Accurate Simulation of the Hubbard Model with Finite Fermionic Projected Entangled Pair States
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1.
California Institute of Technology
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2.
Zhejiang University
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3.
Chinese University of Hong Kong
Abstract
We demonstrate the use of finite-size fermionic projected entangled pair states, in conjunction with variational Monte Carlo, to perform accurate simulations of the ground state of the 2D Hubbard model. Using bond dimensions of up to 𝐷=28, we show that we can surpass state-of-the-art density matrix renormalization group energies that use up to 𝑚=32 000 SU(2) multiplets on eight-leg ladders. We further apply our methodology to 10 ×16, 12 ×16, and 16 ×16 lattices at 1/8 hole doping and observe the dimensional crossover between stripe orientations. Our Letter shows the power of finite-size fermionic tensor networks to resolve the physics of the 2D Hubbard model and related problems.
Copyright and License
© 2025 American Physical Society.
Acknowledgement
This work was primarily supported by the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Systems Accelerator. Additional support for H. Z. (DMRG calculations) was provided by U.S. Air force Office of Scientitic Research under Grant No. AFOSR-FA9550-18-1-0095. G. K. C. acknowledges additional support from the Simons Investigator program. Z.-C. G. is supported by funding from Hong Kong’s Research Grants Council (CRF C7012-21GF and RGC Research Fellow Scheme 2023/24, No. RFS2324-4S02). W.-Y. L. also acknowledges additional support from a start-up grant from Zhejiang University for the final part of this work. The DMRG calculations in this work were performed using block2 [90-92], and the scripts can be found in Ref. [93]. The computations presented in this work were conducted at the Resnick High Performance Computing Center, a facility supported by the Resnick Sustainability Institute at the California Institute of Technology.
Data Availability
The data that support the findings of this Letter are openly available [94].
Supplemental Material
The SM include a review of Grassmann tensor network representation, and additional numerical results for the Hubbard model.
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Additional details
Related works
- Is new version of
- Discussion Paper: arXiv:2502.13454 (arXiv)
- Is supplemented by
- Supplemental Material: https://journals.aps.org/prl/supplemental/10.1103/r4q9-4yvj/fpeps-hubbard-SM.pdf (URL)
- Dataset: https://github.com/LiuWenyuan-Phy/2d-hubbard-data-fPEPS-PRL2025 (URL)
Funding
- United States Department of Energy
- United States Air Force Office of Scientific Research
- AFOSR-FA9550-18-1-0095
- Simons Foundation
- University Grants Committee
- CRF C7012-21GF
- University Grants Committee
- RFS2324-4S02
- Zhejiang University
- Resnick Sustainability Institute
Dates
- Accepted
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2025-06-03