Grassmann corner transfer-matrix renormalization group approach to one-dimensional fermionic models

TL;DR

This paper introduces a novel tensor network method using Grassmann variables and corner transfer-matrix renormalization to study one-dimensional fermionic models, effectively capturing phase diagram features.

Contribution

Develops an accurate Grassmann tensor network approach with a corner transfer-matrix algorithm for 1D interacting fermionic systems, validated on the Hubbard model.

Findings

Successfully captures phase diagram features of the Hubbard model

Validates the method's accuracy in fermionic systems

Provides a promising tensor network approach for fermionic models

Abstract

The strongly correlated fermions play a vital role in modern physics. For a given fermionic Hamiltonian system, the most widely used approach to explore the underlying physics is to study the wave function that incorporates Fermi-Dirac statistics, which can be obtained variationally by energy minimization or by imaginary-time evolution. In this work, we develop an accurate tensor network method for one-dimensional interacting fermionic models based on the coherent-state path-integral representation of the fermionic partition function. Employing the coherent-state representation, the partition function is effectively represented as a (1+1)-dimensional anisotropic Grassmann-valued tensor network, and the Grassmann version of the corner transfer-matrix renormalization group algorithm is developed to contract the tensor network and evaluate physical quantities. We validate our method in the one-dimensional fermionic Hubbard model with a magnetic field, where the essential features of the phase diagram in the $(\mu, B)$ plane are quantitatively captured. Our work offers a promising approach to interacting fermionic models within the framework of tensor networks.