This dissertation studies various aspects of quantum magnetic systems, es- pecially responses of these systems to non-equilibrium conditions. Herein, the term "magnetic" refers to quantum spin, whether ordered at low temperatures (as is the case for magnetic insulators) or not (as is true of spin liquids). These systems and their properties are of great theoretical and practical interest, being the basis for emerging technologies such as spintronics devices and topological quantum computers. In this dissertation, two prototypical cases are considered: the physics of magnons, and the physics of quantum spin liquids. In the first case, effects originating from quantum spin waves, or magnons, the low-lying excita- tions of magnetically ordered systems, are studied. In particular, the effects of a particular form of symmetry breaking on a class of thermal magnon responses are derived, and relevance to current experimental studies is discussed. Building on this foundation, an approximation scheme for capturing higher-order magnon effects, including magnon-magnon interactions, is developed. This pushes the magnon formalism into new regimes of validity, opening the door to the study of higher-energy phenomena in magnetically ordered systems.In the case of quantum spin liquids, I focus on non-equilibrium dynamics of the Kitaev honeycomb model. The motivation for this study is highly practical, and rooted in quantum information theory. The Kitaev model is a canonical ex- ample of a system that hosts anyons - particles proposed for use in topological quantum computation due to their inherent stability. The present study asks the question: "how stable is the Kitaev model itself?" I discuss the fidelity of the Kitaev ground state (and other states within the first flux sector) under several noisy disturbances. A universal form for the fidelity is discovered, suggesting a system-independent feature of noise itself. Along the way, mathematical methods for analyzing highly oscillatory integrals are developed and validated.--Author's abstract
This dissertation studies various aspects of quantum magnetic systems, es- pecially responses of these systems to non-equilibrium conditions. Herein, the term "magnetic" refers to quantum spin, whether ordered at low temperatures (as is the case for magnetic insulators) or not (as is true of spin liquids). These systems and their properties are of great theoretical and practical interest, being the basis for emerging technologies such as spintronics devices and topological quantum computers. In this dissertation, two prototypical cases are considered: the physics of magnons, and the physics of quantum spin liquids. In the first case, effects originating from quantum spin waves, or magnons, the low-lying excita- tions of magnetically ordered systems, are studied. In particular, the effects of a particular form of symmetry breaking on a class of thermal magnon responses are derived, and relevance to current experimental studies is discussed. Building on this foundation, an approximation scheme for capturing higher-order magnon effects, including magnon-magnon interactions, is developed. This pushes the magnon formalism into new regimes of validity, opening the door to the study of higher-energy phenomena in magnetically ordered systems.In the case of quantum spin liquids, I focus on non-equilibrium dynamics of the Kitaev honeycomb model. The motivation for this study is highly practical, and rooted in quantum information theory. The Kitaev model is a canonical ex- ample of a system that hosts anyons - particles proposed for use in topological quantum computation due to their inherent stability. The present study asks the question: "how stable is the Kitaev model itself?" I discuss the fidelity of the Kitaev ground state (and other states within the first flux sector) under several noisy disturbances. A universal form for the fidelity is discovered, suggesting a system-independent feature of noise itself. Along the way, mathematical methods for analyzing highly oscillatory integrals are developed and validated.--Author's abstract
This thesis investigates quantum magnetism in two-dimensional synthetic systems, where strong correlations, geometric frustration, and enhanced quantum fluctuations produce unconventional magnetic phases. I focus on two major classes of engineered platforms: moiré materials and quantum simulators, which offer precise control over lattice geometry, interaction strengths, and dynamics, enabling access to regimes beyond conventional condensed-matter approaches. The first project studies moiré magnetism in strained multilayers of CrBr₃, where strain generates a spatial modulation of the interlayer exchange alternating between ferromagnetic and antiferromagnetic. With S=3/2 moments, the system admits a classical bilayer description with competing interactions. I develop a theoretical framework capturing the resulting non-collinear orders and reproducing experimental signatures, demonstrating how moiré engineering stabilizes non-trivial magnetic textures. The second project examines quantum magnetism in a WSe₂/WS₂ heterobilayer at three-quarters filling, where electrons form an effective kagome lattice. From the underlying Hubbard model, I derive a frustrated Heisenberg Hamiltonian with competing exchanges. Using Schwinger-boson mean-field theory, I map a phase diagram of non-collinear orders and spin-liquid phases. For realistic parameters, the ground state is a chiral spin liquid, highlighting transition-metal dichalcogenide moiré materials as platforms for topological and strongly correlated magnetism. The third project investigates quantum phase-transition dynamics with superconducting circuit quantum simulators, focusing on Hamiltonian ramps in the 2D XY model. An analogue-digital protocol drives the system from a gapped staggered state to the gapless XY phase. Analysis of correlations reveals scaling of the correlation length with ramp rate, broadly consistent with Kibble–Zurek predictions, with deviations reflecting finite-size, dimensionality, and experimental constraints. The fourth project develops a Holstein–Primakoff spin-wave description for the same XY ramps. Adapting the quantization axis to the instantaneous magnetization, this solvable quadratic theory provides magnon dispersions, time- and space-dependent correlations, and single-magnon dynamics, including decay and scattering. This framework offers a detailed picture of non-equilibrium quasiparticle behavior in a 2D magnet under time-dependent fields. Together, these projects show how moiré materials and quantum simulators enable controlled studies of frustrated and strongly correlated magnetism in two dimensions. By combining analytical modeling with experimentally relevant conditions, this thesis advances understanding of how frustration, topology, and non-equilibrium dynamics shape quantum magnetic phenomena in low-dimensional systems.
Quantum spin liquids, systems in which quantum fluctuations prevent the magnetic ordering of the spin degrees of freedom down to zero temperature, have been the source of much recent theoretical and experimental interest. These systems are characterised by their long ranged entangled states, preserve symmetries down to zero Kelvin, and have been shown to exhibit fascinating properties such as a topological ground state degeneracy and fractionalised spin excitations. In this thesis, we study several of these phases. The first, Kitaev spin liquids, appear in strongly spin-orbit coupled systems, where the SU(2) spin symmetry is broken. Within our mean field approach, we study the quantum phase transition from the gapless Z 2 spin liquid to a magnetically ordered phase within the Heisenberg-Kitaev model. Beyond the mean field theory, we argue that the gauge structure of the spin liquid plays a crucial role in this transition, leading to a confinement of spinons and the generation of magnetic order. We also discuss the three-dimensional iridate compounds, where the Kitaev spin liquid phase has topologically protected bulk and surface excitations. We next discuss spin liquids appearing on the geometrically frustrated kagome lattice. First, we consider non-Kramers spin liquids, in which the spin structure of the theory is protected by lattice, rather than time-reversal, symmetry. As a result, more phases are allowed, which have different properties than those which transform as Kramers doublets. In addition, these may have positive experimental signatures in the Raman scattering intensity, offering a clear path to detect such a state. Finally, we examine possible spin liquid phases on a breathing kagome lattice, where we find a stable Z2 spin liquid to be the ground state. This may help to guide future numerical studies of the kagome lattice Heisenberg model, and may also be relevant to DQVOF, a recently discovered spin liquid candidate compound.
Magnetic frustrations are the fundamental cause of many interesting phenomena in materials that have been intensely studied since the middle of the 20th century. Magnetic systems with competing interactions, ranging from insulating antiferromagnets to arrays of superconducting qubits, exhibit nontrivial quantum e ects that arise from the need to satisfy a jagged free energy landscape. The search for and characterization of quantum spin liquids, nontrivial topological phases, and quantum phase transitions is conducted through investigations of such frustrated models. Within the large umbrella of frustrated magnetism I have studied some speci c models with the purpose of answering the following questions: (1) What are the interesting phases and less-interesting phases, and how do they fall in the phase diagram relative to one another? (2) What properties do the phases have, and how can we characterize what happens when one phase transitions to another? Armed with the answers to these questions, researchers can further explore these interesting phenomena and apply them towards new materials and devices. In this thesis, I rst develop a computational methodology for studying both classical and quantum spin models using various forms of Monte Carlo simulation. I use classical Monte Carlo to study highly-frustrated models of Ising spins both at nite temperatures and in the T = 0 limit, to map the phase diagram and determine the universality class of phase transitions. Using these methods, I show that in a dissipative chain of qubits, bath-induced qubit-qubit interactions lead to collective decoherence above a critical dissipation strength. This causes the qubits to lose all stored information and become fully correlated with one another, an e ect that one would need to mitigate in order to perform quantum computation. In another study, I show that in antiferromagnetic insulators with anisotropic interactions, frustration can cause an intermediate paramagnetic phase with oblong \droplets" of correlated spins. This phenomenon is quite general and the presence of these droplets can help explain experimental signatures that occur at unexpected temperatures in such materials. In addition to the classical simulations, I develop a variational Monte Carlo (VMC) technique to search for ground states in Heisenberg-type models, speci cally for spins S = 1. The case of S = 1 is more complicated than the case for S = 1=2 due to an additional local degree of freedom, which has interesting implications for the possible states that can be realized. Using semiclassical energy minimization as well as VMC, I show that spin S = 1 diamond-lattice antiferromagnets experience higher-order spinspin interactions that destroy previously theorized liquid-like spiral spin orderings. However, the presence of these higher-order interactions can also potentially allow other phases such as quantum spin liquids and topological paramagnets. Such results can provide an avenue for explaining anomalous phenomena like low-temperature paramagnetism in future experimental materials.
Frustrated magnetism provides a rich platform for realizing exotic quantum phases in condensed matter systems. Among these, quantum spin liquids (QSLs) are a particularly intriguing class of states that exhibit no magnetic ordering and preserve all symmetries down to zero temperature. Just as conventional magnets can be thought of as spin crystals,QSLs represent their liquid analogs. This thesis explores two broad types of QSLs in two-dimensional magnets, with a focus on their dynamic properties and the nature of transitions from conventional magnetic states into QSL phases. QSLs are topological phases that host fractionalized excitations known as spinons. In these states, mobile spinons are coupled to an emergent gauge field, forming a highly entangled phase of matter. The first part of this thesis focuses on Dirac spin liquids (DSLs), a class of QSLs where spinons exhibit a gapless Dirac dispersion. To study the dynamicsof these spin liquids beyond leading-order mean-field theory, we develop a novel large-N fermionic limit of gapless spinons. In this limit, all gauge excitations are suppressed, and the leading-order corrections instead arise from order parameter fluctuations, which may condense and drive transitions into symmetry-broken phases from the parent DSL. Incorporating random phase approximation (RPA) corrections to the spin susceptibility, we find that sharp, spin-wave–like modes are recovered in the excitation spectrum. This methodology successfully captures characteristic features of the dynamics near phase transitions and in weakly symmetry-broken phases proximate to a DSL. We apply this approach to microscopic models, including the J1-J2 XXZ model on the triangular lattice and the J1-J3 XXZ model on the honeycomb lattice. These models closely represent a wide range of frustrated materials, such as triangular and honeycomb cobaltates and triangular ytterbium compounds. Our theoretical predictions show excellent agreement with experimentally measured inelastic neutron scattering spectra from these materials. Gapless spinons can also sometimes become gapped through chiral symmetry breaking, leading to the formation of a chiral spin liquid (CSL). The CSL is an archetypal bosonic realization of a fractional quantum Hall (FQH) state at half-filling, and has been proposed as a time-reversal–breaking ground state in a variety of frustrated spin models. The second part of this thesis addresses the intriguing possibility of realizing a CSL through the "melting" of a chiral spin crystal—a conventional magnet with non-coplanar ordering. Such a transition offers a physically appealing analogue to the melting of a Wigner crystal into a fermionic FQH liquid. Focusing on the kagome lattice, where chiral interactions are knownto stabilize a CSL ground state, we study the effects of additional long-range Heisenberg interactions and demonstrate a phase transition into a non-coplanar octahedral magnetic order. To describe the universal class of transition between a CSL and a non-coplanar anti-ferromagnetic order, we then develop a novel Chern-Simons–matter field theory framework, constrained by symmetry principles and symmetry fractionalization patterns. This thesis thus provides new insights into the dynamical signatures and phase transitions of quantum spin liquids, offering a bridge between theoretical models and experimental observations in frustrated magnetic systems.
When sizable quantum fluctuations and strong frustration mechanisms act in concert to repel the formation of conventional long-range order in quantum magnets, they can make way for massively entangled spin liquid phases which may imbue the material with extraordinary properties. \nThe search for such curious phases of matter has proceeded for several decades, gaining extra momentum some fifteen years ago when Kitaev proposed an analytically solvable model for a quantum spin liquid with anyonic excitations on the basis of realistic microscopic spin exchange terms [Kitaev, Annals of Physics 321, 2 (2006)]. Attempts to identify different models or materials which harbor quantum spin liquid ground states have kept researchers -- experimentalists and theorists alike -- in suspense ever since. However, the simulation of quantum many-body systems poses a serious challenge even to modern numerical techniques, particularly in the case of frustrated quantum magnetism in three spatial dimensions. Such models evade tractability by many established approaches, leaving a methodological void. \n \nIn this thesis, we report on recent progress in cutting-edge implementations of the pseudo-fermion functional renormalization group (pf-FRG), which has originally been proposed by Reuther and Wölfle in the context of two-dimensional frustrated quantum magnetism with highly symmetric spin interactions [Reuther and Wölfle, Phys. Rev. B 81, 144410 (2010)]. Reflecting the growing interest in models with SU(2) symmetry-breaking spin exchange terms that has followed the unearthing of Kitaev's honeycomb model, we present a generalized implementation of the pf-FRG which is suited to numerically simulate arbitrary microscopic models with diagonal or off-diagonal two-spin interactions, even in three-dimensional frustrated quantum magnets. We provide insight into the inner workings of the method which has emerged over the course of the last couple of years, arguing that the pf-FRG formalism simultaneously combines aspects of a large-S expansion as well as a large-N expansion on equal footing, thus being able to resolve the subtle interplay between magnetic ordering tendencies and disruptive quantum fluctuations. \n \nMoreover, on a case by case basis we explore the stability of quantum spin liquids in paradigmatic models of frustrated quantum magnetism and elucidate the joint action of geometric frustration, exchange frustration, and quantum fluctuations to inhibit the formation of magnetic long-range order. Examples include: (i) a Heisenberg spin model on the three-dimensional diamond lattice where geometric frustration arises from antiferromagnetic next-nearest neighbor interactions. The additional competition with nearest neighbor interactions leads to an unusually large ground state degeneracy already on classical level. The quantum-to-classical transition is studied by systematically varying the spin length and the different roles of quantum fluctuations and thermal fluctuations are discussed. The theory is applied to interpret experiments on the spin-liquid candidate NiRh2O4; (ii) a Heisenberg antiferromagnet on the face centered cubic lattice which is augmented by competing bond-directional interactions, evolving around the concurrent manifestation of geometric frustration and exchange frustration. A situation is identified where both mechanisms collude to give rise to an unusually large degree of frustration over a wide parameter regime. We discuss related experimental findings on the highly frustrated iridate compound Ba2CeIrO6; (iii) a Heisenberg antiferromagnet on the kagome lattice with additional Dzyaloshinskii-Moriya interactions. The robustness of the unperturbed kagome antiferromagnet's spin liquid ground state against low-symmetry Dzyaloshinskii-Moriya interactions is investigated. Implications for the spin-liquid candidate herbertsmithite are discussed.
This dissertation establishes and investigates new phenomena in diverse interacting many-body quantum systems guided by three distinct, but complementary, themes: (i) symmetry and topology, (ii) localization, and (iii) non-Fermi liquids. The first theme concerns how the interplay of symmetry and topology can offer robust protection for a many-body system. We investigate low-dimensional quantum fermionic models from a general structural perspective. These phases can exhibit fractionalized Majorana zero-energy modes on their boundary. We devise experimentally relevant nonlocal measurements that can be used to detect these topological phases. While our primary focus is on quantum systems, topologically protected behavior can arise in classical mechanical models as well. We extend a recent connection between the topological band theory of electrons and classical physics by proposing a mechanical analogue of a topological nodal semimetal.The second theme concerns that of many-body localization. We demonstrate that the combination of localization, symmetry, and topology can have radical consequences for quantum systems at high energies, such as the existence of protected gapless boundary modes. We show that, even at these high energies, quantum information can be preserved, and quantum coherence recovered. Quantum coherent dynamics in this regime is unexpected and of great interest for quantum computation.The third direction in our study of interacting many-body systems concerns non-Fermi liquids. We construct a non-Fermi liquid by bringing together a spin-orbit coupled Fermi surface and fluctuating magnetic order. Using newly developed analytic tools for strongly coupled systems, we demonstrate the stability of the non-Fermi liquid to ordering. This identifies an experimentally accessible candidate for exploring physics that lies beyond Fermi liquid theory.