Status  Confirmed 
Seminar Series  FORUMENS 
Subjects  condmat.statmech 
Date  Wednesday 4 October 2023 
Time  12:45 
Institute  LPENS 
Seminar Room  Seminar room, 3 rue d’Ulm, College de France 
Speaker's Last Name  Scaffidi 
Speaker's First Name  Thomas 
Speaker's Email Address  
Speaker's Institution  UC Irvine, University of Toronto 
Title  Solvable models for 2D quantum critical points: Loop soups of 1+1D conformal field theories 
Abstract  For gapped topological systems, there exist several approaches to construct higherdimensional 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 selfavoiding 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 $O(n=0)$ fullypacked 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 nonlocal in nature. Finally, we provide a verification of our predictions based on Monte Carlo calculations. 
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