Order in Fermion Systems

G. Calucci

The recently proposed method for investigating the large-order behaviour of the perturbative expansion is applied to a quantum thermodynamical system of interacting fermions. The investigation is performed in detail for a system in one space dimension, with the use of the Thomas-Fermi approximation in order to deal with many-fermion systems. Some observations about the influence of the number of dimensions on the large-order behaviour are presented.

S. Mazumdar

I. V. Drozdov, B. Drozdov

The ergodic second-order approach of entropy gradient maximization, applied on the problem of a quantum bosonic system, does not provide dynamic equations for pure fermionic system. The first-order dynamic equation results for a system of bosonic and fermionic \dofs interacting by a conservation of a common sum of quantum occupation numbers.

Pirmin Lemberger, Nicolas Macris

Zheng‐Cheng Gu, Zhenghan Wang, Xiao-Gang Wen

The ${Z}_{2}$ topological order in ${Z}_{2}$ spin liquid and in the exactly solvable Kitaev toric code model is the simplest topological order for 2 + 1D bosonic systems. More general 2 + 1D bosonic topologically ordered states can be constructed via exactly solvable string-net models. However, the most important topologically ordered phases of matter are arguably the fermionic fractional quantum Hall states. Topological phases of matter for fermion systems are strictly richer than their bosonic counterparts because locality has different meanings for the two kinds of systems. In this paper, we describe a simple fermionic version of the toric code model to illustrate many salient features of fermionic exactly solvable models and fermionic topologically ordered states.