Abstract
We consider the real-time evolution of the Hubbard model in the limit of infinite coupling. In this limit the Hamiltonian of the system is mapped into a number-conserving quadratic form of spinless fermions, i.e. the tight binding model. The relevant local observables, however, do not transform well under this mapping and take very complicated expressions in terms of the spinless fermions. Here we show that for two classes of interesting observables the quench dynamics from product states in the occupation basis can be determined exactly in terms of correlations in the tight-binding model. In particular, we show that the time evolution of any function of the total density of particles is mapped directly into that of the same function of the density of spinless fermions in the tight-binding model. Moreover, we express the two-point functions of the spin-full fermions at any time after the quench in terms of correlations of the tight binding model. This sum is generically very complicated but we show that it leads to simple explicit expressions for the time evolution of the densities of the two separate species and the correlations between a point at the boundary and one in the bulk when evolving from the so called generalised nested Néel states.
Highlights
In Ref. [82] we considered Hubbard in the limit of infinite repulsion, when the thermodynamics becomes essentially that of a free model
In this paper we studied the real-time dynamics of the Hubbard model with open boundary conditions in the limit of infinite repulsion
We pointed out that the expectation value of any function of the total density is exactly equal to the analogous quantity in the tight-binding model
Summary
The Hubbard model is the fundamental paradigm of strongly correlated electrons and, as such, is attracting the attention of theoreticians from many different corners of condensed matter. Very few of the aforementioned results, have so far been explicitly tested in the case of the Hubbard model This is mainly because none of the analytical approaches developed to determine the stationary state of out-of-equilibrium integrable systems [24,25,26,27] can be applied to the Hubbard model with finite interaction strength due to its technical complexity. In recent years a number of exact results concerning the finite time dynamics have been found in a special class of integrable systems that can be thought of as strong coupling limits of standard integrable models [63,64,65,66,67,68,69,70,71]
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