Spiral renormalization group flow and universal entanglement spectrum of the non-Hermitian 5-state Potts model

TL;DR

This paper uses tensor network algorithms to study the non-Hermitian 5-state Potts model, revealing spiral RG flow and reconstructing the entanglement spectrum, thus advancing understanding of complex fixed points and conformal invariance.

Contribution

It demonstrates the effectiveness of tensor networks in simulating non-Hermitian models and captures the spiral RG flow and entanglement spectrum of the complex fixed point.

Findings

Tensor networks can simulate non-Hermitian theories despite the breakdown of the variational principle.

Observation of the spiral flow of running couplings up to system size L=28.

Reconstruction of the boundary CCFT spectrum from the entanglement Hamiltonian.

Abstract

The quantum $5$-state Potts model is known to possess a perturbative description using complex conformal field theory (CCFT), the analytic continuation of ``theory space" to a complex plane. To study the corresponding complex fixed point on the lattice, the model must be deformed by an additional non-Hermitian term due to its complex coefficient $\lambda$. Although the variational principle breaks down in this case, we demonstrate that tensor network algorithms are still capable of simulating these non-Hermitian theories. We access system sizes up to $L = 28$, which enable the observation of the theoretically predicted spiral flow of the running couplings. Moreover, we reconstruct the full boundary CCFT spectrum through the entanglement Hamiltonian encoded in the ground state. Our work demonstrates how tensor networks are the correct approach to capturing the approximate conformal invariance of weakly first-order phase transitions.