Truncated Conformal Space at c=1, Nonlinear Integral Equation and Quantization Rules for Multi-Soliton States

TL;DR

This paper develops a numerical method to analyze c=1 conformal field theories, validating a nonlinear integral equation and clarifying quantization rules for multi-soliton states through comparison with TCS results.

Contribution

It introduces a Truncated Conformal Space technique for c=1 theories and confirms the NLIE's validity, resolving quantization ambiguities for multi-soliton states.

Findings

Numerical evidence supports the NLIE at intermediate scales.

Correct quantization involves half-integer quantum numbers for pure hole states.

Impressive agreement between TCS and NLIE results for multi-soliton states.

Abstract

We develop Truncated Conformal Space (TCS) technique for perturbations of c=1 Conformal Field Theories. We use it to give the first numerical evidence of the validity of the non-linear integral equation (NLIE) derived from light-cone lattice regularization at intermediate scales. A controversy on the quantization of Bethe states is solved by this numerical comparison and by using the locality principle at the ultra- violet fixed point. It turns out that the correct quantization for pure hole states is the one with half-integer quantum numbers originally proposed by Mariottini et al. Once the correct rule is imposed, the agreement between TCS and NLIE for pure hole states turns out to be impressive.