Partition Function for 1-Dimensional Kitaev Chain Model Engendering the Majorana Zero Mode

Abstract

Partition function is an important physical quantity and is related to various thermodynamic functions, also is a key link that connects microscopic and macroscopic physical phenomena. In this article for the first time we calculate partition function Tr exp {-iβt γ_j,b γ_j+1,_a) for 1-dimensional Kitaev chain model which engenders the Majorana zero mode (MZM), where $y_{j+1,a}=c_{j+1}^{†}+c_{j+1},y_{j,b}=\left(c_j-c_j^{†}\right)/i,\left(c_{j,}{c}_j^{†}\right)$ are Dirac fermionic annihilation and creation operators. Following Fan's theorem we successfully disentangle exp {-iβt γ_j,b γ_j+1,_a) and derive the partition function by using the fermionic coherent state representation.