One of the main challenges in experimentally identifying a quantum spin liquid (QSL) state is in understanding the influence of disorder. Chemical and structural imperfections exist in many promising QSL candidate materials, and can lead to a spatially inhomogeneous behaviour that obfuscates the interpretation of sample-averaged measurements. This issue highlights the importance of nuclear magnetic resonance (NMR) which can locally probe the intrinsic spin susceptibility χspin (separate from defect contributions) and low-energy spin fluctuations via the Knight shift K and nuclear spin-lattice relaxation rate 1/T1, respectively. The value of 1/T1 is typically ascertained by fitting the net nuclear magnetization M(tD) with an appropriate decay function. However, the M(tD) measured at a given frequency has contributions from many nuclei, which in a disordered material, can exhibit a broad distribution of 1/T1. Analogous to how variations in local χspin are reflected in the distribution of Knight shifts which make up the inhomogeneously broadened NMR lineshape, the distribution of 1/T1 that make up a single M(tD) curve can represent multiple environments whose local magnetic ground states are qualitatively distinct. We developed a program which computes the inverse Laplace transform (ILT) of our measured M(tD) data, in order to deduce a probability density function P(1/T1) representing the 1/T1 distribution. Our ILT algorithm primarily employs Tikhonov regularization, which iv limits the instability of numerically inverting data with finite noise. This 1/T1 analysis method offers significant advantages over the traditional method of fitting M(tD) against a phenonmenological stretched exponential function, which provides only a crude approximation of the spatial average of the 1/T1 distribution. In contrast, our approach of calculating P(1/T1) using ILT can delineate the behavior of multiple distinct 1/T1 components, and hence preserve vital information on the position-by-position distribution of local spin dynamics. In this thesis, we report on our 7Li NMR measurements of the Kitaev honeycomb iridate Ag3LiIr2O6, our 63Cu nuclear quadrupole resonance (NQR) measurements on the kagome Heisenberg antiferromagnets ZnCu3(OD)6Cl2 (herbertsmithite) and ZnCu3(OD)6FBr (Zn-barlowite), and further measurements of ZnCu3(OD)6FBr with 19F NMR. Using ILT, we provide crucial insight into both the intrinsic and disorder-induced low-energy spin excitations of these materials. Firstly, we elucidate the effect of stacking faults and unwanted Ag inclusion by comparing the 7Li NMR lineshape and P(1/T1Li) of Ag3LiIr2O6 samples with varying levels of disorder. Next, we observe in P(1/T1Cu) a fraction of spin singlets with spatially inhomogeneous energy gaps emerging below ∼30 K within the kagome planes of ZnCu3(OD)6Cl2 and ZnCu3(OD)6FBr. Finally, we develop a novel method using ILT to obtain the two-dimensional correlation map between 19K and 1/T1F at the 19F sites of ZnCu3(OD)6FBr, and evidence the existence of spin-polarized domains emerging near interlayer Cu2+ defects. / Thesis / Doctor of Science (PhD) / A quantum spin liquid (QSL) is an exotic state of matter whose magnetism fundamentally differs from those of ordinary materials. At temperatures near absolute zero, the electron spins which make up an ordinary magnet generally freeze in place, whereas in a QSL, they form a highly-entangled quantum superposition. A theoretically attainable QSL state was famously proposed in 1973 by Philip W. Anderson. Since then, several candidate materials have been discovered, and research on QSLs became a major focus in the field of condensed matter physics. The realization of a QSL is predicted to have applications in quantum computing (by hosting more robust quantum bits), and can help us understand the physics of other quantum materials, such as high-temperature superconductors. In this thesis, we report our experimental findings on the QSL candidates Herbertsmithite, Zn-barlowite, and Ag3LiIr2O6, where we use nuclear magnetic resonance (NMR) spectroscopy to probe the behaviour of their spins. Hindering past attempts to study these materials is the ever-present influence of disorder, such as chemical and structural imperfections. To combat this, we developed a novel technique for acquiring and analyzing NMR data, known as inverse Laplace transform (ILT) 1/T1 analysis, and used it to make unprecedented discoveries about the heterogeneous physics of these disordered materials.

Thesis advisor: Michael J. Graf / Quantum spin liquids (QSL)’s have been one of the most hotly researched areas ofcondensed matter physics for the past decade. Yet, science has yet to unconditionally identify any one system as harboring a QSL state. This is because QSL’s are largely defined as systems whose electronic spins do not undergo a thermodynamic transition as T→0. Quantum spin liquids remain fully paramagnetic, including dynamical spin fluctuations, at T=0. As a result, distinguishing a QSL system from a conventionally disordered system remains an outstanding challenge. If a system spin freezes or magnetically orders, it cannot be a QSL. In this thesis I present published experiments I have performed on QSL candidate materials. By using muon spin rotation (μSR) and AC magnetic susceptibility I have evaluated the ground states of several candidates for the absence of long-range magnetic disorder and low-temperature spin-fluctuations. For the systems which order or spin-freeze, my research provided key knowledge to the field of frustrated magnetism. The systems I studied are as follows: The geometrically frustrated systems NaYbO2 and LiYbO2; the Kitaev honeycomb systems Cu2IrO3 and Ag3LiIr2O6; and the metallic kagome system KV3Sb5. Each of these systems brought new physics to the field of frustrated magnetism. NaYbO2 is a promising QSL candidate. LiYbO2 harbors an usual form of spiral incommensurate order that has a staggered transition. Cu2IrO3 has charge state disorder that results in a magnetically inhonogenious state. Ag3LiIr2O6 illustrates the role structural disorder plays in disguising long-range magnetic order. And finally, KV3Sb5 isn’t conventionally magnetic at all; our measurements ruled out ionic magnetism and uncovered a type-II superconductor. Our measurements on KV3Sb5 stimulated further research into KV3Sb5 and it’s unconventional electronic states. / Thesis (PhD) — Boston College, 2022. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

The overarching theme of this thesis is the question of how constraints influence collective behavior. Constraints are crucial in shaping both static and dynamic properties of systems across diverse areas within condensed matter physics and beyond. For example, the simple geometric constraint that hard particles cannot overlap at high density leads to slow dynamics and jamming in glass formers. Constraints also arise effectively at low temperature as a consequence of strong competing interactions in magnetic materials, where they give rise to emergent gauge theories and unconventional magnetic order. Enforcing constraints artificially in turn can be used to protect otherwise fragile quantum information from external noise. This thesis in particular contains progress on the realization of different unconventional phases of matter in constrained systems. The presentation of individual results is organized by the stage of realization of the respective phase. Novel physical phenomena after conceptualization are often exemplified in simple, heuristic models bearing little resemblance of actual matter, but which are interesting enough to motivate efforts with the final goal of realizing them in some way in the lab. One form of progress is then to devise refined models, which retain a degree of simplification while still realizing the same physics and improving the degree of realism in some direction. Finally, direct efforts in realizing either the original models or some refined version in experiment today are mostly two-fold. One route, having grown in importance rapidly during the last two decades, is via the engineering of artificial systems realizing suitable models. The other, more conventional way is to search for realizations of novel phases in materials. The thesis is divided into three parts, where Part I is devoted to the study of two simple models, while artificial systems and real materials are the subject of Part II and Part III respectively. Below, the content of each part is summarized in more detail. After a general introduction to entropic ordering and slow dynamics we present a family of models devised as a lattice analog of hard spheres. These are often studied to explore whether low-dimensional analogues of mean-field glass- and jamming transitions exist, but also serve as the canonical model systems for slow dynamics in granular materials more generally. Arguably the models in this family do not offer a close resemblance of actual granular materials. However, by studying their behavior far from equilibrium, we observe the onset of slow dynamics and a kinetic arrest for which, importantly, we obtain an essentially complete analytical and numerical understanding. Particularly interesting is the fact that this understanding hinges on the (in-)ability to anneal topological defects in the presence of a hardcore constraints, which resonates with some previous proposals for an understanding of the glass transition. As another example of anomalous dynamics arising in a magnetic system, we also present a detailed study of a two-dimensional fracton spin liquid. The model is an Ising system with an energy function designed to give rise to an emergent higher-rank gauge theory at low energy. We show explicitly that the number of zero-energy states in the model scales exponentially with the system size, establishing a finite residual entropy. A purpose-built cluster Monte-Carlo algorithm makes it possible to study the behavior of the model as a function of temperature. We show evidence for a first order transition from a high-temperature paramagnet to a low-temperature phase where correlations match predictions of a higher-rank coulomb phase. Turning away from heuristic models, the second part of the thesis begins with an introduction to quantum error correction, a scheme where constraints are artificially imposed in a quantum system through measurement and feedback. This is done in order to preserve quantum information in the presence of external noise, and is widely believed to be necessary in order to one day harness the full power of quantum computers. Given a certain error-correcting code as well as a noise model, a particularly interesting quantity is the threshold of the code, that is the critical amount of external noise below which quantum error correction becomes possible. For the toric code under independent bit- and phase-flip noise for example, the threshold is well known to map to the paramagnet to ferromagnet transition of the two-dimensional random-bond Ising model along the Nishimori line. Here, we present the first generalization of this mapping to a family of codes with finite rate, that is a family where the number of encoded logical qubits grows linearly with the number of physical qubits. In particular, we show that the threshold of hyperbolic surface codes maps to a paramagnet to ferromagnet transition in what we call the 'dual'' random-bond Ising model on regular tessellations of compact hyperbolic manifolds. This model is related to the usual random-bond Ising model by the Kramers-Wannier duality but distinct from it even on self-dual tessellations. As a corollary, we clarify long-standing issues regarding self-duality of the Ising model in hyperbolic space. The final part of the thesis is devoted to the study of material candidates of quantum spin ice, a three-dimensional quantum spin liquid. The work presented here was done in close collaboration with experiment and focuses on a particular family of materials called dipolar-octupolar pyrochlores. This family of materials is particularly interesting because they might realize novel exotic quantum states such as octupolar spin liquids, while at the same time being described by a relatively simple model Hamiltonian. This thesis contains a detailed study of ground state selection in dipolar-octupolar pyrochlore magnets and its signatures as observable in neutron scattering. First, we present evidence that the two compounds Ce2Zr2O7 and Ce2Sn2O7 despite their similar chemical composition realize an exotic quantum spin liquid state and an ordered state respectively. Then, we also study the ground-state selection in dipolar-octupolar pyrochlores in a magnetic field. Most importantly, we show that the well-known effective one-dimensional physics -- arising when the field is applied along a certain crystallographic axis -- is expected to be stable at experimentally relevant temperatures. Finally, we make predictions for neutron scattering in the large-field phase and compare these to measurements on Ce2Zr2O7.

Dans la description à basse énergie de systèmes fortement corrélés, les champs de jauge peuvent émerger comme excitations collectives couplées à des quasiparticules fractionalisées. En particulier, certains aimants bidimensionnels dits frustrés sont décrits par un liquide de spin de Dirac comportant une symétrie de jauge U(1) compacte. La description infrarouge est donnée par une théorie conforme des champs, soit l'électrodynamique quantique en 2+1 dimensions avec 2N saveurs de fermions sans masse. Dans les aimants typiques, N=2 ou 4. L'aspect compact du champ de jauge implique également l'existence d'excitations topologiques, soit des instantons créés, dans ce contexte, par des opérateurs monopôles. Cette thèse porte sur les transitions de phase quantiques à partir d'un liquide de spin de Dirac et les propriétés des monopôles aux points critiques correspondants. Ces transitions sont induites en activant diverses interactions de type Gross-Neveu. Dans tous les cas à l'étude, la dimension d'échelle des monopôles est obtenue grâce à la correspondance état-opérateur et à un développement en 1/N. L'accent est d'abord mis sur une transition de confinement-déconfinement vers une phase antiferromagnétique décrite par la condensation d'un monopôle. Une levée de dégénérescence est observée au point critique alors que certaines dimensions d'échelle de monopôles sont réduites par rapport à leur valeur dans le liquide de spin de Dirac. Cette hiérarchie est caractérisée quantitativement en comparant les dimensions d'échelle dans des secteurs distincts du spin magnétique à l'ordre dominant en 1/N, puis qualitativement par une analyse en théorie des représentations. Des exposants critiques pour d'autres observables dans la théorie non compacte sont également obtenus. Enfin, deux transitions vers des liquides de spin topologiques, soit le liquide de spin chiral et le liquide de spin Z2, sont considérées. Les dimensions anormales des monopôles sont obtenues à l'ordre sous-dominant en 1/N. Ces résultats permettent de vérifier une dualité conjecturée avec un modèle bosonique et la valeur d'un coefficient universel pour les théories de jauge U(1) / In strongly correlated systems, gauge fields can emerge as collective excitations coupled to fractionalized quasiparticles. In particular, certain frustrated two-dimensional quantum magnets are described by a Dirac spin liquid which has a U(1) gauge symmetry. The infrared description is given by a conformal field theory, namely quantum electrodynamics in 2+1 dimensions with 2N flavours of massless fermions. In typical magnets, N=2 or 4. The compact aspect of the gauge field also implies the existence of topological excitations corresponding to instantons, which are created by monopole operators in this context. This thesis focuses on quantum phase transitions out of a Dirac spin liquid and the properties of monopoles at the corresponding critical points. These transitions are driven by activating various types of Gross-Neveu interactions. In all the cases studied, the scaling dimension of monopoles are obtained using the state-operator correspondence and a 1/N expansion. The confinement-deconfinement transition to an antiferromagnetic order produced by a monopole condensate is first studied. A degeneracy lifting is observed at the critical point, as certain monopoles have their scaling dimension reduced in comparison with the value in the Dirac spin liquid. This hierarchy is charactized quantitatively by comparing monopole scaling dimensions in distinct magnetic spin sector at leading-order in 1/N, and qualitatively by an analysis in representation theory. Critical exponents of various other operators are obtained in the non-compact model. Transitions to two topological spin liquids, namely a chiral spin liquid and a Z2 spin liquid, are also considered. Anomalous dimensions of monopoles are obtained at sub-leading order in 1/N. These results allow the verification of a conjectured duality with a bosonic model and the value of a universal coefficient in U(1) gauge theories.