Single-particle green function of the 1D Hubbard model

Avijit Shee, Dominika Zgid

We investigate the performance of Green's function coupled cluster singles and doubles (CCSD) method as a solver for Green's function embedding methods. To develop an efficient CC solver, we construct the one-particle Green's function from the coupled cluster (CC) wave function based on the non-Hermitian Lanczos algorithm. The major advantage of this method is that its scaling does not depend on the number of frequency points. We have tested the applicability of the CC Green's function solver in the weakly to strongly correlated regimes by employing it for a half-filled one-dimensional (1D) Hubbard model projected onto a single-site impurity problem and a half-filled two-dimensional (2D) Hubbard model projected onto a four-site impurity problem. For the 1D Hubbard model, for all interaction strengths, we observe an excellent agreement with the full configuration interaction (FCI) technique, both for the self-energy and spectral function. For the 2D Hubbard, we have employed an open-shell version of the current implementation and observed some discrepancies from FCI in the strongly correlated regime. Finally, on an example of a small ammonia cluster, we analyze the performance of Green's function CCSD solver within the Self-Energy Embedding Theory (SEET) with Hartree-Fock (HF) and Green's Function second order (GF2) for the treatment of the environment.

M. Gulácsi, Kevin S. Bedell

M. Gulácsi, Kevin S. Bedell

For the one-dimensional Hubbard model we extended the bosonization technique, away from half-filling, in such a way that a general formula is obtained for the zero temperature single-particle Green function with validity over the whole doping range. Our method allows us to calculate, for the first time, the one-body Green function in both Tomonaga-Luttinger and Luther-Emery universality classes, to characterize the crossover between these two behaviors and thus, to describe the metal-insulator transition. We have found that the transition can be characterized as a Brinkman-Rice transition with a diverging effective mass.

N. M. Bogoliubov, V. E. Korepin

A. M. Finkel'Shteǐn

有希子 梅野, Masahiro Shiroishi, Andreas Klümper

The asymptotics of the equal-time one-particle Green's function of the half-filled one-dimensional Hubbard model is studied at finite temperature. We calculate its correlation length by evaluating the largest and the second largest eigenvalues of the Quantum Transfer Matrix (QTM). In order to allow for the genuinely fermionic nature of the one-particle Green's function, we employ the fermionic formulation of the QTM based on the fermionic R -operator of the Hubbard model. The purely imaginary value of the second largest eigenvalue reflects the k F ( = π/2) oscillations of the one-particle Green's function at half-filling. By solving numerically the Bethe ansatz equations with Trotter numbers up to N = 10240, we obtain accurate data for the correlation length at finite temperatures down into the very low-temperature region. The correlation length remains finite even at T = 0 due to the existence of the charge gap. Our numerical data confirm Stafford and Millis' conjecture regarding an analytic expression for the correlation length at T = 0.