Universal subleading terms in ground-state fidelity from boundary conformal field theory

摘要: The study of the (logarithm the) fidelity, i.e., overlap amplitude, between ground states Hamiltonians corresponding to different coupling constants provides a valuable insight on critical phenomena. When parameters are infinitesimally close, it is known that leading term behaves as $O({L}^{\ensuremath{\alpha}})$ ($L$ system size), where $\ensuremath{\alpha}$ equal spatial dimension $d$ for gapped systems, and otherwise depends exponents. Here we show when changed along manifold, subleading $O(1)$ can appear. This term, somewhat similar topological entanglement entropy, only system's universality class encodes nontrivial information about topology system. We relate universal $g$ factors partition functions (boundary) conformal field theory in $d=1$ $d=2$ dimensions. Numerical checks presented simple example $XXZ$ chain.