Supersymmetry breaking and Nambu-Goldstone fermions with cubic dispersion

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 $Q$ and $Q^{†}$. Each supercharge is built solely from spinless fermion operators and depends on a parameter $g$. The system is strongly interacting for small $g$, and in the extreme limit $g=0$, the number of zero-energy ground states grows exponentially with the system size. By contrast, in the large-$g$ limit, the system is non-interacting and SUSY is broken spontaneously. We study the model for modest values of $g$ 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.

arXiv comment13 pages, 5 figures, v3: published version

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• Correlators in the $\mathcal{N}=2$ Supersymmetric SYK Model
• Towards the Holographic Dual of N = 2 SYK
• Supersymmetry Breaking and Nambu-Goldstone Fermions in Interacting Majorana Chains
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• Effective dimension, level statistics, and integrability of Sachdev-Ye-Kitaev-like models
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• $\mathcal{N}=(0,2)$ SYK, Chaos and Higher-Spins
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