2006/04/06 by Angela Kopp, Xun Jia, Sudip Chakravarty · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Dissipative system #Entropy (arrow of time) #Phase transition #Quantum #Quantum and electron transport phenomena #Quantum decoherence #Quantum discord #Quantum dissipation #Quantum many-body systems #Quantum phase transition #Quantum system #Von Neumann entropy #cond-mat.stat-mech #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1016/j.aop.2006.08.002
published as Annals of Physics 322, 1466-1476 (2007) · 8 pages, 6 figures; Annals of Physics, in press (2006)
arxiv created 2006/04/06 · openalex publication_date 2006/09/29 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In the thermodynamic limit two distinct states of matter cannot be analytic continuations of each other. Classical phase transitions are characterized by non-analyticities of the free energy. For quantum phase transitions (QPTs) the ground state energy often assumes the role of the free energy. But in a number of important cases this criterion fails to predict a QPT, such as the three-dimensional metal-insulator transition of non-interacting electrons in a random potential (Anderson localization). It is therefore essential that we find alternative criteria that can track fundamental changes in the internal correlations of the ground state wavefunction. Here we propose that QPTs are generally accompanied by non-analyticities of the von Neumann (entanglement) entropy. In particular, the entropy is non-analytic at the Anderson transition, where it exhibits unusual fractal scaling. We also examine two dissipative quantum systems of considerable interest to the study of decoherence and find that non-analyticities occur if and only if the system undergoes a QPT.