Entanglement scaling for $\lambda\phi_2^4$

TL;DR

This paper investigates the entanglement and scaling properties of the two-dimensional $\lambda\phi^4$ model at criticality, employing tensor network methods to analyze double scaling behaviors and accurately determine the critical point.

Contribution

It introduces a novel application of boundary matrix product state methods to study double scaling in the $\lambda\phi^4$ model, providing improved precision for the critical point.

Findings

Identified double scaling properties of key physical quantities.

Achieved a more precise estimate of the critical point $\alpha_c=11.09698(31)$.

Demonstrated the applicability of tensor network methods beyond traditional contexts.

Abstract

We study the $\lambda\phi^4$ model in $0+2$ dimensions at criticality, and effectuate a simultaneous scaling of UV and IR physics. We demonstrate that the order parameter $\phi$, the correlation length $\xi$ and quantities like $\phi^3$ and the entanglement entropy exhibit useful double scaling properties. The calculations are performed with boundary matrix product state methods on tensor network representations of the partition function, though the technique is equally applicable outside the realm of tensor networks. We find the value $\alpha_c=11.09698(31)$ for the critical point, improving on previous results.