Twisted CP(N-1) instanton projectors and the N-level quantum density matrix

Abstract

Twisted classical solutions to the $\mathbb{C}{P}^{N-1}$ model play a key role in the analysis of such models on the spatially compactified cylinder ${\mathbb{S}}_L^1\times {\mathbb{R}}^1$ and have recently been shown to be important for the resurgent structure of this quantum field theory. Instantons and non-self-dual solutions both fractionalize, and domain walls formed by such topological solutions can be associated with $N$-vacua having maximally repulsive energy eigenvalues. The purpose of this paper is to reinforce this view through the investigation of a number of parallels between the $\mathbb{C}{P}^{N-1}$ model and $N$-level quantum mechanical density matrices. Specifically, we demonstrate the existence of a time-evolution equation for the $\mathbb{C}{P}^{N-1}$ instanton projector analogous to the Liouville-von Neumann equation in the quantum mechanical formalism. The group theoretical analysis of density matrices and the $\mathbb{C}{P}^{N-1}$ model are also closely related. Finally, we explore the emergence of geometrical (Berry) phases in both systems and their interrelationship.

18 pages, reference corrected

References in corpus (3)

• Neutral bions in the $\mathbb{C}{P}^{N-1}$ model
• Measuring Z2 topological invariants in optical lattices using interferometry
• Topological insulators and the QCD vacuum: the theta parameter as a Berry phase

Cited by in corpus (4)

• Resurgence in sine-Gordon quantum mechanics: Exact agreement between multi-instantons and uniform WKB
• Fractional instantons and bions in the O(N) model with twisted boundary conditions
• Non-BPS exact solutions and their relation to bions in $\mathbb{C}{P}^{N-1}$ models
• Josephson instantons and Josephson monopoles in a non-Abelian Josephson junction