エンタングルメントエントロピーからエンタングルメントスペクトルへ: 二次元原子価結合固体中に埋込んだ1+1D CFT

Amin Moharramipour, Dan Sehayek, Thomas Scaffidi

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} 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.

匡 高柳, 西岡辰磨, 笠真生

Jun Tsujimura

K. Nomura

Conformal field theory (CFT) with the central charge c=1 is important both in the field theory and in the condensed matter physics, since it has the continuous internal symmetry (U(1) or SU(2)) and a marginal operator, and it is an effective theory of many 1D quantum spin and 1D electron systems. So it is valuable to understand how the c=1 CFT models become unstable. In this paper we discuss an instability of the c=1 CFT, that is, the transition to the ferromagnetic state. For the U(1) CFT case, we find that the spin wave velocity $v$ and the critical dimension $K$ behave $v, 1/K \propto \sqrt{Δ_c -Δ}$ under reasonable assumptions.

K. Nomura

Conformal field theory (CFT) with the central charge c=1 is important both in the field theory and in the condensed matter physics, since it has the continuous internal symmetry (U(1) or SU(2)) and a marginal operator, and it is an effective theory of many 1D quantum spin and 1D electron systems. So it is valuable to understand how the c=1 CFT models become unstable. In this paper we discuss an instability of the c=1 CFT, that is, the transition to the ferromagnetic state. For the U(1) CFT case, we find that the spin wave velocity v and the critical dimension K behave v,1/K ∝ √ �c − � under reasonable assumptions.

Jun Tsujimura