Thesis (Ph.D.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / Quantum spin models are useful in many areas of physics, such as strongly correlated materials and quantum phase transitions, or, generally, quantum many-body systems. Most of the models of interest are not analytically solvable. Therefore they are often investigated using computational methods. However, spin models with frustrated interactions are not easily simulated numerically with existing methods, and more effective algorithms are needed. In this thesis, I will cover two areas of quantum spin research: 1. studies of several quantum spin models and 2. development of more efficient computational methods. The discussion of the computational methods and new algorithms is integrated with the physical properties of the models and new results obtained. I study the frustrated S=1/2 J1-J2 model Heisenberg model, the J-Q model, the Ising model with a transverse magnetic field, and a two-orbital spin model describing the magnetic properties of iron pnictides. I will discuss several computational algorithms, including a cluster variational method using mean-field boundary conditions, variational quantum Monte Carlo simulation with clusters-based wave functions, as well as a method I call "optilization" -- an algorithm constructed in order to accelerate the process of optimization with a large number of parameters. I apply it to matrix product states. / 2031-01-02

Quantum phenomena in high-Tc superconductors and dimerized quantum Heisenberg antiferromagnets are studied analytically in this thesis. The implications of the Fermi surface consisting of the disjoint pieces, observed in cuprate superconductors, are considered. It is demonstrated that in this case the g-wave superconducting pairing is closely related to d-wave pairing. The superconductivity in this system can be described in terms of two almost degenerate superconducting condensates. As a result a new spatial scale lg, much larger than the superconducting correlation length x, arises and a new collective excitation corresponding to the relative phase oscillation between condensates, the phason, should exist. The Josephson tunneling for such a two-component system has very special properties. It is shown that the presence of g-wave pairing does not contradict the existing SQUID experimental data on tunneling in the ab-plane. Possible ways to experimentally reveal the g-wave component and the phason in a single tunnel junction, as well as in SQUID experiments, are discussed. The dimerized quantum spin models studied in this thesis include double-layer and alternating chain Heisenberg antiferromagnets. To account for strong correlations between the S=1 elementary excitations (triplets) in the dimerized phase; the analytic Brueckner diagram approach based on a description of the excitations as triplets above a strong-coupling singlet ground state; has been applied. The quasiparticle spectrum is calculated by treating the excitations as a dilute Bose gas with infinite on-site repulsion. Analytical calculations of physical observables are in excellent agreement with numerical data.Results obtained for double layer antiferromagnet near the (zero temperature) quantum critical point coincide with those previously obtained within the nonlinear s model approach Additional singlet (S=0) and triplet (S=1) modes are found as two-particle bound states of the elementary triplets in the Heisenberg chain with frustration.

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The open spin-1/2 XXZ quantum spin chain with general integrable boundary terms is a fundamental integrable model. Finding a Bethe Ansatz solution for this model has been a subject of intensive research for many years. Such solutions for other simpler spin chain models have been shown to be essential for calculating various physical quantities, e.g., spectrum, scattering amplitudes, finite size corrections, anomalous dimensions of certain field operators in gauge field theories, etc. The first part of this dissertation focuses on Bethe Ansatz solutions for open spin chains with nondiagonal boundary terms. We present such solutions for some special cases where the Hamiltonians contain two free boundary parameters. The functional relation approach is utilized to solve the models at roots of unity, i.e., for bulk anisotropy values eta = i pi/(p+1) where p is a positive integer. This approach is then used to solve open spin chain with the most general integrable boundary terms with six boundary parameters, also at roots of unity, with no constraint among the boundary parameters. The second part of the dissertation is entirely on applications of the newly obtained Bethe Ansatz solutions. We first analyze the ground state and compute the boundary energy (order 1 correction) for all the cases mentioned above. We extend the analysis to study certain excited states for the two-parameter case. We investigate low-lying excited states with one hole and compute the corresponding Casimir energy (order 1/N correction) and conformal dimensions for these states. These results are later generalized to many-hole states. Finally, we compute the boundary S-matrix for one-hole excitations and show that the scattering amplitudes found correspond to the well known results of Ghoshal and Zamolodchikov for the boundary sine-Gordon model provided certain identifications between the lattice parameters (from the spin chain Hamiltonian) and infrared (IR) parameters (from the boundary sine-Gordon S-matrix) are made.

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.

This dissertation deals with the dynamics of interacting quantum and classical spin models and the question of whether and to which degree the dynamics of these models agree with each other. For this purpose, XXZ models are studied on different lattice geometries of finite size, ranging from one-dimensional chains and quasi-one-dimensional ladders to two-dimensional square lattices. Particular attention is paid to the high-temperature analysis of the temporal behavior of autocorrelation functions for both the local density of magnetization (spin) and energy, which are closely related to transport properties of the considered models. Due to the conservation of total energy and total magnetization, the dynamics of such densities are expected to exhibit hydrodynamic behavior for long times, which manifests itself in a power-law tail of the autocorrelation function in time. From a quantum mechanical point of view, the calculation of these autocorrelation functions requires solving the linear Schrödinger equation, while classically Hamilton’s equations of motion need to be solved. An efficient numerical pure-state approach based on the concept of typicality enables circumventing the costly numerical method of exact diagonalization and to treat quantum autocorrelation functions with up to N = 36 lattice sites in total. While, in full generality, a quantitative agreement between quantum and classical dy- namics can not be expected, contrarily, based on large-scale numerical results, it is demonstrated that the dynamics of the quantum S = 1/2 and classical spins coincide, not only qualitatively, but even quantitatively, to a remarkably high level of accuracy for all considered lattice geometries. The agreement particularly is found to be best in the case of nonintegrable quantum models (quasi-one-dimensional and two-dimensional lattice), but still satisfactory in the case of integrable chains, at least if transport properties are not dominated by the extensive number of conservation laws. Additionally, in the context of disordered spin chains, such an agreement of the dynamics is found to hold even in the presence of small values of disorder, while at strong disorder the agreement is pronounced most for larger spin quantum numbers. Finally, it is shown that a putative many-body localization transition within the one- dimensional spin chain is shifted to stronger values of disorder with increasing spin quantum number. It is concluded that classical or semiclassical simulations might provide a meaningful strategy to investigate the quantum dynamics of strongly interacting quantum spin models, even if the spin quantum number is small and far from the classical limit.

The Kitaev model has become a source of much excitement in the field of condensed matter. It is a two dimensional model of spins ½ on a honeycomb lattice with bond-dependent interactions. Its interesting properties include a quantum spin liquid ground state and anyonic excitations. These properties could lead to exciting applications in quantum computing if materials were found to behave similarly to the Kitaev model. Such materials have been found, however the Kitaev model is too simple to describe these materials and additional interactions must be considered. The Heisenberg interaction is one such additional interaction. As such, we can define the Kitaev-Heisenberg model by combining the Kitaev and Heisenberg interactions. We can now ask ourselves if the quantum spin liquid ground state and anyonic excitations still exist in the Kitaev-Heisenberg model. To answer this question, a non-local string order parameter has been defined which is non-zero inside the quantum spin liquid phase and zero outside of it. This string order parameter was shown to exist and survive the Heisenberg interaction on the 2-leg ladder. In this thesis, we look to expand this result to multileg ladders such as the 3-leg, 4-leg, and 5-leg ladders to see if the string order parameter survives in the Kitaev-Heisenberg model in 2 dimensions. Our results show that the string order parameter does exist in multileg ladders, however the phase space window in which it survives the Heisenberg interaction is narrower than in the 2-leg ladder. / Thesis / Master of Science (MSc)

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.

<p> Effects of electron correlations on a two dimensional quantum spin Hall system are studied. We examine possible phases of a generalized Hubbard model on a bilayer honeycomb lattice with a spin-orbit coupling and short range electron-electron repulsions at half filling, based on the slave rotor mean-field theory. The phase diagram of the model is found for a special case where the interlayer Coulomb repulsion is comparable to the intralayer Coulomb repulsion.</p> <p> Besides the conventional quantum spin Hall phase and a broken-symmetry insulating phase, we find a new phase, a fractionalized quantum spin Hall phase, where the quantum spin Hall effect arises for fractionalized spinons which carry only spin but not charge. Experimental manifestations of the exotic phase and effects of fluctuations beyond the saddle point approximation are also discussed.</p> <p> We finally study a toy Bose-Hubbard model for the charge sector of the theory to gain some insight into the phase diagram away from the special Coulomb repulsion values.</p> / Thesis / Master of Science (MSc)