Exact fermionic dual of the Bose-Hubbard model
Abstract
Recent developments have established exact bosonization and fermionization with a ℤ2 symmetry as dualities through gauging. In this work, we apply fermionic gauging, which realizes generalized Jordan-Wigner transformations, to the Bose-Hubbard (BH) model with a global U(1) symmetry and derive an exact dual description in terms of fermionic composites, built from bosons and fermions. In 1D, this duality generalizes the exact mapping between the extended hard-core BH model and the spinless Fermi-Hubbard model to include soft-core bosons. At low energies, the mapping reduces to the well-known equivalence between the sine-Gordon model and the Thirring model. The oscillation wave vector of the fermionic composite correlation function in the gapless phase is fixed by their density, providing a novel manifestation of Luttinger's theorem. We verify the exact duality using density matrix renormalization group (DMRG) calculations and demonstrate that the gapless phase and the phase transition are governed by the compact boson conformal field theory. Our construction naturally extends to generic bosonic systems and higher dimensions, opening new avenues for studying Bose-Fermi mixtures in optical lattices and other strongly correlated quantum systems.
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BibTeX
@misc{su2026exact,
title = {{Exact fermionic dual of the Bose-Hubbard model}},
author = {Lei Su and Ivar Martin and Aashish A. Clerk},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.07830},
eprint = {2609.07830},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07830},
}
RIS
TY - UNPB
TI - Exact fermionic dual of the Bose-Hubbard model
AU - Lei Su
AU - Ivar Martin
AU - Aashish A. Clerk
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2609.07830
UR - https://arxiv.org/abs/2609.07830
AB - Recent developments have established exact bosonization and fermionization with a ℤ_2 symmetry as dualities through gauging. In this work, we apply fermionic gauging, which realizes generalized Jordan-Wigner transformations, to the Bose-Hubbard (BH) model with a global U(1) symmetry and derive an exact dual description in terms of fermionic composites, built from bosons and fermions. In 1D, this duality generalizes the exact mapping between the extended hard-core BH model and the spinless Fermi-Hubbard model to include soft-core bosons. At low energies, the mapping reduces to the well-known equivalence between the sine-Gordon model and the Thirring model. The oscillation wave vector of the fermionic composite correlation function in the gapless phase is fixed by their density, providing a novel manifestation of Luttinger's theorem. We verify the exact duality using density matrix renormalization group (DMRG) calculations and demonstrate that the gapless phase and the phase transition are governed by the compact boson conformal field theory. Our construction naturally extends to generic bosonic systems and higher dimensions, opening new avenues for studying Bose-Fermi mixtures in optical lattices and other strongly correlated quantum systems.
ER -