Compact unary coding for bosonic states as efficient as conventional binary encoding for fermionic states

We introduce a unary coding of bosonic occupation states based on the famous balls and walls counting for the number of configurations of N indistinguishable particles on L distinguishable sites. Each state is represented by an integer with a human readable bit string that has a compositional structure allowing for the efficient application of operators that locally modify the number of bosons. By exploiting translational and inversion symmetries, we identify a speedup factor of order L over current methods when generating the basis states of bosonic lattice models. The unary coding is applied to a one-dimensional Bose-Hubbard Hamiltonian with up to L = N = 20, and the time needed to generate the ground-state block is reduced to a fraction of the diagonalization time. For the ground state symmetry resolved entanglement, we demonstrate that variational approaches restricting the local bosonic Hilbert space could result in an error that scales with system size.

Automated summary

This paper introduces a unary coding method for bosonic occupation states based on the famous balls and walls counting. By utilizing this coding method, operators that can locally modify the number of bosons can be efficiently applied. By exploiting translational and inversion symmetries, a speedup factor of order L over current methods is identified when generating the basis states of bosonic lattice models. For symmetry resolved entanglement of the ground state, it is demonstrated that variational approaches restricting the local bosonic Hilbert space could lead to an error that scales with system size.