Real-Time Evolution in the Hubbard Model with Infinite Repulsion

TL;DR

This paper analyzes the real-time dynamics of the infinite-coupling Hubbard model, mapping it to a quadratic fermionic model and deriving exact expressions for certain observables' evolution, including densities and correlations.

Contribution

It provides an exact solution for the quench dynamics of specific observables in the infinite-repulsion Hubbard model using a mapping to a tight-binding model.

Findings

Exact expressions for density evolution in the Hubbard model.

Explicit formulas for boundary-bulk correlations after a quench.

Simplified results for dynamics from generalized nested Néel states.

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 N\'eel states.