Excitation spectra of systems of indistinguishable particles by the autocorrelation function technique: Circumventing the exponential scaling for bosons

We consider the autocorrelation function technique for obtaining excitation spectra for indistinguishable particles. The interacting particles are described by coherent superpositions of configurations built from time-dependent spin-orbitals. The fermionic or bosonic character of the particles is taken into account by considering Slater determinants or permanents, respectively. The approach involves the calculation of overlaps between nonorthonormal Slater determinants for fermions and permanents for bosons. Efficient methods already exist for fermions. In the case of bosons, the evaluation of permanents generally scales exponentially with system size. We present an efficient approach for bosons for calculating the excitation spectrum, which circumvents this scaling. The approach is illustrated and validated by comparison with an analytical model for interacting bosons, for a system with a number of bosons so large that the autocorrelation technique could not be applied without the present development.We consider the autocorrelation function technique for obtaining excitation spectra for indistinguishable particles. The interacting particles are described by coherent superpositions of configurations built from time-dependent spin-orbitals. The fermionic or bosonic character of the particles is taken into account by considering Slater determinants or permanents, respectively. The approach involves the calculation of overlaps between nonorthonormal Slater determinants for fermions and permanents for bosons. Efficient methods already exist for fermions. In the case of bosons, the evaluation of permanents generally scales exponentially with system size. We present an efficient approach for bosons for calculating the excitation spectrum, which circumvents this scaling. The approach is illustrated and validated by comparison with an analytical model for interacting bosons, for a system with a number of bosons so large that the autocorrelation technique could not be applied without the present development.