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

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.

5+11 pages, 5+4 figures

References in corpus (5)

• Tensor renormalization group approach to 2D classical lattice models
• Numerical evidence for a Haagerup conformal field theory
• A critical lattice model for a Haagerup conformal field theory
• Extraction of conformal data in critical quantum spin chains using the Koo-Saleur formula
• Exact solution of the $2d$ dimer model: Corner free energy, correlation functions and combinatorics

Cited by in corpus (1)

• Virasoro Generators in the Fibonacci Model Tensor Network -- Tackling Finite Size Effects