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Résumé |
For gapped topological systems, there exist several approaches to construct higher-dimensional models by combining lower-
dimensional ones (e.g. coupled wires or decorated domain wall constructions). In this talk, we will propose a generalization of this
approach to gapless systems. 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. Our local Hamiltonian attaches gapless spin chains to the domain walls of a
triangular lattice Ising antiferromagnet. The macroscopic degeneracy between antiferromagnetic configurations is only split by
the Casimir energy of each decorating CFT, which is usually thought to be a universal function of the central charge $E_{Cas} = - (\pi
c)/(3 L)$. Remarkably, we found several examples of 1D Hamiltonians realizing CFTs for which the Casimir energy is positive (i.e.
$c<0$ in the last formula, making it favorable for domain walls to condense into a single self-avoiding random walk (or "snake") visiting every site of the 2D
lattice. Since the snake is macroscopically long, the CFT living on it has a vanishing gap, and the resulting 2+1D theory is thus gapless. We obtain predictions
for critical exponents and for entanglement by combining results about 1+1D CFTs and about the statistical fluctuations of the snake (which are described by
the $O(n=0)$ fully-packed loop model). We show that the area law for entanglement is restored for the 2D state (despite the log term for the entanglement of
the 1+1D CFTs) but that it is non-local in nature. Finally, we provide a verification of our predictions based on Monte Carlo calculations. |
