# The Toda$_2$ chain

## TL;DR

This paper demonstrates that discretizing the Virasoro algebra naturally leads to a quantum integrable model equivalent to the Toda chain in its second Hamiltonian structure.

## Contribution

It introduces a novel discretization of the Virasoro algebra that results in a quantum Toda chain model.

## Key findings

- Establishes a connection between Virasoro algebra discretization and quantum Toda chain.
- Provides a new approach to constructing quantum integrable models from algebraic structures.
- Shows that the discretized Virasoro algebra reproduces the Toda chain dynamics.

## Abstract

We show that a natural discretisation of Virasoro algebra yields a quantum integrable model which is the Toda chain in the second Hamiltonian structure.