Hamiltonian Bootstrap

TL;DR

Hamiltonian bootstrap is a semidefinite relaxation technique that estimates lower bounds on quantum Hamiltonian ground state energies and correlations, leveraging symmetries to improve efficiency, demonstrated on the 1D Hubbard model.

Contribution

The paper introduces Hamiltonian bootstrap, a novel semidefinite relaxation method that incorporates symmetries to efficiently approximate ground state energies and correlations in quantum systems.

Findings

Accurately estimates ground state energies of the 1D Hubbard model.

Uses symmetry to reduce computational resources significantly.

Achieves results in agreement with exact methods.

Abstract

We introduce a semidefinite relaxation method called Hamiltonian bootstrap which finds lower bounds to the ground state energy of a quantum Hamiltonian subject to Hermitian linear constraints, along with approximations of the corresponding ground state correlation functions. We show that symmetry can be used to significantly reduce both the memory and time requirements, and we include unitary, antiunitary, discrete, and continuous symmetries in our analysis. We demonstrate Hamiltonian bootstrap using the 1D Hubbard model and find quantitative agreement with both exact diagonalization and the Bethe ansatz.