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

TL;DR

This paper extends a tensor network method to implement Virasoro operators in the Fibonacci model, addressing finite size effects and demonstrating the generation of descendant states, thus broadening the method's applicability.

Contribution

It introduces an improved approach to identify the stress tensor in the Fibonacci model using topological projections and optimization, enhancing tensor network techniques for finite systems.

Findings

Successfully generated descendant states in the Fibonacci model

Demonstrated the method's effectiveness despite finite size effects

Extended the applicability of Virasoro operator implementation in tensor networks

Abstract

In this paper, we extend the method implementing Virasoro operators in a tensor network we proposed in arXiv:2205.04500 and test it on the Fibonacci model, which is known to suffer from far more finite size effects. To pick up the "seed" state that would flow to the stress tensor in the thermodynamic limit, we make use of the topological idempotent that projects the transfer matrix to the trivial sector. Combined with an optimization method, the seed state can be identified. We demonstrate that the descendant states in the Fibonacci model can be correctly generated with this approximate stress tensor, giving further evidence that the method applies more generally.