# On asymptotic behaviour in truncated conformal space approach

## TL;DR

This paper investigates the asymptotic behavior of the truncated conformal space approach (TCSA) in quantum field theory, focusing on boundary RG flows beyond the first fixed point and their sensitivity to truncation schemes.

## Contribution

It provides a detailed numerical analysis of boundary RG flows in TCSA beyond the first fixed point, exploring their nature and dependence on truncation modifications.

## Key findings

- Flows can approximate reversed physical RG flows in some models
- Spectrum approaches a stable regime not linked to local boundary conditions
- Flows beyond the first fixed point are highly sensitive to truncation scheme modifications

## Abstract

The Truncated conformal space approach (TCSA) is a numerical technique for finding finite size spectrum of Hamiltonians in quantum field theory described as perturbations of conformal field theories. The truncation errors of the method have been systematically studied near the UV fixed point (when the characteristic energy related to the coupling is less than the truncation cutoff) where a good theoretical understanding has been achieved. However numerically the method demonstrated a good agreement with other methods for much larger values of the coupling when the RG flow approaches a new fixed point in the infrared. In the present paper we investigate this regime for a number of boundary RG flows testing the leading exponent and truncation errors. We also study the flows beyond the first fixed point which have been observed numerically but yet lack a theoretical understanding. We show that while in some models such flows approximate reversed physical RG flows, in other models the spectrum approaches a stable regime that does not correspond to any local boundary condition. Furthermore we find that in general the flows beyond the first fixed point are very sensitive to modifications of the truncation scheme.