Bose-Hubbard Chain

Purpose and Hamiltonian

The truncated Bose-Hubbard chain describes hopping bosons with onsite interaction and chemical potential:

$$ H=-t\sum_{\langle i,j\rangle}(a_i^\dagger a_j+a_j^\dagger a_i) +\frac U2\sum_i n_i(n_i-1)-\mu\sum_i n_i. $$

Truncated boson basis

Basis and scaling

Each site uses occupations $0,\ldots,n_{\max}$, giving dimension $(n_{\max}+1)^N$. Dense and CSR builders are available.

Package use

from quantum_lattice_models import bose_hubbard_chain_sparse

H = bose_hubbard_chain_sparse(
    n_sites=4, hopping=0.6, interaction=1.5, max_occupancy=2
)

Parameters

Builder Parameter Type Default Constraint
bose_hubbard_chain n_sites int 3 >= 1
bose_hubbard_chain hopping float 0.6
bose_hubbard_chain interaction float 1.5
bose_hubbard_chain chemical_potential float 0.0
bose_hubbard_chain max_occupancy int 2 >= 1
bose_hubbard_chain periodic bool False
bose_hubbard_chain_sparse n_sites int 3 >= 1
bose_hubbard_chain_sparse hopping float 0.6
bose_hubbard_chain_sparse interaction float 1.5
bose_hubbard_chain_sparse chemical_potential float 0.0
bose_hubbard_chain_sparse max_occupancy int 2 >= 1
bose_hubbard_chain_sparse periodic bool False

Validation and cautions

Single-site energies and particle-number conservation are tested. Sparse storage does not remove exponential basis growth.