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Merhej, Elie
(2024).
DOI: https://doi.org/10.21954/ou.ro.00099135
Abstract
In this thesis, we study the dynamics of the two-leg half-filled Hubbard ladder model when pushed out-of-equilibrium. To achieve this, we use matrix product state methods for finite and infinite length Hubbard ladders, to first study the ground state properties of the model in equilibrium, then to allow the time-evolution of the initial state in a specific non-equilibrium format. We benchmark our numerical methods against exact diagonalisation algorithms for small system sizes, and against a field theory calculation for the Heisenberg spin ladder model.
Two non-equilibrium scenarios are considered. In the first one, we study the dynamics of the Hubbard ladder under a pump-probe protocol relevant to time-resolved resonant inelastic X-ray spectroscopies. To achieve this, we calculate time-dependent quantities, including the doublon number, the total magnetisation and spin/charge correlation functions. Furthermore, we compute experimentally relevant quantities, known as the non-equilibrium dynamical structure factors for both the spin and charge. Such quantities offer a detailed understanding into the evolution of the excitations at different momenta and energies. We demonstrate the role of pump anisotropy: pumping energy along the legs of the ladder suppresses the magnetic correlations more than pumping along the rungs direction, for the same pump fluence. In contrast, density correlations are enhanced, and the charge spectral weight is shifted to lower energies. We also find that the late-time physics is dominated by nearest neighbour correlations.
In the second non-equilibrium scenario, we study the response of the Hubbard ladder, when subjected to a time-dependent square form variation of its rung direction. In the first part of the study, we analyse the local antiferromagnetic correlation functions in the strong coupling limit, by calculating the spin gaps in the different sectors of the Hilbert space, and therefore relating the energy of the spin excitations to the period of oscillations of these local correlations. Moreover, we compare our findings with the Heisenberg spin ladder case. In the second part of the study, we highlight the role of the charge dynamics as the Hubbard ladder model transitions from the spin ladder limit in the strong interaction coupling regime, to a mixture of strongly correlated charge and spin degrees of freedom for intermediate and weak couplings.
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