Excited-state quantum phase transitions in many-body systems with infinite-range interaction : localization, dynamics, and bifurcation

Excited state quantum phase transitions (ESQPTs) are generalizations of quantum phase transitions (QPTs) to excited levels. They are associated with local divergences in the density of states. Here, we investigate how the presence of an ESQPT can be detected from the analysis of the structure of the Hamiltonian matrix, the level of localization of the eigenstates, the onset of bifurcation, and the speed of the system evolution. Our findings are illustrated for a Hamiltonian with infinite-range Ising interaction in a transverse field. This is a version of the Lipkin-Meshkov-Glick (LMG) model and the limiting case of the one-dimensional spin-1/2 system with tunable interactions realized with ion traps. From our studies for the dynamics, we uncover similarities between the LMG and the noninteracting XX models.LFS and MT were supported by the NSF grant No. DMR- 1147430. FPB was funded by MINECO grant FIS2014- 53448-C2- 2-P and by Spanish Consolider-Ingenio 2010 (CPANCSD2007- 00042). LFS and FPB thank Pedro Perez- Fernandez and Jorge Dukelsky for discussions, as well as the hospitality of Alejandro Frank and the Centro de Ciencias de la Complejidad (C3) at the UNAM in Mexico, where part of this work was carried out

Realistic Many-Body Quantum Systems vs. Full Random Matrices: Static and Dynamical Properties

We study the static and dynamical properties of isolated many-body quantum systems and compare them with the results for full random matrices. In doing so, we link concepts from quantum information theory with those from quantum chaos. In particular, we relate the von Neumann entanglement entropy with the Shannon information entropy and discuss their relevance for the analysis of the degree of complexity of the eigenstates, the behavior of the system at different time scales and the conditions for thermalization. A main advantage of full random matrices is that they enable the derivation of analytical expressions that agree extremely well with the numerics and provide bounds for realistic many-body quantum systems

Differential hemodynamic adaptations to tilt test in patients with idiopathic atrial fibrillation

Abstract The hemodynamic response during the transition from the supine to standing position in idiopathic atrial fibrillation (AF) patients is not completely understood. This study aimed to analyze the hemodynamic changes that occur during the head‐up tilt test in idiopathic AF patients. We investigated the hemodynamic changes during the head‐up tilt test with impedance cardiography in 40 AF patients (12 with AF rhythm‐AFr and 28 with sinus rhythm‐AFsr) and 38 non‐AF controls. Patients with AFr had attenuated SVI decrease after standing when compared to AFsr and non‐AF [ΔSVI in mL/m2: −1.3 (−3.4 to 1.7) vs. −6.4 (−17.3 to −0.1) vs. −11.8 (−18.7 to −8.0), respectively; p < 0.001]. PVRI decreased in AFr but increased in AFsr and non‐AF [ΔPVRI in dyne.seg.m2/cm5: −477 (−1148 to 82.5) vs. 131 (−525 to 887) vs. 357 (−29 to 681), respectively; p < 0.01]. Similarly, compared with non‐AF patients, AFr patients also had a greater HR and greater CI increase after standing. The haemodynamic response to orthostatic challenge suggests differential adaptations between patients with AF rhythm and those reverted to sinus rhythm or healthy controls. Characterizing the hemodynamic phenotype may be relevant for the individualized treatment of AF patients