# Six-vertex model and non-linear differential equations II. Continuous symmetries

## TL;DR

This paper extends a differential equations approach to analyze the spectrum of the six-vertex model, revealing continuous symmetries via Lie group methods, and builds upon prior spectral problem formulations.

## Contribution

It advances the differential equations method for the six-vertex model spectrum, focusing on continuous symmetries and Lie group analysis.

## Key findings

- Differential approach uncovers continuous symmetries in the spectrum.
- Lie groups method effectively analyzes spectral properties.
- Extension of previous spectral problem work.

## Abstract

This paper is a continuation of our previous work "Six-vertex model and non-linear differential equations I. Spectral problem" in which we have put forward a method for studying the spectrum of the six-vertex model based on non-linear differential equations. Here we intend to elaborate on that approach and also discuss properties of the spectrum unveiled by the aforementioned differential formulation of the transfer matrix's eigenvalue problem. In particular, we intend to demonstrate how this differential approach allows one to study continuous symmetries of the transfer matrix's spectrum through the Lie groups method.