Supersymmetry breaking and Nambu-Goldstone fermions in an extended Nicolai model

Abstract

We study a model of interacting spinless fermions in a one dimensional lattice with supersymmetry (SUSY). The Hamiltonian is given by the anti-commutator of two supercharges $Q$ and $Q^{†}$, each of which is comprised solely of fermion operators and possesses one adjustable parameter $g$. When the parameter $g$ vanishes, the model is identical to the one studied by Nicolai [H. Nicolai, J. Phys. A: Math. Gen. \textbf{9}, 1497 (1976)], where the zero-energy ground state is exponentially degenerate. On the other hand, in the large-$g$ limit the model reduces to the free-fermion chain with a four-fold degenerate ground state. We show that for finite chains SUSY is spontaneously broken when $g>0$. We also rigorously prove that for sufficiently large $g$ the ground-state energy density is nonvanishing in the infinite-volume limit. We further analyze the nature of the low-energy excitations by employing various techniques such as rigorous inequalities, exact numerical diagonalization, and renormalization group method with bosonization. The analysis reveals that the low-energy excitations are described by massless Dirac fermions (or Thirring fermions more generally), which can be thought of as Nambu-Goldstone fermions from the spontaneous SUSY breaking.

arXiv comment13 pages, 4 figures, v2: typos corrected. This version will appear in Phys. Rev. D

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Cited by in corpus (10)

• Counting Rules of Nambu-Goldstone Modes
• Complete random matrix classification of SYK models with $\mathcal{N}=0$, $1$ and $2$ supersymmetry
• Supersymmetry breaking and Nambu-Goldstone fermions with cubic dispersion
• Supersymmetry Breaking and Nambu-Goldstone Fermions in Interacting Majorana Chains
• Realization of supersymmetry and its spontaneous breaking in quantum Hall edges
• Spontaneously broken supersymmetric fracton phases with fermionic subsystem symmetries
• Goldstino in supersymmetric Bose-Fermi mixtures in the presence of Bose Einstein condensate
• Supersymmetry breakdown for an extended version of the Nicolai supersymmetric fermion lattice model
• Characterization of degenerate supersymmetric ground states of the Nicolai supersymmetric fermion lattice model by symmetry breakdown
• Emergent spacetime supersymmetry in an interacting Kitaev chain with explicit supersymmetry