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April 20 Supersymmetry, lattice fermions, independence complexes and cohomology theory
Liza Huijse, Kareljan Schoutens
Adv. Theor. Math. Phys. 14(2): 643-694 (April 20).

Abstract

We analyze the quantum ground state structure of a specific model of itinerant, strongly interacting lattice fermions. The interactions are tuned to make the model supersymmetric. Due to this, quantum ground states are in one-to-one correspondence with cohomology classes of the so-called independence complex of the lattice. Our main result is a complete description of the cohomology, and thereby of the quantum ground states, for a two-dimensional square lattice with periodic boundary conditions. Our work builds on results by Jonsson, who determined the Euler characteristic (Witten index) via a correspondence with rhombus tilings of the plane. We prove a theorem, first conjectured by Fendley, which relates dimensions of the cohomology at grade $n$ to the number of rhombus tilings with $n$ rhombi.

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Liza Huijse. Kareljan Schoutens. "Supersymmetry, lattice fermions, independence complexes and cohomology theory." Adv. Theor. Math. Phys. 14 (2) 643 - 694, April 20.

Information

Published: April 20
First available in Project Euclid: 1 November 2010

zbMATH: 1208.81187
MathSciNet: MR2721658

Rights: Copyright © 2010 International Press of Boston

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Vol.14 • No. 2 • April 20
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