Exact spectral function and nonequilibrium dynamics of the strongly interacting Hubbard model

TL;DR

This paper derives exact determinant formulas for correlation functions in the strongly interacting 1D Hubbard model, applicable in equilibrium and nonequilibrium, enabling efficient numerical analysis of spectral functions and dynamical phenomena.

Contribution

It provides the first exact determinant representations for correlation functions in the 1D Hubbard model under trapping potentials, valid in both equilibrium and nonequilibrium states.

Findings

Exact determinant formulas for correlation functions.

Observation of dynamical quasicondensation in trapped systems.

Efficient numerical implementation surpassing previous methods.

Abstract

Analytical results on the correlation functions of strongly correlated many-body systems are rare in the literature and their importance cannot be overstated. We present determinant representations for the space-, time-, and temperature-dependent correlation functions of the strongly interacting one-dimensional Hubbard model in the presence of an external trapping potential. These representations are exact and valid in both equilibrium and nonequilibrium scenarios like the ones initiated by a sudden change of the confinement potential. In addition, they can be implemented numerically very easily significantly outperforming other numerical approaches. As applications of our results we investigate the single particle spectral functions of systems with harmonic trapping and show that dynamical quasicondensation occurs for both fermionic and bosonic spin-$1/2$ systems released from a Mott insulator state.