Abstract
We introduce a lattice fermion model in one spatial dimension with supersymmetry (SUSY) but without particle number conservation. The Hamiltonian is defined as the anticommutator of two nilpotent supercharges and . Each supercharge is built solely from spinless fermion operators and depends on a parameter . The system is strongly interacting for small , and in the extreme limit , the number of zero-energy ground states grows exponentially with the system size. By contrast, in the large- limit, the system is noninteracting and SUSY is broken spontaneously. We study the model for modest values of and show that under certain conditions spontaneous SUSY breaking occurs in both finite and infinite chains. We analyze the low-energy excitations both analytically and numerically. Our analysis suggests that the Nambu-Goldstone fermions accompanying the spontaneous SUSY breaking have cubic dispersion at low energies.
- Received 28 December 2016
DOI:https://doi.org/10.1103/PhysRevD.95.065001
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