University of Kentucky UKnowledge Theses and Dissertations--Physics and Astronomy Physics and Astronomy 2020 Quantum Phases and Phase Transitions in Designer Spin Models Nisheeta Desai University of Kentucky, [email protected] Author ORCID Identifier: https://orcid.org/0000-0001-9647-4945 Digital Object Identifier: https://doi.org/10.13023/etd.2020.283 Right click to open a feedback form in a new tab to let us know how this document benefits ou.y Recommended Citation Desai, Nisheeta, "Quantum Phases and Phase Transitions in Designer Spin Models" (2020). Theses and Dissertations--Physics and Astronomy. 71. https://uknowledge.uky.edu/physastron_etds/71 This Doctoral Dissertation is brought to you for free and open access by the Physics and Astronomy at UKnowledge. It has been accepted for inclusion in Theses and Dissertations--Physics and Astronomy by an authorized administrator of UKnowledge. For more information, please contact [email protected]. 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Nisheeta Desai, Student Dr. Ribhu Kaul, Major Professor Dr. Christopher Crawford, Director of Graduate Studies QUANTUM PHASES AND PHASE TRANSITIONS IN DESIGNER SPIN MODELS DISSERTATION A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the College of Arts and Sciences at the University of Kentucky By Nisheeta Desai Lexington, Kentucky Director: Dr. Ribhu Kaul, Professor of Physics Lexington, Kentucky 2020 Copyright c Nisheeta Desai 2020 https://orcid.org/0000-0001-9647-4945 ABSTRACT OF DISSERTATION QUANTUM PHASES AND PHASE TRANSITIONS IN DESIGNER SPIN MODELS This work focuses on numerical studies of quantum spin systems. These simple models are known to exhibit a variety of phases, some of which have no classical counterpart. Phase transitions between them are driven by quantum fluctuations and the uncon- ventional nature of some such transitions make them a fascinating avenue of study. Quantum Monte Carlo (QMC) is an indispensable tool in the study of these phases and phase transitions in two and higher dimensions. Nevertheless, we are limited by our inability to simulate models that suffer from the infamous sign problem. While 1 the case of S = 2 has been studied extensively due to availability of sign problem free models, not much progress has been made for higher S. In a first part of this dissertation, a systematic procedure to write down a large family of \designer hamil- tonians", i.e. models constructed to be free from the sign problem (\de-signed"), for arbitrary spin-S is given. Three applications of this procedure are also presented. As a first application, a S = 1 interaction is constructed on the square lattice realizing a novel \Haldane Nematic (HN)" phase that breaks the lattice rotational symme- try while preserving lattice translational symmetry and spin rotational symmetry. By supplementing our model with a two-spin Heisenberg interaction, a study of the transition between N´eeland HN phase is presented, which we find to be of first order. In a second application, the N´eelto four-fold columnar valence bond solid (cVBS) phase transition in a sign free S = 1 square lattice model is studied. Our simulations provide unambiguous evidence for a direct conventional first-order quantum phase 1 transition demonstrating a sharp contrast with the S = 2 case, where this transition is a prototypical example of an unconventional continuous transition. In our third application, all possible sign-free two-site spin-S interactions are constructed and the phases that are realized by these new nearest neighbour models are investigated on the square lattice. In a second part, the superfluid-VBS quantum phase transition is studied in a spin model in presence of easy plane anisotropy, i.e. spins preferentially align in a plane. The model studied is an interpolation of two models: (a) a rotationally symmetric model that appears to host a continuous transition even on the biggest lattices stud- ied (b) the other is an easy plane version of the aforementioned model that clearly shows a first order transition even on relatively small lattices. In our simulations, the nature of the transition was found to be first order in the presence of an easy plane anisotropy, indicating the superfluid-VBS transition in the two-component easy plane model is generically discontinuous. In a third part, we study the SU(N) generalization of the Heisenberg antiferro- magnet on the BCC lattice. Our numerical studies of the model show that magnetic order present for N = 2 is destroyed for N > 15 and valence bond solid order is observed for N 17. The nature of the phase at N = 16 and the nature of the phase transition between≥ different phases is investigated. KEYWORDS: Quantum Magnetism, Quantum Phase Transitions, Quantum Monte Carlo, Heisenberg Model, Spin Liquids Nisheeta Desai June 11, 2020 QUANTUM PHASES AND PHASE TRANSITIONS IN DESIGNER SPIN MODELS By Nisheeta Desai Ribhu Kaul Director of Dissertation Christopher Crawford Director of Dissertation June 11, 2020 ACKNOWLEDGMENTS I am grateful to the Department of Physics & Astronomy at the University of Ken- tucky for providing a pleasant and amicable environment essential for a graduate student to thrive. I would like to express a special thanks to the condensed matter theory group here for making the environment conducive for learning and research. I am thankful to Prof Ganpathy Murthy for discussions, guidance and for pushing all students to meet incredibly high standards and to Prof Joseph Straley for his warm and constructive feedback on all my talks. I am especially grateful to my PhD advisor Prof Ribhu Kaul for giving me the opportunity to work in this field, for investing a generous amount of time and effort to teach, discuss and provide valuable advice and for providing constant motivation, inspiration and encouragement. I would also like to thank Prof A. W. Sandvik for helpful discussions on chapter 5. I am very grateful to my undergraduate advisor Prof Kedar Damle in TIFR Mumbai for introducing me to this field of research and for suggesting to apply to the graduate program at UK. I would also like to thank Prof Sumit Das, Prof Chad Risko, Prof Joseph Straley and Prof David Herrin for agreeing to be on my defense committee. I am very thankful to Dr Jonathan D'Emidio for being an inspiring, knowledgeable and a very approachable senior graduate student during my initial stages of research. I have also greatly benefited from discussions with all my fellow graduate students in the condensed matter theory group. I would like to thank my husband and collaborator, Sumiran Pujari, for always being available to discuss and for his undying contagious enthusiasm for physics and also my parents for their moral support. I would like to acknowledge financial support from NSF DMR-1611161 and Keith B. MacAdam Graduate Excellence Fellowship. The numerical results were produced on SDSC comet cluster through the NSF supported XSEDE award TG-DMR140061 as well as the DLX cluster at UK and the Art & sciences computer cluster Holly. iii TABLE OF CONTENTS Acknowledgments . iii List of Tables . vi List of Figures . vii Chapter 1 Introduction . 1 1.1 Introduction to Spin Models . 3 1.2 Quantum phases and phase transitions . 7 1.3 Quantum Monte Carlo and designer hamiltonians . 14 1.4 Outline of Dissertation . 23 Chapter 2 Spin-S designer Hamiltonians and square lattice S = 1 Haldane Nematic . 25 2.1 Introduction . 25 2.2 Designer Models in \Mini-Spin" Representation . 26 2.3 Haldane Nematic . 30 2.4 Conclusions . 35 Chapter 3 First-order N´eel-cVBStransition in a model square lattice S = 1 antiferromagnet . 37 3.1 Introduction . 37 3.2 Model . 39 3.3 Numerical Results . 42 3.4 Conclusions . 43 Chapter 4 Two site designer spin-S interactions . 45 4.1 Introduction . 45 4.2 Models . 47 4.3 Results of numerical simulations . 50 4.4 Conclusion . 50 Chapter 5 First order phase transitions in the square lattice \easy-plane" J-Q model . 51 5.1 Introduction . 51 5.2 The Model . 53 5.3 Numerical Simulations . 54 5.4 Conclusions . 61 Chapter 6 Quantum phases of SU(N) spins on a BCC lattice . 62 6.1 Introduction . 62 iv 6.2 Model . 64 6.3 Analytic results .