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University of Massachusetts Amherst ScholarWorks@UMass Amherst Doctoral Dissertations Dissertations and Theses July 2018 Emergent Phenomena in Quantum Critical Systems Kun Chen University of Massachusetts Amherst Follow this and additional works at: https://scholarworks.umass.edu/dissertations_2 Part of the Atomic, Molecular and Optical Physics Commons, Condensed Matter Physics Commons, Other Physics Commons, Quantum Physics Commons, and the Statistical, Nonlinear, and Soft Matter Physics Commons Recommended Citation Chen, Kun, "Emergent Phenomena in Quantum Critical Systems" (2018). Doctoral Dissertations. 1224. https://doi.org/10.7275/11928423.0 https://scholarworks.umass.edu/dissertations_2/1224 This Open Access Dissertation is brought to you for free and open access by the Dissertations and Theses at ScholarWorks@UMass Amherst. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of ScholarWorks@UMass Amherst. For more information, please contact [email protected]. EMERGENT PHENOMENA IN QUANTUM CRITICAL SYSTEMS A Dissertation Presented by KUN CHEN Submitted to the Graduate School of the University of Massachusetts Amherst in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY May 2018 Department of Physics c Copyright by Kun Chen 2018 All Rights Reserved EMERGENT PHENOMENA IN QUANTUM CRITICAL SYSTEMS A Dissertation Presented by KUN CHEN Approved as to style and content by: Nikolay Prokof'ev, Co-chair Boris Svistunov, Co-chair Jonathan Machta, Member Murugappan Muthukumar, Member Narayanan Menon, Department Chair Department of Physics ACKNOWLEDGMENTS First and foremost I would like to express my sincere gratitude to my supervisors Prof. Nikolay Prokof'ev and Prof. Boris Svistunov for the continuous support of my Ph.D study and related research, for their patience, motivation, intensive discussion, and immense knowl- edge. Their guidance helped me in all the time of research and writing of this thesis. I want to acknowledge Prof. Youjin Deng, who is my former Ph.D advisor at University of Science and Technology of China. I benefit a lot from his support and guidance during my Ph.D study. I also want to acknowledge Prof. Anatoly Kuklov and Prof. Lode Pollet, who supported my visit to their groups and collaborated with me for a long time. The quantum critical dynamics studies in this dissertation would not have been possible without Longxiang Liu, Youjing Deng, Manuel Endres, Lode Pollet and Nikolay Prokof'ev. In these projects, Longxiang carried out a substantial part of the simulations and helped to write the papers. Youjin, Manuel, Lode and Nikolay all made significant contributions. In the quantum critical impurity studies, Yuan Huang, Youjin Deng, Nikolay Prokof'ev and Boris Svistunov contribute a great amount of ideas, simulations and writings. These projects can not be done without their collaborations. During my Ph.D. studies, I talked to many great physicists from different fields. The inspiring discussions with them really opened my mind so I want to thank all these great minds. In particular, I want to thank Subir Sachdev, Immanuel Bloch, Markus Greiner, Qimiao Si, Daniel Podolsky, Andrey Mishchenko, Felix Werner, William Witczak-Krempa, Snir Gazit, Erik Sørensen, Ajay Singh, Ippei Danshita, Takeshi Fukuhara, Yoshiro Takahashi. I benefit a lot from the discussions with them. iv The members of our Theoretical Quantum Fluids Group have been a great source of friendship as well as good advice and collaboration. I especially want to thank Zhiyuan Yao, Yuan Huang, Olga Goulko, Johan Carlstr¨omfor enjoyable time with me. I would like to thank the rest of my thesis committee: Prof. Jonathan Machta, and Prof. Murugappan Muthukumar for their insightful comments and hard questions which incented me to widen my research from various perspectives. Last but not the least, I would like to thank my beloved wife Yuan for \suffering” together with me during my whole Ph.D studies. Yuan is behind all of my achievements in this thesis. Thank you! v ABSTRACT EMERGENT PHENOMENA IN QUANTUM CRITICAL SYSTEMS MAY 2018 KUN CHEN B.Sc., UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA Ph.D., UNIVERSITY OF MASSACHUSETTS AMHERST Directed by: Professor Nikolay Prokof'ev and Professor Boris Svistunov A quantum critical point (QCP) is a point in the phase diagram of quantum matter where a continuous phase transition takes place at zero temperature. Low-dimensional quantum critical systems are strongly correlated, therefore hosting nontrivial emergent phenomena. In this thesis, we first address two decades-old problems on quantum critical dynamics. We then reveal two novel emergent phenomena of quantum critical impurity problems. In the first part of the thesis, we address the linear response dynamics of the (2 + 1)- dimensional O(2) quantum critical universality class, which can be realized in the ultracold bosonic system near the superfluid (SF) to Mott insulator (MI) transition in two dimensions. The first problem we address is about the fate of the massive Goldstone (Higgs) mode in the two-dimensional relativistic theory. Using large-scale Monte Carlo simulations and numerical analytical continuation, we obtain universal spectral functions in SF, MI and normal quantum critical liquid phases and reveal that they all have a relatively sharp resonant vi peak before saturating to the critical plateau behavior at higher frequencies. The universal resonance peak in SF reveals a critically-defined massive Goldstone boson, while the peaks in the last two phases are beyond the predictions of previous theories. The second problem we address is to controllably calculate one of the most fundamental transport properties|optical conductivity|in the quantum critical region. We precisely determine the conductivity on the quantum critical plateau, σ( ) = 0:359(4)σQ with σQ the conductivity quantum. For 1 the first time, the shape of the σ(i!n) σ( ) function in the Matsubara representation − 1 is accurate enough to compare a holographic gauge-gravity duality theory for transport properties [Myers, Sachdev, and Singh, Phys. Rev. D 83, 066017 (2011)] to the reality. We find that the theory|in the original form|can not account for our data, thereby inspiring the theorists to modify the corresponding holographic theory. The second part of this thesis discusses two exotic impurity states hosted by quantum crit- ical environments. The first one is the halon, a novel critical state of an impurity in O(N 2) ≥ quantum critical environment. We find that varying the impurity-environment interaction leads to a boundary quantum critical point (BQCP) between two competing ground states with charges differing by 1. In the vicinity of the BQCP, the halon phenomenon emerges. ± The hallmark of the halon physics is that a well-defined integer charge carried by the im- purity gets fractionalized into two parts: a microscopic core with half-integer charge and a critically large halo carrying a complementary charge of 1=2. The halon can be generalized ± to other incompressible quantum-critical environments with particle-hole symmetry. The second novel phenomenon we reveal is termed "trapping collapse". We address a simple fundamental question of how many repulsively interacting bosons can be localized by a trapping potential. We find that under rather generic conditions, for both weakly and strongly repulsive particles, in two and three dimensions|but not in one-dimension!|this potential well can trap infinitely many bosons. Even hard-core repulsive interactions do not vii prevent this effect from taking place. Our results imply that an attractive impurity in a generic SF-MI quantum critical environment can carry divergent charges. viii TABLE OF CONTENTS Page ACKNOWLEDGMENTS ................................................... iv ABSTRACT ................................................................ vi LIST OF FIGURES........................................................ xii CHAPTER INTRODUCTION ........................................................... 1 1. MICROSCOPIC MODELS AND NUMERICAL METHODS .............. 8 Part I Quantum Critical Dynamics 2. FATE OF THE MASSIVE GOLDSTONE MODE NEAR QUANTUM CRITICALITY ...................................................... 13 2.1 Introduction . 13 2.2 The Method . 17 2.3 Numerical Results . 20 2.4 Conclusions . 24 3. OBSERVING THE MASSIVE GOLDSTONE MODE IN ULTRACOLD ATOMS IN OPTICAL LATTICES .................... 26 3.1 Introduction . 26 3.2 The model . 29 3.3 Spectral density measurement: Theory . 30 3.4 Measuring the spectral density in simulations . 33 3.5 On the experimental observation of the massive Goldstone peak . 36 3.6 Conclusions . 39 ix 4. QUANTUM CRITICAL TRANSPORT ................................. 42 4.1 Introduction . 42 4.2 Models............................................................... 44 4.3 Methods . 44 4.3.1 Finite system size extrapolation . 46 4.3.2 Zero temperature extrapolation . 49 4.4 Extreme sensitivity to the QCP position . 50 4.5 J-current model . 51 4.6 Quantum model . 53 4.7 Experimental verification . 55 4.8 Conlusions . 55 Part II Impurity Problems at Quantum Criticality 5. THE NOTION OF THE QUASIPARTICLE CHARGE .................. 58 5.1 Introduction . 58 5.2 Effect of the environment on the impurity charge: Possible scenarios . 61 5.3 Absence of charge quantization for a static impurity in a charge-compressible environment . 65 6. THE HALON: A QUASIPARTICLE FEATURING CRITICAL CHARGE FRACTIONALIZATION .................................. 68 6.1
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