Transições de fase quânticas dinâmicas do modelo de Creutz com hopping de longo alcance

Abstract

In this dissertation, we investigate dynamical quantum phase transitions (DQPTs) in the Creutz model with hopping of range D, decaying according to a power-law with exponent ν. We obtain the exact solution of a generic two-band model, of which the Creutz model is a particular case. We derive analytical expressions for dynamical quantities which are relevant to the study of DQPTs, such as the Loschmidt amplitude and the dynamical free energy of the system. This allows us to analytically determine the Yang-Lee-Fisher (YLF) zeros associated with the Loschmidt amplitude. Consequently, we identify the critical times at which non-analyticities in the dynamical free energy occur in the Creutz model with long-range hopping. Our results indicate that the number of YLF zeros increases with increasing D and decreasing ν. In particular, our findings suggest that in the limit D → ∞ e ν → 0, the dynamical free energy becomes non-analytic at almost all times. A similar consequence, when considering these limits, has already been observed in the case of the Su-Schrieffer-Heeger (SSH) model with long-range hopping.