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arXiv:cond-mat/9902113 · Physics Letters A

Exact results of strongly correlated systems at finite temperature

Sze-Shiang Feng

Published May 1, 1999• 1 citation
arXivHTMLPDF
DOI
10.1016/s0375-9601(99)00169-3

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We present a method to compute dynamical correlation functions in quantum many-body systems at zero temperature. The ground state of a finite system is evaluated exactly by a modified Lanczos method and from it the real-frequency correlation functions are obtained by a projective technique for the memory-function formalism. We apply the method to the density-density correlation function of a one-dimensional spinless fermion system. Exact results are recovered in the noninteracting limit; in the strong-coupling limit our results are compared with Monte Carlo simulation and analytical approximations.
Lectures deal with the theory of electronic transport, in particular with the electrical conductivity, in systems dominated by strong electron ‐ electron repulsion. The concept of charge stiffness is introduced to distinguish conductors and insulators at T = 0, but as well usual resistors, possible ideal conductors and ideal insulators at finite temperature. It is shown that the latter singular transport appears in many integrable systems of interacting fermions, the evidence coming from the relation with level dynamics, from the existence of conserved quantities as well as from numerical studies and exact results. Then, exact duagonalization approaches for the calculation of static and dynamical quantities in small correlated systems are described, with the emphasis on the finite‐temperature Lanczos method applicable to transport quantities. Finally, anomalous dynamical conductivity within the planar single‐band model is discussed in relation with experiments on cuprates.