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Physical review. B, Condensed matter

Binding of holes in one-dimensional Hubbard chains

Richard M. Fye, Marcio Jose Martins, Richard T. Scalettar

Published Oct 1, 1990• 40 citations
Publisher

Abstract

Using the Bethe ansatz, we calculate the binding energies of two holes just off half-filling in one-dimensional Hubbard chains. Somewhat surprisingly, we find binding comparable to that seen in two-dimensional systems in chains that have a degeneracy at the Fermi level in the noninteracting (U=0) limit. The binding initially IincreasesR with lattice size before beginning a slow decay to zero in the thermodynamic limit. We discuss the general implications of our results for binding energy and other numerical calculations of high-${\mathit{T}}_{\mathit{c}}$ models.

DOI
10.1103/physrevb.42.6809

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Using the Bethe ansatz, we calculate the binding energies of two holes just off half-filling in one-dimensional Hubbard chains. Somewhat surprisingly, we find binding comparable to that seen in two-dimensional systems in chains that have a degeneracy at the Fermi level in the noninteracting (U=0) limit. The binding initially IincreasesR with lattice size before beginning a slow decay to zero in the thermodynamic limit. We discuss the general implications of our results for binding energy and other numerical calculations of high-Tc{\mathit{T}}_{\mathit{c}}Tc​ models.
Using variational Monte-Carlo method and choosing an antiferromagnetic trial wave function, we have calculated the binding energies just off half-filling in one-dimensional Hubbard chains. We found the binding for the lattice length N being less than 40 in the degenerate case, but no binding at all in the non-degenerate case. However, with lattice length increasing gradually, difference between the two cases becomes smaller and smaller. Finally, there is no binding at all no matter whether or not the chains have a degeneracy at the Fermi level in the non-interacting limit. It may be an indication of the independence of the final calculation results on the boundary conditions for the large enough system or in thermodynamic limit.
We present a new numerical method for the study of binding energies of particles in fermionic systems. Working with an imaginary chemical potential we can obtain results in the canonical ensemble by simple modifications of standard numerical techniques. We applied the technique to the two-dimensional Hubbard model observing binding of holes at half-filling on lattices of 4\ifmmode\times\else\texttimes\fi{}4 sites. For U/t=4 we estimate that the binding energy is \ensuremath{\Delta}=-0.10\ifmmode\pm\else\textpm\fi{}0.02.
The fate of a local two-hole doublon excitation in the one-dimensional Fermi-Hubbard model is systematically studied for strong Hubbard interaction UUU in the entire filling range using the density-matrix renormalization group (DMRG) and the Bethe ansatz. For strong UUU, two holes at the same site form a compound object whose decay is impeded by the lack of phase space. Still, a partial decay is possible on an extremely short time scale where phase-space arguments do not yet apply. We argue that the initial decay and the resulting intermediate state are relevant for experiments performed with ultracold atoms loaded into an optical lattice as well as for (time-resolved) CVV Auger-electron spectroscopy. The detailed discussion comprises the mixed ballistic-diffusive real-time propagation of the doublon through the lattice, its partial decay on the short time scale as a function of filling and interaction strength, as well as the analysis of the decay products, which are metastable on the intermediate time scale that is numerically accessible and which show up in the two-hole excitation (Auger) spectrum. The ambivalent role of singly occupied sites is key to understanding the doublon physics; for high fillings, ground-state configurations with single occupancies are recognized to strongly relax the kinematic constraints and to open up decay channels. For fillings close to half-filling, however, their presence actually blocks the doublon decay. Finally, the analysis of the continua in the two-hole spectrum excludes a picture where the doublon decays into unbound electron holes for generic fillings, different from the limiting case of the completely filled band. We demonstrate that the decay products as well as the doublon propagation should rather be understood in terms of Bethe ansatz eigenstates.
The one-dimensional Hubbard model at half-filling is studied in the framework of the Composite Operator Method using a static approximation. A solution characterized by strong antiferromagnetic correlations and a gap for any non-zero on-site interaction U is found. The corresponding ground-state energy, double occupancy and specific heat are in excellent agreement with those obtained within the Bethe Ansatz. These results show that the Composite Operator Method is an appropriate framework for the half-filled Hubbard chain and can be applied to evaluate properties, like the correlation functions, which cannot be obtained by means of the Bethe Ansatz, except for some limiting cases.