Replacing energy by von Neumann entropy in quantum phase transitions

摘要

In the thermodynamic limit two distinct states of matter cannot be analyticcontinuations of each other. Classical phase transitions are characterized bynon-analyticities of the free energy. For quantum phase transitions (QPTs) theground state energy often assumes the role of the free energy. But in a numberof important cases this criterion fails to predict a QPT, such as thethree-dimensional metal-insulator transition of non-interacting electrons in arandom potential (Anderson localization). It is therefore essential that wefind alternative criteria that can track fundamental changes in the internalcorrelations of the ground state wavefunction. Here we propose that QPTs aregenerally 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 dissipativequantum systems of considerable interest to the study of decoherence and findthat non-analyticities occur if and only if the system undergoes a QPT.