Solvable models for 2+1D quantum critical points: Loop soups of 1+1D conformal field theories

TL;DR

This paper introduces a class of exactly solvable 2+1D quantum critical models constructed by attaching 1+1D conformal field theories to fluctuating domain walls, revealing novel critical behavior and entanglement properties.

Contribution

It presents a new solvable model framework for 2+1D quantum critical points using loop soups of 1+1D CFTs attached to domain walls, with novel critical exponents and entanglement features.

Findings

Casimir energy influences domain wall configurations

Identification of a 'snake' phase with gapless CFT behavior

Verification of theoretical predictions through Monte Carlo simulations

Abstract

We construct a class of solvable models for 2+1D quantum critical points by attaching 1+1D conformal field theories (CFTs) to fluctuating domain walls forming a ``loop soup''. Specifically, our local Hamiltonian attaches gapless spin chains to the domain walls of a triangular lattice Ising antiferromagnet. The macroscopic degeneracy between antiferromagnetic configurations is split by the Casimir energy of each decorating CFT, which is usually negative and thus favors a short loop phase with a finite gap. However, we found a set of 1D CFT Hamiltonians for which the Casimir energy is effectively positive, making it favorable for domain walls to coalesce into a single ``snake'' which is macroscopically long and thus hosts a CFT with a vanishing gap. The snake configurations are geometrical objects also known as fully-packed self-avoiding walks or Hamiltonian walks which are described by an $\mathrm{O}(n=0)$ loop ensemble with a non-unitary 2+0D CFT description. Combining this description with the 1+1D decoration CFT, we obtain a 2+1D theory with unusual critical exponents and entanglement properties. Regarding the latter, we show that the $\log$ contributions from the decoration CFTs conspire with the spatial distribution of loops crossing the entanglement cut to generate a ``non-local area law''. Our predictions are verified by Monte Carlo simulations.