Tensor network representations of parton wave functions

TL;DR

This paper establishes a connection between tensor network states and parton wave functions, enabling efficient representation, compression, and accurate computation of physical quantities in quantum many-body systems.

Contribution

It demonstrates that various parton wave functions can be exactly represented as tensor networks and introduces efficient compression schemes for practical calculations.

Findings

Tensor network representations of parton wave functions are exact and efficient.

High-fidelity compression schemes for projected Fermi sea using Wannier orbitals.

Method surpasses Monte Carlo in accuracy of energy and correlation functions.

Abstract

Tensor network states and parton wave functions are two pivotal methods for studying quantum many-body systems. This work connects these two subjects as we demonstrate that a variety of parton wave functions, such as projected Fermi sea and projected fermionic or bosonic paired states, can be represented exactly as tensor networks. The results can be compressed into matrix product states with moderate bond dimensions so various physical quantities can be computed efficiently. For the projected Fermi sea, we develop an excellent compression scheme with high fidelity using maximally localized Wannier orbitals. Numerical calculations on two parton wave functions demonstrate that our method exceeds commonly adopted Monte Carlo methods in some aspects. It produces energy and correlation function with very high accuracy that is difficult to achieve using Monte Carlo method. The entanglement measures that were almost impossible to compute before can also be obtained easily using our method.