Lower bounds for the conductivities of correlated quantum systems

Details Lower bounds for the conductivities of correlated quantum systems Lower bounds for the conductivities of correlated quantum systems

2007-04-06

arxiv.org/abs/0704.0886v2

Phys. Rev. B 75, 245104 (2007)

Physics

Condensed Matter

Strongly Correlated Electrons

Title changed; 9 pages, 2 figures

Scientific paper

10.1103/PhysRevB.75.245104

We show how one can obtain a lower bound for the electrical, spin or heat conductivity of correlated quantum systems described by Hamiltonians of the form H = H0 + g H1. Here H0 is an interacting Hamiltonian characterized by conservation laws which lead to an infinite conductivity for g=0. The small perturbation g H1, however, renders the conductivity finite at finite temperatures. For example, H0 could be a continuum field theory, where momentum is conserved, or an integrable one-dimensional model while H1 might describe the effects of weak disorder. In the limit g to 0, we derive lower bounds for the relevant conductivities and show how they can be improved systematically using the memory matrix formalism. Furthermore, we discuss various applications and investigate under what conditions our lower bound may become exact.

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