Lanczos diagonalizations of the 1-D Peierls-Hubbard model

Conference · Sun Jan 01 04:00:00 EST 1989

DOI:https://doi.org/10.1007/978-1-4613-0565-1_12· OSTI ID:5505014

Loh, E Y; Campbell, D K; Gammel, J T

In studies of interacting electrons in reduced dimensions'' one is trapped between the Scylla of exponential growth of the number of states in any exact many-body basis and the Charybdis of the failure of mean-field theories to capture adequately the effects of interactions. In the present article we focus on one technique -- the Lanczos method -- which, at least in the case of the 1-D Peierls-Hubbard model, appears to allow us to sail the narrow channel between these two hazards. In contrast to Quantum Monte Carlo methods, which circumvent the exponential growth of states by statistical techniques and importance sampling, the Lanczos approach attacks this problem head-on by diagonalizing the full Hamiltonian. Given the restrictions of present computers, this approach is thus limited to studying finite clusters of roughly 12--14 sites. Fortunately, in one dimension, such clusters are usually sufficient for extracting many of the properties of the infinite system provided that one makes full use of the ability to vary the boundary conditions. In this article we shall apply the Lanczos methodology and novel phase randomization'' techniques to study the 1-D Peierls-Hubbard model, with particular emphasis on the optical absorption properties, including the spectrum of absorptions as a function of photon energy. Despite the discreteness of the eigenstates in our finite clusters, we are able to obtain optical spectra that, in cases where independent tests can be made, agree well with the known exact results for the infinite system. Thus we feel that this combination of techniques represents an important and viable means of studying many interesting novel materials involving strongly correlated electrons. 26 refs., 6 figs.

• Research Organization: Los Alamos National Lab., NM (USA)
• Sponsoring Organization: DOE/MA
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 5505014
• Report Number(s): LA-UR-89-3008; CONF-8810299--5; ON: DE90000537
• Country of Publication: United States
• Language: English

Related Subjects

656002* -- Condensed Matter Physics-- General Techniques in Condensed Matter-- (1987-)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ABSORPTION SPECTRA
ANALYTICAL SOLUTION
ELECTRON-ELECTRON COUPLING
ELECTRON-PHONON COUPLING
HAMILTONIANS
MANY-BODY PROBLEM
MATHEMATICAL OPERATORS
MATRICES
MEAN-FIELD THEORY
PEIERLS METHOD
QUANTUM OPERATORS
QUASI PARTICLES
SOLITONS
SPECTRA