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More information about this series at http://www.springer.com/series/8790 Adam Iaizzi Magnetic Field Effects in Low-Dimensional Quantum Magnets Doctoral Thesis accepted by Boston University, MA, USA 123 Adam Iaizzi Department of Physics National Taiwan University Taipei, Taiwan ISSN 2190-5053 ISSN 2190-5061 (electronic) Springer Theses ISBN 978-3-030-01802-3 ISBN 978-3-030-01803-0 (eBook) https://doi.org/10.1007/978-3-030-01803-0 Library of Congress Control Number: 2018960268 © Springer Nature Switzerland AG 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. 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It’s a way of thinking, a way of skeptically interrogating the universe with a fine understanding of human fallibility. If we are not able to ask skeptical questions, to interrogate those who tell us that something is true, to be skeptical of those in authority, then we’re up for grabs for the next charlatan, political or religious, who comes ambling along. Carl Sagan Timestamp 3:52 from this May 1996 interview with Charlie Rose https://charlierose.com/videos/9094. This thesis is dedicated to: Dr. Arianna Wright Rosenbluth The author of the first-ever implementation of Metropolis Algorithm Monte Carlo Supervisor’s Foreword A goal of computational materials science is to reproduce or predict physical properties as precisely as possible. However, in many cases it is impossible to include all interactions and quantum mechanical effects and still be able to carry out reliable calculations. From the standpoint of fundamental condensed matter physics, many details pertaining to specific materials are mere distractions, and one would instead like to construct the simplest possible models to describe physical phenomena of interest. A successful approach to studying quantum phases of matter and the phase transitions taking place between them is to construct field theories that are only constrained by relevant symmetries. If a given field theory can be solved, or treated with sufficiently good approximations, a wealth of information can be extracted on possible ground states and their excitations. However, solving quantum field theories is also no easy task, and it is not always possible to draw definite conclusions. Another approach is to formulate simplified lattice models inspired by real materials but not using the exact lattice structure and interactions of any specific material. If successful, these models (Hamiltonians) host the low-energy quantum states of interest, and they can sometimes be characterized in an approximation- free manner by numerical simulations. Since the low-energy physical properties of the lattice models should correspond exactly to some quantum field theory, direct connections can be made with theory as well as with experiments probing generic features. Even simplified lattice models are not automatically amenable to efficient numerical simulations. In particular, Monte Carlo simulations of quantum systems are often hampered by mixed signs of the weight function characterizing the configuration space—the infamous sign problem. Models tailored both from the perspective of interesting physics and computational tractability have been termed “designer Hamiltonians”1 and are playing an increasingly important role in quantum many-body physics. Adam Iaizzi’s thesis is devoted to constructing and studying a class of designer Hamiltonians in the field of quantum magnetism. 1R.K. Kaul, R.G. Melko, and A.W. Sandvik, Annu. Rev. Condens. Matter Phys. 4, 179 (2013). ix x Supervisor’s Foreword The work starts from the J -Q family of S = 1/2 quantum spin models on the 2D square lattice.2 These models contain the common Heisenberg exchange interaction of strength J and a multi-spin interaction of strength Q. When Q = 0 the system has an antiferromagnetic ground state. The Q interaction favors the formation of spatially correlated singlets, and, above a critical value of Q/J ,a spontaneously dimerized ground state. The transition separating the antiferromag- netic and dimerized phases is an intriguing “deconfined” quantum critical point, at which the excitations become fractionalized and exhibit unusual behaviors normally not found in 2D antiferromagnets. The J -Q model has been extensively studied in this context. Iaizzi expands on the J -Q model in both one and two dimensions by adding an external magnetic field, thereby accessing a broader range of physical phenomena. The quantum Monte Carlo algorithms, which can be adapted to many other models as well, are described in detail in this thesis and many new results are presented. Even in the conventional (Q = 0) Heisenberg model the field effects have not previously been fully characterized; the Q interactions introduce further rich behaviors that mimic some of the properties expected in traditional frustrated quantum magnets (which are difficult to study because of the aforementioned sign problems). Iaizzi studies the experimentally important transition into a fully polar- ized ferromagnetic state and discovers a case of metamagnetism—a discontinuous jump in the magnetization versus field above a threshold value of Q/J .This threshold value itself corresponds to a kind of quantum criticality, which is here characterized quantitatively, including an exact analytical solution in one dimension. A previous theory for the continuous transition into full polarization for lower Q/J is tested in detail in both one and two dimensions. At weaker fields and Q/J close to the deconfined critical point, it is interesting to study the consequences of the spinons (the putative deconfined excitations) induced by the field in two dimensions. Iaizzi’s work here aims to resolve the thermodynamic behaviors distinguishing spinons from the conventional magnon (spin waves) excitations. In addition to solving some key problems, the thesis points to intriguing open questions that could be addressed in future work. Professor of Physics Anders W. Sandvik Boston University, Boston, MA, USA 2A.W. Sandvik, Phys. Rev. Lett. 98, 227202 (2007). Acknowledgments My work was supported by the NSF under grants No. DMR-1710170 and DMR- 1410126. The collaboration with Kedar Damle at the Tata Institute of Fundamental Research in Mumbai was supported by a travel grant from the APS-IUSSTF Physics PhD Student Visitation Program. My travel for presentations and other collaboration was supported by the