HubbardNet: Efficient predictions of the Bose-Hubbard model spectrum with deep neural networks
We present a deep neural network (DNN) -based model (HubbardNet) to variationally find the ground-state and excited-state wave functions of the one-dimensional and two-dimensional Bose-Hubbard model. Using this model for a square lattice with M sites, we obtain the energy spectrum as an analytical f...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2023-10-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.5.043084 |
| _version_ | 1797210386331598848 |
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| author | Ziyan Zhu Marios Mattheakis Weiwei Pan Efthimios Kaxiras |
| author_facet | Ziyan Zhu Marios Mattheakis Weiwei Pan Efthimios Kaxiras |
| author_sort | Ziyan Zhu |
| collection | DOAJ |
| description | We present a deep neural network (DNN) -based model (HubbardNet) to variationally find the ground-state and excited-state wave functions of the one-dimensional and two-dimensional Bose-Hubbard model. Using this model for a square lattice with M sites, we obtain the energy spectrum as an analytical function of the on-site Coulomb repulsion, U, and the total number of particles, N, from a single training. This approach bypasses the need to solve a new Hamiltonian for each different set of values (U,N) and generalizes well even for out-of-distribution (U,N). Using HubbardNet, we identify the two ground-state phases of the Bose-Hubbard model (Mott insulator and superfluid). We show that the DNN-parametrized solutions are in excellent agreement with results from the exact diagonalization of the Hamiltonian, and it outperforms exact diagonalization in terms of computational scaling. These advantages suggest that our model is promising for efficient and accurate computation of exact phase diagrams of many-body lattice Hamiltonians. |
| first_indexed | 2024-04-24T10:09:46Z |
| format | Article |
| id | doaj.art-924eeb5d2e9b4f99875357e0da1be607 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:09:46Z |
| publishDate | 2023-10-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-924eeb5d2e9b4f99875357e0da1be6072024-04-12T17:35:28ZengAmerican Physical SocietyPhysical Review Research2643-15642023-10-015404308410.1103/PhysRevResearch.5.043084HubbardNet: Efficient predictions of the Bose-Hubbard model spectrum with deep neural networksZiyan ZhuMarios MattheakisWeiwei PanEfthimios KaxirasWe present a deep neural network (DNN) -based model (HubbardNet) to variationally find the ground-state and excited-state wave functions of the one-dimensional and two-dimensional Bose-Hubbard model. Using this model for a square lattice with M sites, we obtain the energy spectrum as an analytical function of the on-site Coulomb repulsion, U, and the total number of particles, N, from a single training. This approach bypasses the need to solve a new Hamiltonian for each different set of values (U,N) and generalizes well even for out-of-distribution (U,N). Using HubbardNet, we identify the two ground-state phases of the Bose-Hubbard model (Mott insulator and superfluid). We show that the DNN-parametrized solutions are in excellent agreement with results from the exact diagonalization of the Hamiltonian, and it outperforms exact diagonalization in terms of computational scaling. These advantages suggest that our model is promising for efficient and accurate computation of exact phase diagrams of many-body lattice Hamiltonians.http://doi.org/10.1103/PhysRevResearch.5.043084 |
| spellingShingle | Ziyan Zhu Marios Mattheakis Weiwei Pan Efthimios Kaxiras HubbardNet: Efficient predictions of the Bose-Hubbard model spectrum with deep neural networks Physical Review Research |
| title | HubbardNet: Efficient predictions of the Bose-Hubbard model spectrum with deep neural networks |
| title_full | HubbardNet: Efficient predictions of the Bose-Hubbard model spectrum with deep neural networks |
| title_fullStr | HubbardNet: Efficient predictions of the Bose-Hubbard model spectrum with deep neural networks |
| title_full_unstemmed | HubbardNet: Efficient predictions of the Bose-Hubbard model spectrum with deep neural networks |
| title_short | HubbardNet: Efficient predictions of the Bose-Hubbard model spectrum with deep neural networks |
| title_sort | hubbardnet efficient predictions of the bose hubbard model spectrum with deep neural networks |
| url | http://doi.org/10.1103/PhysRevResearch.5.043084 |
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