Quantum digital simulation of the Fermi-Hubbard model under a uniform electric field

Abstract

In this study, we investigate the behaviour of the Fermi-Hubbard model when subjected to a uniform electric field, employing a digital quantum computing approach. Our research focuses on lattices with varying geometries, fillings, and interaction strengths between electrons. Initially, we develop an efficient adiabatic algorithm on a quantum circuit to prepare interacting ground states in the absence of electromagnetic fields. Afterwards, electric fields of different intensities are applied, and we employ the same quantum circuit to solve the time-dependent Schrödinger equation, enabling us to explore the system’s response. Furthermore, we simulate a quench to gain further insights into the behaviour of the system. Finally, we implement a measurement protocol to obtain the expected value of the current at different times during the system’s evolution. Our findings demonstrate that the response of the Fermi-Hubbard model is strongly influenced by the magnitude and duration of the applied electric field, as well as the electron-electron interaction. This work establishes a fundamental framework for studying the dynamics of strongly correlated electrons using digital quantum computers.