Energy States of Quantum Spin Chain Systems with \(p\)-adic Coupling

Abstract

The correspondence between string theory on anti-de Sitter space and conformal field theories on the boundary of the space has advanced our understanding of the connection between the fields of general relativity and quantum mechanics. It is possible to construct a discrete analog to AdS/CFT in which the AdS space and its Euclidean boundary are replaced by the p-adic Bruhat-Tits tree and the p- adic numbers Qp. This thesis will investigate the quantum mechanical side of the AdS/CFT duality through a treatment of spin chain systems with p-adic coupling. First, we present an overview of the simpler Heisenberg ferromagnet in order to develop the tools needed to analyze the more complex p-adic system. Then, a numeric calculation of the ground state for finite systems identifies regimes where single magnons dominate. Under the assumption of non-interacting magnons at low temperature, the thermodynamic limit is discussed and the specific heat and magnetization are calculated. Like in the Heisenberg model, the specific heat and magnetization increase as a power of the temperature, but the exact exponent depends on the strength of the p-adic, non-local interaction.