Combining Grassmann algebra with entanglement renormalization method

TL;DR

This paper introduces GMERA, a novel numerical method combining Grassmann algebra with MERA to efficiently simulate 2D strongly correlated electronic systems, handling fermionic properties and various tensor network structures.

Contribution

The paper presents GMERA, a new unbiased and effective tensor network method that integrates Grassmann algebra with MERA for simulating fermionic systems.

Findings

Successfully applied to free fermion model

Effective in tight binding model simulations

Accurate results for t-J model with doping

Abstract

By combining the Grassmann algebra with multi-scale entanglement renormalization ansatz (MERA), we introduce a new unbiased and effective numerical method for simulating 2D strongly correlated electronic systems. The new GMERA method inherits all the advantages of MERA, which constructs the variational wave function based on complicated tensor network. Besides it can deal with fermionic properties of the system due to Grassmann algebra through local tensor contractions. This general method can treat different tensor network structures in a universal way. We show several benchmark calculations of the GMERA method, including the free fermion model, tight binding model, as well as the t-J model with hole doping.