3 years ago

Logarithmic Rainbow Free Energy on a Topological Manifold.

Lei Chen, Hao-Xin Wang, Wei Li, Hai Lin

In this work, a boundary matrix-product-state technique is employed to extract the universal data of the conformal field theory (CFT) on nonorientable surfaces. On the Klein bottle manifold, we demonstrate that each crosscap boundary contributes a free energy term $\frac{1}{2} \ln{k}$, where $k$ is a universal constant in two-dimensional CFT. On the $\mathbb{RP}^2$ manifold, we uncover that, besides the universal crosscap term, the rainbow boundary gives rise to a logarithmic free energy $\frac{c}{4 \mathcal{A}} \ln{\beta}$, where $\beta$ is the width (or inverse temperature) of the system with infinite length $L$, $c$ is the central charge, and $\mathcal{A}$ is a geometry-dependent coefficient. Our calculations reveal that $\mathcal{A} = \sin{\frac{2\pi}{3}}$ for statistical models on the hexagonal, triangular, and kagome lattices, and $\mathcal{A} = \sin{\frac{2\pi}{4}}$ (i.e., $1$) for the square lattice models as well as 1+1D quantum critical chains.

Publisher URL: http://arxiv.org/abs/1801.07635

DOI: arXiv:1801.07635v1

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