# Conformal Thermal Tensor Network and Universal Entropy on Topological Manifolds

Lei Chen, Beihang University

29.08.2017 at 10:00

Thermal quantum critical systems, with partition functions expressed as conformal tensor networks, are revealed to exihbit universal entropy corrections on non-orientable manifolds. Through high-precision tensor network simulations of several quantum chains, we identify the universal entropy S_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_K has no boundary dependence or surface energy terms accompanied, and can be very conveniently extracted from thermal data. On the M\"obius-strip manifold, we uncover an entropy S_M= 1/2 [ln(g) + ln(k)] in CFT, where 1/2 ln(g) is associated with the only open edge of the M\"obius strip, and 1/2 ln(k) with the non-orientable topology. As an useful application, we employ the universal entropy to accurately pinpoint the quantum phase transitions, even for those without local order parameters.

A 318, Theresienstr. 37