Virasoro and Kac-Moody algebra in generic tensor network representations of 2d critical lattice partition functions

TL;DR

This paper introduces a method to implement Virasoro and Kac-Moody algebra generators in tensor network representations of 2D critical lattice models, enabling analysis without a known Hamiltonian.

Contribution

It provides a novel approach to realize algebraic structures in tensor networks for critical systems, applicable even when the Hamiltonian is unknown.

Findings

High accuracy in 2D Ising and dimer models

Effective generation of descendant states across system sizes

Applicable without explicit Hamiltonian knowledge

Abstract

In this paper, we propose a general implementation of the Virasoro generators and Kac-Moody currents in generic tensor network representations of 2-dimensional critical lattice models. Our proposal works even when a quantum Hamiltonian of the lattice model is not available, which is the case in many numerical computations involving numerical blockings. We tested our proposal on the 2d Ising model, and also the dimer model, which works to high accuracy even with a fairly small system size. Our method makes use of eigenstates of a small cylinder to generate descendant states in a larger cylinder, suggesting some intricate algebraic relations between lattice of different sizes.