Truncated Gaussian basis approach for simulating many-body dynamics

TL;DR

The paper introduces a Truncated Gaussian Basis Approach (TGBA) for efficient simulation of quantum many-body dynamics, enabling larger system sizes and accurate results by using a reduced subspace of Gaussian states.

Contribution

The novel TGBA method constructs an effective Hamiltonian in a Gaussian state subspace and leverages symmetries for scalable quantum many-body simulations.

Findings

Accurately computed dynamic structure factor matching analytical predictions.

Successfully simulated long-time quench dynamics in large systems.

Demonstrated scalability through symmetry exploitation and parallel computation.

Abstract

We propose a Truncated Gaussian Basis Approach (TGBA) for simulating the dynamics of quantum many-body systems. The approach constructs an effective Hamiltonian within a reduced subspace, spanned by fermionic Gaussian states, and diagonalizes it to obtain approximate eigenstates and eigenenergies. Symmetries can be exploited to perform parallel computation, enabling to simulate systems with much larger sizes. As an example, we compute the dynamic structure factor and study quench dynamics in a non-integrable quantum Ising chain, known as ``$E_8$ magnet''. The mass ratios calculated through the dynamic structure factor show excellent agreement with Zamolodchikov's analytical predictions. For quench dynamics we observe that time-evolving wave functions in the truncated subspace facilitates the simulation of long-time dynamics.