Fermionic many-body models

Xindong Wang, Hai‐Ping Cheng

Using a separable many-body variational wavefunction, we formulate a self-consistent effective Hamiltonian theory for fermionic many-body system. The theory is applied to the two-dimensional (2D) Hubbard model as an example to demonstrate its capability and computational effectiveness. Most remarkably for the Hubbard model in 2D, a highly unconventional quadruple-fermion non-Cooper pair order parameter is discovered.

Yi‐Zhuang You, Andreas W. W. Ludwig, Cenke Xu

The Sachdev-Ye-Kitaev (SYK) model is a quantum mechanical model for randomly interaction fermions in a quantum dot. This paper studies the properties of the many-body spectrum of the SYK model and finds a periodicity of the spectral properties in term of the number of fermion modes in the quantum dot. In particular, the level statistics of SYK spectrum are investigated. It is found that the many-body level spacing of the SYK model follows Wigner-Dyson statistics, consistent with the thermalizing nature of the SYK model. Interestingly, the level statistics goes through those of different random matrix ensembles periodically. The periodicity can be explained by viewing the SYK model as an effective model for the boundary of 1D interacting fermionic symmetry-protected topological states. The periodicity in the SYK spectrum is therefore tied to the classification of fermionic topological states in one dimension.

Joachim Alexander Maruhn, P.‐G. Reinhard, E. Suraud

José M. Arias, María Isabel Gallardo, Manuel Lozano

Y. Wang, Fu‐Cho Pu

A one-dimensional boson–fermion model with two-body interactions between the two types of chiral fermions is considered. It is shown that the model is exactly soluble and the general Bethe eigenstates are constructed. On the basis of the Bethe ansatz equations, the ground state, the low lying elementary excitations, and the thermodynamics are also given in some closed integral equations.