Disentangling Interacting Systems with Fermionic Gaussian Circuits: Application to Quantum Impurity Models

TL;DR

This paper introduces fermionic Gaussian circuits to optimize basis choices in tensor network states, reducing entanglement and computational complexity in simulating interacting fermionic systems like quantum impurity models.

Contribution

It presents a novel method using fermionic Gaussian circuits for basis transformation, enhancing tensor network efficiency and interpretability in strongly correlated fermionic systems.

Findings

Reduced entanglement entropy in ground states

Improved performance of DMRG algorithms

Enhanced simulation of impurity models

Abstract

Tensor network quantum states are powerful tools for strongly correlated systems, tailored to capture local correlations such as in ground states with entanglement area laws. When applying tensor network states to interacting fermionic systems, a proper choice of the basis or orbitals can reduce the bond dimension of tensors and provide physically relevant orbitals. We introduce such a change of basis with unitary gates obtained from compressing fermionic Gaussian states into quantum circuits corresponding to various tensor networks. These circuits can reduce the ground state entanglement entropy and improve the performance of algorithms such as the density matrix renormalization group. We study the Anderson impurity model with one and two impurities to show the potential of the method for improving computational efficiency and interpreting impurity physics. Furthermore, fermionic Gaussian circuits can also suppress entanglement during the time evolution out of low-energy state. Last, we consider Gaussian multi-scale entanglement renormalization ansatz (GMERA) circuits which compress fermionic Gaussian states hierarchically. The emergent coarse-grained physical models from these GMERA circuits are studied in terms of their entanglement properties and suitability for performing time evolution.