Supersymmetry, lattice fermions, independence complexes and cohomology theory

Details Supersymmetry, lattice fermions, independence complexes and cohomology theory Supersymmetry, lattice fermions, independence complexes and cohomology theory

2009-03-04

arxiv.org/abs/0903.0784v2

Adv. Theor. Math. Phys., 14.2 (2010), 643-694

Physics

Condensed Matter

Strongly Correlated Electrons

40 pages, 28 figures

Scientific paper

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 J. Jonsson, who determined the Euler characteristic (Witten index) via a correspondence with rhombus tilings of the plane. We prove a theorem, first conjectured by P. Fendley, which relates dimensions of the cohomology at grade n to the number of rhombus tilings with n rhombi.

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