Quantum corrections to phi^4 model solutions and applications to Heisenberg chain dynamics

TL;DR

This paper investigates quantum corrections to classical solutions of the phi^4 model within the context of the Heisenberg spin chain, employing zeta-function regularization to analyze energy and dynamics.

Contribution

It introduces a method to compute quantum corrections to phi^4 solutions in spin chains using zeta-function formalism, extending classical models with quantum effects.

Findings

Quantum corrections to energy are explicitly calculated.

Elementary solutions and their quantum modifications are derived.

Applications to spin chain dynamics demonstrate the impact of quantum effects.

Abstract

The Heisenberg spin chain is considered in phi^4 model approximation. Quantum corrections to classical solutions of the one-dimensional phi^4 model within the correspondent physics are evaluated with account of rest $d-1$ dimensions of a d-dimensional theory. A quantization of the models is considered in terms of space-time functional integral. The generalized zeta-function formalism is used to renormalize and evaluate the functional integral and quantum corrections to energy in quasiclassical approximation. The results are applied to appropriate conditions of the spin chain models and its dynamics, which elementary solutions, energy and the quantum corrections are calculated.