This thesis is devoted to the study of a class of antifferomagnetic spin–1 chains with astrong easy plane anisotropy in the presence of magnetic field H. At zero temperature thesystem undergoes two quantum phase transitions at critical fields H1 and H2. Reliableand detailed theoretical analysis is provided on the Electron Spin Resonance (ESR)spectrum, thermodynamics and the thermal transport of the model. The tools at handrange from exact analytical solutions and to numerical simulation techniques. The S = 1antiferromagnet in a magnetic field can be systematically mapped onto an S = 1/2XXZ chain in a longitudinal magnetic field. This effective S = 1/2 description has beenextensively used in order to gain a better physical understanding of the original S = 1chain.For the Electron Spin Resonance spectrum, apart from the theoretical analysis, high-field ESR experimental studies of the compound N iCl2 − 4SC(NH2)2 (abbreviatedas DTN) are presented and found consistent with theoretical predictions. The mostinteresting feature is the experimental signature of the single–ion two–magnon boundstate.Part of this thesis is devoted to the magnetic–field and temperature dependence ofmagnetization and specific heat for the whole field–region and a wide range of temperatures,with special emphasis at the critical behaviour of these quantities at the criticalfields. Finally, the calculation of dynamic correlation functions pertinent to the studyof thermal transport is addressed for the S = 1 model with easy plane anisotropy andthe S = 1/2 XXZ model in the presence of finite magnetic field.
This thesis is devoted to the study of a class of antifferomagnetic spin–1 chains with astrong easy plane anisotropy in the presence of magnetic field H. At zero temperature thesystem undergoes two quantum phase transitions at critical fields H1 and H2. Reliableand detailed theoretical analysis is provided on the Electron Spin Resonance (ESR)spectrum, thermodynamics and the thermal transport of the model. The tools at handrange from exact analytical solutions and to numerical simulation techniques. The S = 1antiferromagnet in a magnetic field can be systematically mapped onto an S = 1/2XXZ chain in a longitudinal magnetic field. This effective S = 1/2 description has beenextensively used in order to gain a better physical understanding of the original S = 1chain.For the Electron Spin Resonance spectrum, apart from the theoretical analysis, high-field ESR experimental studies of the compound N iCl2 − 4SC(NH2)2 (abbreviatedas DTN) are presented and found consistent with theoretical predictions. The mostinteresting feature is the experimental signature of the single–ion two–magnon boundstate.Part of this thesis is devoted to the magnetic–field and temperature dependence ofmagnetization and specific heat for the whole field–region and a wide range of temperatures,with special emphasis at the critical behaviour of these quantities at the criticalfields. Finally, the calculation of dynamic correlation functions pertinent to the studyof thermal transport is addressed for the S = 1 model with easy plane anisotropy andthe S = 1/2 XXZ model in the presence of finite magnetic field.
We present a study of the one-dimensional S=1 antiferromagnetic spin chain with large easy-plane anisotropy, with special emphasis on field-induced quantum phase transitions. Temperature and magnetic field dependence of magnetization, specific heat, and thermal conductivity is presented using a combination of numerical methods. In addition, the original S=1 model is mapped into the low-energy effective S=1/2XXZ Heisenberg chain, a model which is exactly solvable using the Bethe ansatz technique. The effectiveness of the mapping is explored, and we show that all considered quantities are in qualitative, and in some cases quantitative, agreement. The thermal conductivity of the considered S=1 model is found to be strongly influenced by the underlying effective description. Furthermore, we elucidate the low-lying electron spin resonance spectrum based on a semianalytical Bethe ansatz calculation of the effective S=1/2 model.
This thesis investigates exotic phases of matter in magnetic materials that present anisotropic properties in two dimensions. Using the microscopic spin Hamiltonians, the study addresses two problems: (i) the appearance of a novel class of magnetic excitations in the spectra of anisotropic magnets at zero temperature, and (ii) the quantum-to-classical correspondence of spins for the description of magnetic solids in the disordered phase above the critical temperature. Different analytical and numerical means are used to this purpose.In the first part, motivated by experimental observations of multipolar excitations in afamily of strongly-anisotropic van der Waals antiferromagnets, we have developed ageneral theory for these excitations as a distinct type of quasi-particles. We called themlongitudinal magnons. They appear in easy-axis magnetic materials, and are characterized by the quantum number Sz = ±2S. They can exist as coherent long-lived excitations for D ≥ |J|, where D and J are the typical single-ion and exchange coupling constants, respectively. Starting with the strong-coupling limit, this work presented different approaches to compute the dispersion of longitudinal magnons. First, a mapping to an effective spin-1/2 model was performed and illustrated for several lattice spin models: the honeycomb-lattice zigzag antiferromagnet and the square-lattice ferro- and antiferromagnet. The excitation energy was derived for different spin values S = 1, 3/2, 2and 5/2. Second, a thorough study explored the S = 1 anisotropic square-lattice, wherethe analytical results of the effective model are compared to the multi-boson spin-wavetheory, the linked-cluster calculations in antiferromagnetic coupling J > 0, and the exactsolution of the two-magnon problem in ferromagnetic coupling J < 0. In the limit of largeJ/D, the longitudinal magnons start to overlap with the multi-magnon continuum, andtheir finite lifetime can be computed using the multi-boson theory, which is specificallyshown for two-magnon decay processes in S = 1. Moreover, critical values of J/D forthe stability of longitudinal magnons are obtained along high-symmetry lines of the Brillouin zone. Third, we investigated the appearance and condensation of the longitudinal magnons in triangular S = 1 antiferromagnets under high magnetic field. As suggested by recent experiments on a candidate material, a spin nematic phase may appear upon condensation of the multipolar excitations, opening the way for realizations of new phases of matter in classically-ordered magnets.In the second part, the correspondence between quantum and classical spins is investigated for spin Hamiltonians at finite temperature. Given a model of quantum spins, it is useful to determine the classical model that best describes its thermodynamics, which is of interest for semi-classical analyses, e.g. by classical Monte Carlo methods. Based on high-temperature series expansions, we established the scaling laws of the different microscopic constants in a quantum spin model, involving quadratic and biquadratic exchange interactions, single-ion anisotropy and the Zeeman energy. We showed that quantum corrections to the thermodynamic quantities are power series in S(S + 1). Subsequently, the findings were applied to numerically determine the phase transition temperature in several ferro- and antiferromagnetic compounds, using classical Monte Carlo simulations. To this aim, the lattice spin models were constructed with microscopic coupling constants from the literature, and the transition temperatures were compared to the experimental values.This illuminates complex collective magnetic behaviors in different models and materials.
Earlier work on the T=0 dynamics of spin-1 chains with a strong easy-plane anisotropy is extended to include thermodynamics. Thus we carry out a systematic strong-coupling expansion to obtain analytical approximations for the spectrum of elementary excitations, the specific heat, and the magnetic susceptibility. Comparison with numerical data for the specific heat available in some important special cases indicates that our result is accurate for practically the entire temperature range. Similarly our calculation of the magnetic susceptibility reproduces to leading order a result obtained earlier through a molecular-field approximation and provides a definite improvement by including the two-loop correction. These theoretical predictions are directly relevant for a number of magnetic materials of current experimental interest.
We discuss electron spin resonance (ESR) shifts in spin-1 Heisenberg antiferromagnetic chains with a weak single-ion anisotropy, based on several effective field theories: the O(3) nonlinear sigma model (NLSM) in the Haldane phase, free-fermion theories around the lower and the upper critical fields. In the O(3) NLSM, the single-ion anisotropy corresponds to a composite operator which creates two magnons at the same time and position. Therefore, even inside a parameter range where free magnon approximation is valid for thermodynamics, we have to take interactions among magnons into account in order to include the single-ion anisotropy as a perturbation. Although the O(3) NLSM is only valid in the Haldane phase, an appropriate translation of Faddeev-Zamolodchikov operators of the O(3) NLSM to fermion operators enables one to treat ESR shifts near the lower critical field in a similar manner to discussions in the Haldane phase. Our theory gives quantitative agreements with a numerical evaluation using quantum Monte Carlo simulation, and also with recent ESR experimental results on a spin-1 chain compound Ni(C5H14N2)2N3(PF6).
This thesis is concerned with the numerical study of one-dimensional (1D) spin-1/2 quantum magnets and related method development. Its focus is on the calculation of dynamical spin correlation functions both at zero and finite temperature. This is motivated by the accessibility of dynamical quantities in experiments such as inelastic neutron scattering (INS) and electron spin resonance (ESR). The numerical methods used in this thesis are based on extensions of the density-matrix renormalization group (DMRG) and are formulated in the framework of matrix product states (MPS). While zero-temperature dynamical correlation functions are computed with existing MPS frequency-domain methods, an MPS frequency-domain approach for their calculation at finite temperature is developed in this thesis. The new method combines the Liouville-space formulation of the dynamics with a moment expansion of the dynamical correlation function. The majority of the results are obtained via MPS-based Chebyshev expansions. These numerical techniques are applied to two different model systems describing real materials. The first one is the material copper pyrimidine dinitrate (Cu-PM) which is modeled by a 1D spin-1/2 Heisenberg antiferromagnet with Dzyaloshinskii-Moriya interactions. The spin dynamics of this model is studied in an applied magnetic field and compared to ESR experiments. Zero-temperature calculations for momentum- and frequency-resolved dynamical quantities give direct access to the intensity of the elementary excitations and go beyond the low-energy description by the quantum sine-Gordon model. Thus, a deviation from the Lorentz invariant dispersion for the single-soliton resonance is found. The presence of the strongest boundary bound state previously predicted from a boundary sine-Gordon field theory is confirmed, while composite boundary-bulk excitations have too low intensities to be found in the numerical results. At finite temperature, there is a temperature-induced crossover of the soliton. Moreover, additional temperature effects such as interbreather transitions emerge, which is confirmed by accompanying ESR experiments on Cu-PM over a wide range of the applied field strength. The second system studied in this thesis is the compound BaCu2V2O8. It is shown that the magnetic properties of this quasi-1D material can be described by a strongly alternating antiferromagnetic-ferromagnetic spin-1/2 Heisenberg chain. As found for other dimerized systems, the strong correlations in BaCu2V2O8 persist even at elevated temperatures. Moreover, these correlations lead to an asymmetric lineshape broadening of the magnetic excitations at finite temperature. Upon raising the temperature, an increasingly asymmetric lineshape is observed in high-resolution INS experiments for BaCu2V2O8. In this thesis, the lineshape is calculated by the MPS finite-temperature method developed as a part of this work. Comparing these results to the INS data and the lineshape obtained by a diagrammatic approach, excellent agreement is found over a broad temperature range. This demonstrates that coherent quantum behavior persists at elevated temperatures in BaCu2V2O8 and that it can be predicted quantitatively.
This thesis consists in a theoretical study of some one-dimensional models. Special attention is given to simple but non-trivial soluble models. The study starts with a resume of the Green function method which is the formalism used throughout the work. A discussion of coupled electron-phonon and spin-phonon systems is presented and a decoupling scheme introduced. The approximation gives the transition temperature for one-dimensional systems exactly, namely T = 0, and consequently represents a great improvement on the mean-field approximation. The impure XY-chain in a transverse field is studied and the formal solution presented. The static and time-dependent correlations are discussed, and the effect of the boundary term reviewed in details. The one-impurity case is solved for the isotropic chain, and it is shown how to derive from it the open chain result in the thermodynamic limit. The heat-flux operator is obtained for the impure isotropic chain by solving the continuity equation for energy density. The dynamics of the one-dimensional transverse Ising model is discussed within several approximations. The limitations of each approximation are examined in detail and the time-dependent correlations are calculated using the most successful approximation. It is also shown that this approximation is only valid in the high temperature limit in which case no critical behaviour is to be observed. The one-impurity solution of the isotropic impure XY-chain is extended to many impurities in two different cases. In the first case the specific heat of the dilute chain is calculated in the framework of the average t-matrix approximation, and the results compared with exact numerical calculations for finite chains. In the second case the specific heat and thermal conductivity of the isotropic XY-chain in a random transverse field are calculated using the coherent-potential approximation (CPA). The results are used to explain the low temperature thermal properties of praseodymium ethyl sulphate. Finally, two interacting systems, an electron-phonon system and a spin-phonon system, are studied after a brief discussion of the so-called Peierls instability. The first model is solved exactly in the framework of the approximation discussed at the beginning of the work. It presents a giant Kohn anomaly at zero temperature which drives a Peierls transition. The renormalized modes are discussed, and the real and imaginary parts of the phonon propagator are presented for wave vector π⁄a and several coupling constants and temperatures. The spin-phonon system is also studied in the framework of the approximation discussed initially in the work, and it is chosen in such a way that the relevant properties are given in terms of Green functions calculated in the transverse Ising model. The results obtained for the dynamics of this model are used, and since they are valid only in the high temperature limit, the discussion is restricted to this temperature region. Since this region is far away from the critical one, no critical behaviour is observed, and the study is restricted to a simple discussion of modes. The real and imaginary parts of the renormalized phonon propagator are presented for the wave vector π⁄a, high temperature and various coupling constants.