We introduce a supersymmetric lattice fermion model that contains both fermion pairing and the interacting Nicolai model. This model possesses a single control parameter,
g, introduced through the anticommutator of the supersymmetry generators (supercharge), and it is shown that supersymmetry is broken in both finite and infinite systems as long as
g is finite. Additionally, the single-mode approximation is employed to establish an upper bound on the dispersion relation of Nambu-Goldstone (NG) fermions, demonstrating their gaplessness. Finally, it is shown, through numerical and analytic calculations, that the anticipated extensive ground-state degeneracy and a zero-energy flat band does not occur for generic values of the parameter
g.
The entanglement spectrum of a pure state of a bipartite system is the full set of eigenvalues of the reduced density matrix obtained from tracing out one part. Such spectra are known in several cases to contain important information beyond that in the entanglement entropy. This paper studies the entanglement spectrum for a variety of critical and near-critical quantum lattice models in one dimension, chiefly by the infinite time evolving block decimation (iTEBD) numerical method, which enables both integrable and non-integrable models to be studied. We find that the distribution of eigenvalues in the entanglement spectra agrees with an approximate result derived by Calabrese and Lefevre to an accuracy of a few per cent for all models studied. This result applies whether the correlation length is intrinsic or generated by the finite matrix size accessible in iTEBD. For the transverse Ising model, the known exact results from Peschel and Eisler for the entanglement spectrum are used to confirm the validity of the iTEBD approach. For more general models, no exact result is available but the iTEBD results directly test the hypothesis that all moments of the reduced density matrix are determined by a single parameter.