for probing effective phase transitions at finite temperatures. In Hawking-Page phase transitions, we observe that all entanglement measures effectively diagnose both first-order and second-order phase transitions, with EWCS showing configuration-independent behavior. Importantly, we discover that all geometry-related quantities, including entanglement measures, demonstrate a universal critical exponent of 1/3 near the second-order phase transition point. This result suggests a fundamental connection between quantum information theory and critical phenomena in gravitational systems, and also highlights the potential of EWCS as a powerful probe for phase transitions.

Julien Vidal, Rémy Mosseri, J. Dukelsky

We analyze the entanglement properties of the ground state for a system of spins half embedded in a magnetic field, mutually interacting antiferromagnetically. Contrary to the ferromagnetic case where a second-order quantum phase transition occurs, a first-order transition is obtained at zero field and the so-called concurrence which measures the two-spin entanglement displays a jump at the transition point.

Ivan Deutsch, Paul M. Alsing, Barry C. Sanders +1 more

Aydin Deger

In this work, we give a detailed analytic treatment of one-dimensional anisotropic XY model in the transverse field. We present a multipartite geometric measure of entanglement per site and per block and use it for quantifying global entanglement in many-body systems. We also investigate spontaneous symmetry breaking and Quantum Phase Transition (QPT) in the model. Further, we extend the solution of the XY model to the n-site interaction and diagonalize the Hamiltonian and obtain energy levels and eigenvalues. We also examine Quantum Entanglement and QPT for next-nearest neighbor interaction and halfway interaction. At last, we introduce a Generalized Cluster-XY Hamiltonian with n-site interaction. Through this, one can diagonalize many suitable bilinear Hamiltonians by defining parameters that characterize the model. By using the model, we investigate QPT between Ferromagnetic-Paramagnetic state, GHZ-Cluster state and symmetry protected topological order and an antiferromagnetic state. | 96 pages