Lanczos diagonalizations of the 1-D Peierls-Hubbard model

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

doi:10.1007/978-1-4613-0565-1_12

Title: Lanczos diagonalizations of the 1-D Peierls-Hubbard model

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Abstract

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 amore »« less

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

Publication Date:: Sun Jan 01 00:00:00 EST 1989

Research Org.:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: DOE/MA

OSTI Identifier:: 5505014

Report Number(s):: LA-UR-89-3008; CONF-8810299-5
Journal ID: ISSN 0258--1221; ON: DE90000537

DOE Contract Number:: W-7405-ENG-36

Resource Type:: Conference

Resource Relation:: Journal Volume: 213; Conference: Interacting electrons in reduced dimensions, Torino (Italy), 3-7 Oct 1988

Country of Publication:: United States

Language:: English

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

Citation Formats


                    Loh, E Y, Campbell, D K, and Gammel, J T. Lanczos diagonalizations of the 1-D Peierls-Hubbard model.  United States: N. p., 1989. 
        Web.  doi:10.1007/978-1-4613-0565-1_12.

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                    Loh, E Y, Campbell, D K, & Gammel, J T. Lanczos diagonalizations of the 1-D Peierls-Hubbard model.  United States.  https://doi.org/10.1007/978-1-4613-0565-1_12

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                    Loh, E Y, Campbell, D K, and Gammel, J T. 1989.  
        "Lanczos diagonalizations of the 1-D Peierls-Hubbard model".  United States.  https://doi.org/10.1007/978-1-4613-0565-1_12.  https://www.osti.gov/servlets/purl/5505014.

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@article{osti_5505014,

  title        = {Lanczos diagonalizations of the 1-D Peierls-Hubbard model},

  author       = {Loh, E Y and Campbell, D K and Gammel, J T},

  abstractNote = {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.},

  doi          = {10.1007/978-1-4613-0565-1_12},

  url          = {https://www.osti.gov/biblio/5505014},
  journal      = {},

  issn         = {0258--1221},

  number       = ,

  volume       = 213,

  place        = {United States},

  year         = {Sun Jan 01 00:00:00 EST 1989},

  month        = {Sun Jan 01 00:00:00 EST 1989}

}

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