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Generalization of the Luttinger Theorem for Fermionic Ladder Systems

Patrick Gagliardini·Stephan Haas·T. M. Rice
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Abstract

We apply a generalized version of the Lieb-Schultz-Mattis Theorem to fermionic ladder systems to show the existence of a low-lying excited state (except for some special fillings). This can be regarded as a non-perturbative proof for the conservation under interaction of the sum of the Fermi wave vectors of the individual channels, corresponding to a generalized version of the Luttinger Theorem to fermionic ladder systems. We conclude by noticing that the Lieb-Schultz-Mattis Theorem is not applicable in this form to show the existence of low-lying excitations in the limit that the number of legs goes to infinity, e.g. in the limit of a 2D plane.

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Patrick Gagliardini, Stephan Haas, T. M. Rice. 1998-03-03. Generalization of the Luttinger Theorem for Fermionic Ladder Systems. https://doi.org/10.1103/physrevb.58.9603

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