The spectrum of perturbed (3, 10) minimal model

TL;DR

This paper investigates renormalization group flows between non-unitary minimal models and massive theories using TCSA, focusing on the Yang-Lee model and the $M(3,10)$ model, and finds evidence supporting a specific flow to a massive phase with characteristic spectrum.

Contribution

It provides the first detailed TCSA analysis of the $M(3,10)$ model perturbed by $_{1,3}$, confirming the flow to a massive phase with a kink and breathers.

Findings

TCSA performed up to level N=15 for $M(2,5)+i$.

The $M(3,10)$ model flows to a massive phase with a kink and two breathers.

Results support the conjecture about the spectrum and phase of the perturbed $M(3,10)$ model.

Abstract

We study RG flows between non-unitary minimal models and massive quantum theories using Truncated Conformal Space Approach (TCSA). We consider the integrable non-unitary Yang-Lee model perturbed by $i\phi$ and the $D$-series version of $M(3,10)$ which is a product of two Yang-Lee models, perturbing the latter by relevant operators $\phi_{1,3}$ and $i\phi^+_{1,5}$. Utilizing the quasi-primary fields we find, TCSA is performed up to the level $N=15$ for $M(2,5)+i\phi$. The conjecture about the $M(3,10)$ perturbed by $\phi_{1,3}$ is stated: this theory flows to a massive phase; its spectrum contains a kink and two breathers, whose masses we find. Our TCSA results support the conjecture.