title: Universal Signatures of Quantum Critical Points from Finite-Size Torus Spectra: A Window into the Operator Content of Higher-Dimensional Conformal Field Theories.
abstract: The low-energy spectra of many body systems on a torus, of finite size L, are well understood in magnetically ordered and gapped topological phases. However, the spectra at quantum critical points separating such phases are largely unexplored for (2+1)D systems. Using a combination of analytical and numerical techniques, we accurately calculate and analyze the low-energy torus spectrum at an Ising critical point which provides a universal fingerprint of the underlying quantum field theory, with the energy levels given by universal numbers times 1/L. We highlight the implications of a neighboring topological phase on the spectrum by studying the Ising* transition (i.e. the transition between a Z_{2} topological phase and a trivial paramagnet), in the example of the toric code in a longitudinal field, and advocate a phenomenological picture that provides qualitative insight into the operator content of the critical field theory.
authors.affiliation: Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria.
authors.forename: Michael
authors.initials: M
authors.lastname: Schuler
authors.affiliation: Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: Seth
authors.initials: S
authors.lastname: Whitsitt
authors.affiliation: Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria.
authors.forename: Louis-Paul
authors.initials: LP
authors.lastname: Henry
authors.affiliation: Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.|Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.
authors.forename: Subir
authors.initials: S
authors.lastname: Sachdev
authors.affiliation: Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria.
authors.forename: Andreas M
authors.initials: AM
authors.lastname: Läuchli