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

TL;DR

This study uses advanced numerical techniques to explore the complex two-hole excitation spectra of the 1D Hubbard model, revealing multiplon phenomena, their stability, and the influence of symmetries across various fillings.

Contribution

It introduces a comprehensive analysis of multiplon states in the Hubbard model using DMRG and Chebyshev expansion, including a novel filter-operator technique for state-specific insights.

Findings

Multiplon states such as doublons and quadruplons are stable resonances.

The lifetime of doublons varies with momentum and is infinite at Brillouin zone edges.

The charge-SU(2) symmetry influences the stability and dynamics of multiplon states.

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 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 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 four-hole 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.