hbar is a PyTorch-based library for simulating quantum many-body systems, specifically the 2D Fermi-Hubbard model. It provides tools for Hamiltonian construction and Krylov-based time evolution methods. Examples od usage can be found in notebooks/ directory. Arbitrary adjacency matrices for system connectivity are supported up to 64 lattice sites.
The system follows the 2D Fermi-Hubbard Hamiltonian:
where:
- t is the hopping amplitude
- u is the on-site interaction strength
- v is the external potential strength
- Vⱼ is an external potential
For more discussion on localization and thermalization, see my essay.