Exact SU(N) symmetry resolution of bosonic Hubbard models: general boson-fermion mappings and flat-band singlet-cluster states
Abstract
We show how to perform exact diagonalization of SU(N)-symmetric Bose-Hubbard models separately in each irreducible representation of SU(N), by exploiting the Howe duality between U(L) and U(N). Three structural consequences follow for any lattice and any Hamiltonian built from the U(L) generators: (i) the spectrum in a given orbital sector is independent of N and of the particle statistics, (ii) the canonical partition functions for bosons and fermions obey the exact identity Zb(−N)=(−1)NbZf(N), (iii) with unfrustrated hopping the groundstate is always a color ferromagnet, so that the color-resolved method we introduce is useful to study excited sectors, frustrated lattices and finite temperatures. As applications, we first derive the finite-temperature phase diagram of attractive SU(N) bosons on few-site rings at large N for arbitrary filling. We then show the emergence of singlet-cluster states from frustrated hopping, the counterpart of fermionic ferromagnetism, with the example of the sawtooth and kagome lattice.
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BibTeX
@misc{herviou2026exact,
title = {{Exact SU($N$) symmetry resolution of bosonic Hubbard models: general boson-fermion mappings and flat-band singlet-cluster states}},
author = {Loïc Herviou},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14183},
eprint = {2610.14183},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05844598v1},
note = {CC BY-NC 4.0},
}
RIS
TY - UNPB
TI - Exact SU(N) symmetry resolution of bosonic Hubbard models: general boson-fermion mappings and flat-band singlet-cluster states
AU - Loïc Herviou
PY - 2026
DA - 2026/10/09
PB - HAL
DO - 10.48550/arxiv.2610.14183
UR - https://hal.science/hal-05844598v1
AB - We show how to perform exact diagonalization of SU(N)-symmetric Bose-Hubbard models separately in each irreducible representation of SU(N), by exploiting the Howe duality between U(L) and U(N). Three structural consequences follow for any lattice and any Hamiltonian built from the U(L) generators: (i) the spectrum in a given orbital sector is independent of N and of the particle statistics, (ii) the canonical partition functions for bosons and fermions obey the exact identity Z_b(−N)=(−1)^N_bZ_f(N), (iii) with unfrustrated hopping the groundstate is always a color ferromagnet, so that the color-resolved method we introduce is useful to study excited sectors, frustrated lattices and finite temperatures. As applications, we first derive the finite-temperature phase diagram of attractive SU(N) bosons on few-site rings at large N for arbitrary filling. We then show the emergence of singlet-cluster states from frustrated hopping, the counterpart of fermionic ferromagnetism, with the example of the sawtooth and kagome lattice.
ER -