Conformal Thermal Tensor Network and Universal Entropy on Topological Manifolds

Abstract

Partition functions of quantum critical systems, expressed as conformal thermal tensor networks, are defined on various manifolds which can give rise to universal entropy corrections. Through high-precision tensor network simulations of several quantum chains, we identify the universal entropy $S_{\mathcal{K}}=\ln k$ on the Klein bottle, where $k$ relates to quantum dimensions of the primary fields in conformal field theory (CFT). Different from the celebrated Affleck-Ludwig boundary entropy $\ln g$ ($g$ reflects non-integer groundstate degeneracy), $S_{\mathcal{K}}$ has \textit{no} boundary dependence or surface energy terms accompanied, and can be very conveniently extracted from thermal data. On the Möbius-strip manifold, we uncover an entropy $S_{\mathcal{M}}=\frac{1}{2}(\ln g+\ln k)$ in CFT, where $\frac{1}{2}\ln g$ is associated with the only open edge of the Möbius strip, and $\frac{1}{2}\ln k$ with the non-orientable topology. We employ $S_{\mathcal{K}}$ to accurately pinpoint the quantum phase transitions, even for those without local order parameters.

4 pages + references, 5 figures, supplementary material; minor revisions

References in corpus (4)

• Topological characterization of quantum phase transitions in a S=1/2 spin model
• Linearized Tensor Renormalization Group Algorithm for Thermodynamics of Quantum Lattice Models
• Tensor operators: constructions and applications for long-range interaction systems
• Universal Boundary Entropies in Conformal Field Theory: A Quantum Monte Carlo Study

Cited by in corpus (1)

• Universal entropy of conformal critical theories on a Klein bottle