Formação de ordenamento de carga e spin: evolução temporal após quenches em sistemas interagentes unidimensionais

Abstract

In this master’s dissertation, we explore non-equilibrium phenomena in strongly interacting electron systems. Our main focus is on investigating the emergence of charge and spin orderings in one-dimensional systems under non-equilibrium conditions. Starting from an initially disordered non-interacting state, we track its time evolution under an interacting Hamiltonian—a protocol known as a quantum quench.

Specifically, we concentrate on the development of charge and spin orderings within the half-filled one-dimensional extended Hubbard model, characterized by repulsive interactions and exhibiting the charge density wave (CDW) and spin density wave (SDW) phases. We simulate the progression of the initial state under the Hamiltonian of the mentioned model, considering that the electronic interactions progressively scale up over a finite time interval, eventually reaching values corresponding to the CDW or SDW phase.

The non-equilibrium dynamics are examined using the time-dependent extension of the density matrix renormalization group (t-DMRG) method, implemented through the ITensor software. Inspired by tensor diagrams, ITensor facilitates efficient and accurate numerical simulations, enabling comprehensive analyses of the system time evolution under different degrees of electronic interactions.

After reproducing results obtained in our research group for the evolution during the quench, we proceed to investigate the post-quench free evolution. Analyzing the order parameters of the CDW and SDW phases, we identify three temporal regimes for the quenches: instantaneous, intermediate, and adiabatic. The system that achieved the adiabatic regime during the quench remained stable in the post-quench analysis. The system subject to the instantaneous regime during the quench did not converge to the ground state in the post-quench, exhibiting a significant increase in entropy. In the case of the intermediate regime, after reaching a peak during the quench, the parameters exhibited oscillatory behavior, which was also observed in larger chains.