The critical point of a topological phase transition is described by a conformal field theory, where finite-size corrections to energy are uniquely related to its central charge. We investigate the finite-size scaling away from criticality and find a scaling function, which discriminates between phases with different topological indices. This function appears to be universal for all five Altland-Zirnbauer symmetry classes with nontrivial topology in one spatial dimension. We obtain an analytic form of the scaling function and compare it with numerical results.
Bibliographical noteFunding Information:
National Science Foundation http://dx.doi.org/10.13039/100000001 NSF http://sws.geonames.org/6252001/ NSF DMR1306734 We are grateful to A. Abanov and I. Gruzberg for valuable discussions. The work was supported by NSF Grant No. DMR1306734.