CFT and Lattice Correlators Near an RG Domain Wall between Minimal Models

TL;DR

This paper studies the RG domain wall between minimal models, specifically the Tricritical Ising and Ising models, by comparing analytical conformal field theory results with numerical lattice simulations, confirming their agreement.

Contribution

It provides a nonperturbative check of Gaiotto's algebraic construction of the RG domain wall for the minimal case k=2, linking CFT and lattice models.

Findings

Analytical correlation functions match numerical DMRG results.

Confirmed the RG domain wall construction for the Tricritical Ising and Ising models.

Discussed potential experimental realizations.

Abstract

Conformal interfaces separating two conformal field theories (CFTs) provide maps between different CFTs, and naturally exist in nature as domain walls between different phases. One particularly interesting construction of a conformal interface is the renormalization group (RG) domain wall between CFTs. For a given Virasoro minimal model $\mathcal{M}_{k+3,k+2}$, an RG domain wall can be generated by a specific deformation which triggers an RG flow towards its adjacent Virasoro minimal model $\mathcal{M}_{k+2,k+1}$ with the deformation turned on over part of the space. An algebraic construction of this domain wall was proposed by Gaiotto in \cite{Gaiotto:2012np}. In this paper, we will provide a study of this RG domain wall for the minimal case $k=2$, which can be thought of as a nonperturbative check of the construction. In this case the wall is separating the Tricritical Ising Model (TIM) CFT and the Ising Model (IM) CFT. We will check the analytical results of correlation functions from the RG brane construction with the numerical density matrix renormalization group (DMRG) calculation using a lattice model proposed in \cite{Grover:2012bm,Grover:2013rc}, and find a perfect agreement. We comment on possible experimental realizations of this RG domain wall.