Lightcone renormalization and quantum quenches in one-dimensional Hubbard models

TL;DR

This paper introduces an efficient light cone-based renormalization group algorithm to study real-time dynamics in one-dimensional Hubbard models, revealing relaxation behaviors, thermalization, and spin-charge separation.

Contribution

The authors develop a novel light cone renormalization method that handles non-translationally invariant systems and local conservation laws for real-time evolution.

Findings

Power-law decay of double occupancies in integrable Hubbard models

Exponential decay with added nearest neighbor interactions

Long-time states approximate thermal averages, sometimes requiring negative temperatures

Abstract

The Lieb-Robinson bound implies that the unitary time evolution of an operator can be restricted to an effective light cone for any Hamiltonian with short-range interactions. Here we present a very efficient renormalization group algorithm based on this light cone structure to study the time evolution of prepared initial states in the thermodynamic limit in one-dimensional quantum systems. The algorithm does not require translational invariance and allows for an easy implementation of local conservation laws. We use the algorithm to investigate the relaxation dynamics of double occupancies in fermionic Hubbard models as well as a possible thermalization. For the integrable Hubbard model we find a pure power-law decay of the number of doubly occupied sites towards the value in the long-time limit while the decay becomes exponential when adding a nearest neighbor interaction. In accordance with the eigenstate thermalization hypothesis, the long-time limit is reasonably well described by a thermal average. We point out though that such a description naturally requires the use of negative temperatures. Finally, we study a doublon impurity in a N\'eel background and find that the excess charge and spin spread at different velocities, providing an example of spin-charge separation in a highly excited state.