Improving the Gutzwiller Ansatz with Matrix Product States

TL;DR

This paper demonstrates that Matrix Product States (MPS) can enhance the Gutzwiller variational wavefunction approach, providing a more efficient and general framework for simulating correlated quantum systems across dimensions.

Contribution

It introduces a unifying MPS-based framework to improve Gutzwiller wavefunctions and proposes a corrected algorithm for particle number conservation during dynamics.

Findings

MPS generalizes and improves Gutzwiller wavefunctions.

The proposed algorithm conserves particle number in dynamics.

MPS-based methods outperform traditional Gutzwiller approaches.

Abstract

The Gutzwiller variational wavefunction (GVW) is commonly employed to capture correlation effects in condensed matter systems such as ferromagnets, ultracold bosonic gases, correlated superconductors, etc. By noticing that the grand-canonical and number-conserving Gutzwiller Ans\"atze are in fact the zero-order approximation of an expansion in the truncation parameter of a Matrix Product State (MPS), we argue that MPSs, and the algorithms used to operate on them, are not only flexible computational tools but also a unifying theoretical framework that can be used to generalize and improve on the GVW. In fact, we show that a number-conserving GVW is less efficient in capturing the ground state of a quantum system than a more general MPS which can be optimized with comparable computational resources. Moreover, we suggest a corrected time-dependent density matrix renormalization group algorithm that ensures the conservation of the expectation value of the number of particles when a GVW or a MPS are not explicitly number-conserving. The GVW dynamics obtained with our algorithm compares very well with the exact one in 1D. Most importantly, the algorithm works in any dimension for a GVW. We thus expect it to be of great value in the study of the dynamics of correlated quantum systems.