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TT: Fachverband Tiefe Temperaturen
TT 86: Correlated Electrons: Method Development
TT 86.9: Talk
Friday, March 22, 2024, 11:45–12:00, H 3007
Numerical linked-cluster expansions applied to a problem with bound-state decay — •Max Hörmann and Kai Phillip Schmidt — Department Physik, Staudtstraße 7, Friedrich-Alexander Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany
Using numerical linked-cluster expansions (NLCEs) we investigate the Hamiltonian H = ∑i − ni ni+1 + x (ai ai+1†+ h.c.) = H0 + x V on a chain in the sector of two hardcore-bosons. For x < 1/2 the Hamiltonian has a bound-state solution ωbs(k) = −1− 2 x2(1+cos(k)) below the continuum for each momentum and a local quasi-particle picture, which decouples bound states and continuum, exists. The perturbative solution for the bound-state energies is exact in second order. For x>1/2 these energies are only eigenstates for ωbs(kbs)< 4x |cos(kbs)|. We explain how the breakdown of this formula for k<kbs can be understood in the framework of NLCEs.
For x>1/2 conventional NLCEs do not converge any more. We try to modify them to obtain a convergent expansion, that shall yield a continuation of the bound-state energy dispersion for k<kbs. For k>kbs we want to still find the energies ωbs(k), but for k<kbs we want those, where the finite lifetime of the bound states is maximal.
Keywords: Linked-cluster expansions; Particle decay; Bound states; Quasi particles