Majorana string simulation of nonequilibrium dynamics in two-dimensional lattice fermion systems

TL;DR

This paper introduces a novel Majorana-string based algorithm for simulating the real-time dynamics of two-dimensional lattice fermion systems, achieving high accuracy and efficiency in regimes previously difficult to simulate.

Contribution

The authors develop a Heisenberg-picture algorithm using Majorana-string basis truncation, extending the capability to simulate 2D fermionic dynamics beyond quadratic Hamiltonians.

Findings

High accuracy on 2D Fermi-Hubbard quenches

Comparable timescales to tensor network methods and experiments

Effective for both quadratic and interacting regimes

Abstract

The study of real-time dynamics of fermions remains one of the last frontiers beyond the reach of classical simulations and is key to our understanding of quantum behavior in chemistry and materials, with implications for quantum technology. Here we introduce a Heisenberg-picture algorithm that propagates observables expressed in a Majorana-string basis using a truncation scheme that preserves Trotter accuracy and aims at maintaining computational efficiency. The framework is exact for quadratic Hamiltonians--remaining restricted to a fixed low-weight sector determined by the physical observable--admits variational initial states, and can be extended to interacting regimes via systematically controlled truncations. We benchmark our approach on one- and two-dimensional Fermi-Hubbard quenches, comparing against tensor network methods (MPS and fPEPS) and recent experimental data. The method achieves high accuracy on timescales comparable to state-of-the-art variational techniques and experiments, demonstrating that controlled Majorana-string truncation is a practical tool for simulating two-dimensional fermionic dynamics.