The effects of quantum instantons on the thermodynamics of the CP^(N-1) model

TL;DR

This paper investigates how quantum instantons affect the thermodynamics of the CP^(N-1) model in 1+1 dimensions, focusing on pressure calculations and the role of instantons at different temperatures.

Contribution

It introduces a next-to-leading order calculation of pressure in the 1/N expansion, highlighting the impact of quantum instantons on thermodynamic properties.

Findings

Quantum instantons significantly influence pressure at intermediate temperatures.

The pressure for N=3 aligns with the O(3) sigma model up to 1/N^2 corrections.

Assuming 1/N expansion validity suggests instantons dominate thermodynamics at certain regimes.

Abstract

Using the 1/N expansion, we study the influence of quantum instantons on the thermodynamics of the CP^(N-1) model in 1+1 dimensions. We do this by calculating the pressure to next-to-leading order in 1/N, without quantum instanton contributions. The fact that the CP^1 model is equivalent to the O(3) nonlinear sigma model, allows for a comparison to the full pressure up to 1/N^2 corrections for N=3. Assuming validity of the 1/N expansion for the CP^1 model makes it possible to argue that the pressure for intermediate temperatures is dominated by the effects of quantum instantons. A similar conclusion can be drawn for general N values by using the fact that the entropy should always be positive.