Multiplons in the two-hole excitation spectra of the one-dimensional Hubbard model

Abstract

Using the density-matrix renormalization group in combination with the Chebyshev polynomial expansion technique, we study the two-hole excitation spectrum of the one-dimensional Hubbard model in the entire filling range from the completely occupied band (n = 2) down to half-filling (n = 1). For strong interactions, the spectra reveal multiplon physics, i.e., relevant final states are characterized by two (doublon), three (triplon), four (quadruplon) and more holes, potentially forming stable compound objects or resonances with finite lifetime. These give rise to several satellites in the spectra with largely different spectral weights as well as to different two-hole, doublon-hole, two-doublon etc continua. The complex multiplon phenomenology is analyzed by interpreting not only local and k-resolved two-hole spectra but also three-and four-hole spectra for the Hubbard model and by referring to effective low-energy models. In addition, a filter-operator technique is presented and applied which allows to extract specific information on the final states at a given excitation energy. While multiplons composed of an odd number of holes do neither form stable compounds nor well-defined resonances unless a nearest-neighbor density interaction V is added to the Hamiltonian, the doublon and the quadruplon are well-defined resonances. The k-resolved fourhole spectrum at n=2 represents an interesting special case where a completely stable quadruplon turns into a resonance by merging with the doublon-doublon continuum at a critical wave vector. For all fillings with n 1 > , the doublon lifetime is strongly k-dependent and is even infinite at the Brillouin zone edges as demonstrated by k-resolved two-hole spectra. This can be traced back to the 'hidden' charge-SU(2) symmetry of the model which is explicitly broken off half-filling and gives rise to a massive collective excitation, even for arbitrary higher-dimensional but bipartite lattices. available for a dissociation into two particles moving independently through the lattice [8]. The latter situation is described by states which belong to a scattering continuum at energies within twice the bandwidth W 2 . If there is, on the other hand, a finite concentration of bosons or fermions [9] in the conduction band, the doublon may decay by transferring its energy Ũ in a high-order scattering process to several low-lying excitations of the continuum. This implies a finite lifetime of the doublon and poses an intricate many-body problem. The lifetime has been measured [10] for a well-controlled Fermi gas trapped in an optical lattice and was estimated theoretically for Fermi [10,11] and for Bose systems [12]. Studies of the real-time dynamics of an initially doubly occupied state t c t c t 0, where 0ñ | is the vacuum state or the few-particle ground state, have been done with exact-diagonalization methods [13,14]. For 0ñ | being the ground state of the extended Hubbard model at half-filling, time-dependent density-matrix renormalization group (DMRG) [15,16] has been used to stud...

Pump-probe Auger-electron spectroscopy of Mott insulators

“…This has been verified for a Mott insulator at half-filling where the calculation shows a quadruplon peak in the nonequilibrium spectrum at much higher binding energies compared to the doublon satellite, which is impossible in the equilibrium case at half-filling but shows up at higher fillings. 12 As the location of the main doublon satellite and additional features, such as a quadruplon peak, sensitively depend on the average number of doubly occupied sites, pump-probe AES could be used as a tool to measure the doublon concentration in the initial transient state as a function of the pump parameters.…”

“…"D" denotes the doublon satellite, "B" is the band-like part, see Ref. 12 and discussion in the text. = 2U + E c − U cc marks the barycenter of the band-like part which has a width of 2W .…”

Magnetic Doublon Bound States in the Kondo Lattice Model

“…For the doublon problem in the Hubbard model, the two-electron removal spectrum for the case of a completely filled band serves as a demonstrative and paradigmatic example [14]. At low fillings or for an empty band, one should rather perform a two-electron addition spectroscopy, defined by the following spectral function:…”

“…To calculate the spectral function, we have used a density-matrix renormalization group (DMRG) code which actually exploits the full SU(2) spin symmetry along with the U(1) charge symmetry of the model, combined with the Chebyshev polynomial technique [14,25]. As before, we control the total spin S, but are able to resolve the result according to M in a post-processing step from a single calculation.…”

Dynamic structure factor of the spin-12XXZ chain in a transverse field

“…CheMPS has been frequently applied in practice [22][23][24][25][52][53][54][55], but no conclusive answer has yet been presented to the question whether it provides a computationally more efficient framework over real-time evolution to simulate spectral functions. Whereas tackling this question in full generality would go beyond the scope of this work, we present below a brief analysis of the efficiency of CheMPS in the present context.…”