Stochastic and Tensor Network simulations of the Hubbard Model

Abstract

The Hubbard model is an important tool to understand the electrical properties of various materials. More specifically, on the honeycomb lattice it is used to describe graphene predicting a quantum phase transition from a semimetal to a Mott insulating state. In this work two different numerical techniques are presented that have been employed for simulations of the Hubbard model: The Hybrid Monte Carlo algorithm on the one hand allowed us to simulate unprecedentedly large lattices, whereas Tensor Networks can be used to completely avoid the sign problem. Respective strengths and weaknesses of the methods are discussed.

13 pages, 9 figures; LATTICE2022 proceedings

References in corpus (8)

• The electronic properties of graphene
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• Monte-Carlo simulation of the tight-binding model of graphene with partially screened Coulomb interactions
• Mitigating the Hubbard Sign Problem with Complex-Valued Neural Networks
• Simulating both parity sectors of the Hubbard Model with Tensor Networks
• A density of states approach to the hexagonal Hubbard model at finite density
• Real Time Simulations of Quantum Spin Chains: Density-of-States and Reweighting approaches
• The Semimetal-Antiferromagnetic Mott Insulator Quantum Phase Transition of the Hubbard Model on the Honeycomb Lattice