Transições de fase quânticas dinâmicas na cadeia XX desordenada

Abstract

The theory of Dynamical Quantum Phase Transitions (DQPTs) is explored in search of some nonequilibrium analogue for the so-called Quantum Griffiths Phases. That is done by taking the disordered XX chain (dXX) as exploratory model. This problem is equivalent to that of free-fermions with random hoppings, as can be obtained via Jordan-Wigner transformation. We obtain a general solution for quench protocols between arbitrary equilibrium phases with generic random free-fermion models whose ground state is given at half-filling; given that the result is given by a \frac{L}{2}x\frac{L}{2} matrix' determinant, where L is the number of chain sites, the immediate physical interpretation of the dynamical mechanisms is unclear, even though we have reduced the complexity of the original problem (a 2^{L}-sized Hilbert space). In order to suppress interpretational difficulties, two exact analytical results are derived: the quench between two XX chains, each of them characterized by two alternating - but fixed - couplings, sheding some light over the “clean” system; the other result is a particular case of the quench between disordered systems that turns out to be useful in various practical circumstances. Our numerical results suggest the existence of a First Order DQPT. The positive answer to the existence of such dynamical transitions for the chosen disordered model is but one of a few, if not the only, that were presented in the literature.