Showing 1–1 of 1 results for author: Usadi, C

Balls and Walls: A Compact Unary Coding for Bosonic States

Authors: Hatem Barghathi, Caleb Usadi, Micah Beck, Adrian Del Maestro

Abstract: 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 boso… ▽ More 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. △ Less

Submitted 15 September, 2021; originally announced September 2021.

Comments: Main text: 7 pages, 3 figures + Supplementary material: 3 pages 1 figure. For associated data and code repository see: https://github.com/DelMaestroGroup/papers-code-UnaryBosonicBasis

Journal ref: Phys. Rev. B 105, L121116 (2022)