TITLE:
Thermodynamic Parameters of Central Spin Coupled to an Antiferromagnetic Bath: Path Integral Formalism
AUTHORS:
Christian Platini Fogang Kuetche, Nsangou Issofa, Mathurin Esouague Ateuafack, Lukong Cornelius Fai
KEYWORDS:
Path Integral, Grassmann Algebra, Antiferromagnetic Environment, Partition Function
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.9 No.1,
January
26,
2021
ABSTRACT: A path-integral representation of central spin system immersed in an antiferromagnetic environment was investigated. To carry out this study, we made use of the discrete-time propagator method associated with a basic set involving coherent states of Grassmann variables which made it possible to obtain the analytical propagator which is the centerpiece of the study. In this study, we considered that the environment was in the low-temperature and low-excitation limit and was split into 2 subnets that do not interact with each other. The evaluation of our system was made by considering the first neighbor approximation. From the formalism of the path integrals, it is easy to evaluate the partition function and thermodynamic properties followed from an appropriate tracing over Grassmann variables in the imaginary time domain. We show that the energy of the system depends on the number of sites n when β → 0.