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Daniel Adam Roberts CHAOS, Holography, And Other Science by Daniel Adam Roberts Submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2016 (cid:13)c Massachusetts Institute of Technology 2016. All rights reserved. Author ............................................................................ Department of Physics April 29, 2016 Certified by........................................................................ Allan Wilfred Adams III Associate Professor of Physics Thesis Supervisor Accepted by....................................................................... Nergis Mavalvala Associate Department Head for Education CHAOS, Holography, And Other Science by Daniel Adam Roberts Submitted to the Department of Physics on April 29, 2016, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics Abstract This thesis focuses on the relationship between black holes in holography, chaos in strongly- coupled quantum systems, and the computational complexity of holographic states. By directly considering the time evolution of local operators, I am led to a simple diagnostic of many-body chaos: a commutator of such operators separated in time and space. Using this diagnostic, I study the growth of operators—a manifestation of the butterfly effect—in a variety of quantum systems. By considering the butterfly effect in holography, I find evi- dence for a detailed correspondence between the tensor network (or quantum circuit) that builds the holographic state and the interior geometry (or Einstein-Rosen bridge) of the black hole. Ultimately, I try to understand these connections by considering entanglement across time: the entanglement between an output system following time evolution and a record or memory perfectly correlated with the initial system. Thesis Supervisor: Allan Wilfred Adams III Title: Associate Professor of Physics This thesis is based on the following four papers: • [1] written with Douglas Stanford and Leonard Susskind • [2] written with Adam Brown, Leonard Susskind, Brian Swingle, and Ying Zhao • [3] written with Douglas Stanford • [4] written with Pavan Hosur, Xiao-Liang Qi, and Beni Yoshida Acknowledgments In many of my papers, acknowledgments have been a space for sincere thanks, literal ac- knowledgments (of funding sources), and hidden jokes. This is made possible by the fact that in all of my papers, the acknowledgments have come at the end. In this work, we are instructed to do things sdrawkcab. It is my pleasure to thank many people: My advisor, Allan Adams, for enthusiastically supporting all my varied interests and for always clearly smiling (frowning) when I would say something correct (incorrect) so that in discussions I always had “experimental” means of determining right from wrong. My numerous collaborators ...for collaborating. Many of you literally helped me write this thesis. Special acknowledgment to Douglas Stanford, for essentially becoming my second advisor when he was only a graduate student. My entire approach to physics is derivedfromthethingsIlearnedduringourcollaborations. ToLennySusskind,foradopting meatStanfordandalwaysmakingmefeelwelcomedattheSITP.ToJesseThaler, fordoing the same for me at the CTP (and for working with me on the project that legitimately entitles me to add “Other Science”). To Yoni Kahn, for convincing me to come to MIT, for finding a way for us to collaborate even though we work on dissimilar things, (for introducing me to Jesse,) and for being the person who instantly alleviates all of my silly confusions. And to Beni Yoshida, Adam Brown, and Brian Swingle, for treating me like an adult physicist when I was probably more like an adolescent (if not a child). Finally, to Steve Shenker for his support, encouragement, and help.1 I’d also like to thank potential future collaborators (i.e. current and former CTP mem- bers): Tarek Anous (my Pufu), Michael Crossley, Ethan Dyer, Paolo Glorioso, my five-year officemate Dan Kolodrubetz (especially, for tolerating five years of distracting behavior and encouraging all my shenanigans), Mark Mezei, Ian Moult, Lina Necib, Nikhil Raghuram, Shu-Heng Shao, Zach Thomas, and Yifan Wang. Next, I would like to more than merely acknowledge two of my funding sources: the Marshall Scholarship and the Fannie and John Hertz Foundation, both of which are respon- sible for providing all the opportunities that brought me where I am today (at any future date you happen to be reading this!). Also to the latter for actually standing by its mission 1Though technically he is not (yet) a collaborator, he is acknowledged on nearly all of my papers and this thesis is indebted to his and Douglas’s work. statement and giving me the freedom to pursue all of my academic interests (i.e. chaos, holography, and other science), and for introducing me to John Frank, Kelly Moynihan, Josh Mueller, Vyas Ramanan, and Thomas Segall-Shapiro, whom I thank for science, etc. Although I feel (hope) that all my collaborators are close friends, the converse does not necessarily hold.2 First, ack. to Kyle Mahowald, my longest running roommate (six years). That alone should indicate the level of thanks that he deserves. (It also occurs to me that I should probably thank him for teaching me the value of constraints and “constraint-based activities.”) Thanks to my other roommate Robbie Kubala, who provides well-needed balance. Thanks to Max Kleiman-Weiner, for work on projects best classified as “other science” (i.e for cultivating my interest in machine learning and AI). And finally, an extra thanks to all three of them for all of the things. Finally, I’d like to thank my family: my sister, Nicole Roberts, for agreeing to my strange request to design a cover page for my thesis (and actually designing it and making itabsolutelyamazing!);andmyparents,DavidandLindaRoberts,forexplainingeverything to me before I learned how to learn. This work was supported by the DOD through the NDSEG Program, by the Fannie and John Hertz Foundation, and by the U.S. Department of Energy under cooperative research agreement Contract Number DE-SC0012567. This Ph.D. has been brought to you by the letters A, C, H, O, and S. 2This means that I have friends who are not physicists.
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