Transições de fase quânticas dinâmicas na cadeia XX desordenada

• Autor(a) principal: Costa, Rafael Freitas Pereira
• Data de Publicação: 2021
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFU
• Texto Completo: https://repositorio.ufu.br/handle/123456789/32464; http://doi.org/10.14393/ufu.di.2021.351
• topic: Elétrons fortemente correlacionados; Amplitude de Loschmidt; SDRG; Grupo de renormalização; Dinâmica exata; Modelo XX; Desordem de ligação; Sistemas críticos; Fase de Griffiths; DQPT; Transições de fase quânticas dinâmicas; Strongly correlated electrons; Loschmidt amplitude; Renormalization group; Exact dynamics; XX model; Bond disorder; Critical phenomena; Quantum Griffiths phase; Dynamical quantum phase transitions; CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA; Teoria quântica; Física

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.