Dynamics of magnetization at infinite temperature in a Heisenberg spin chain
Eliott Rosenberg, T. I. Andersen, Rhine Samajdar, A. Petukhov, Jesse C. Hoke, Dmitry A. Abanin, Andreas Bengtsson, Ilya Drozdov, Catherine Erickson, P. V. Klimov, Xiao Mi, Alexis Morvan, M. Neeley, C. Neill, Rajeev Acharya, R. M. Allen, K. R. Anderson, M. Ansmann, Frank Arute, Kunal Arya, Abraham Asfaw, Juan Atalaya, Joseph C. Bardin, Alexander Bilmes, Gina Bortoli, Alexandre Bourassa, Jenna Bovaird, L. Brill, Michael Broughton, Bob B. Buckley, David A. Buell, Tim Burger, Brian Burkett, Nicholas Bushnell, Juan Campero, Hung-Shen Chang, Z. Chen, B. Chiaro, D. Chik, J. Cogan, Roberto Collins, P. Conner, William Courtney, A. L. Crook, Ben Curtin, D. M. Debroy, Alexander Del Toro Barba, Sean Demura, Agustín Di Paolo, A. Dunsworth, Clifford J. Earle, Lara Faoro, Edward Farhi, Reza Fatemi, V. S. Ferreira, Leslie Flores Burgos, Ebrahim Forati, Austin G. Fowler, Brooks Foxen, G. Garcia, Élie Genois, William Giang, Craig Gidney, D. Gilboa, Marissa Giustina, Raja Gosula, Alejandro Grajales Dau, Jonathan A. Gross, Steve Habegger, Michael C. Hamilton, M. Hansen, Matthew P. Harrigan, Sean D. Harrington, P. Heu, Gordon Hill, M. R. Hoffmann, Sabrina Hong, Trent Huang, Ashley Huff, William J. Huggins, L. B. Ioffe, S. V. Isakov, Justin Iveland, E. Jeffrey, Z. Jiang, C. Jones, Pavol Juhás, Dvir Kafri, Tanuj Khattar, Mostafa Khezri, Mária Kieferová, Seon Kim, Alexei Kitaev, A. R. Klots, A. N. Korotkov, Fedor Kostritsa, John Mark Kreikebaum, David Landhuis, Pavel Laptev, K.-M. Lau
Abstract
Understanding universal aspects of quantum dynamics is an unresolved problem in statistical mechanics. In particular, the spin dynamics of the one-dimensional Heisenberg model were conjectured as to belong to the Kardar-Parisi-Zhang (KPZ) universality class based on the scaling of the infinite-temperature spin-spin correlation function. In a chain of 46 superconducting qubits, we studied the probability distribution of the magnetization transferred across the chain's center, [Formula: see text]. The first two moments of [Formula: see text] show superdiffusive behavior, a hallmark of KPZ universality. However, the third and fourth moments ruled out the KPZ conjecture and allow for evaluating other theories. Our results highlight the importance of studying higher moments in determining dynamic universality classes and provide insights into universal behavior in quantum systems.