Level crossings and chiral transitions in transverse-field Ising models of adatom and Rydberg chains

This thesis is motivated by recent experiments on systems described by extensions of the one-dimensional transverse-field Ising (TFI) model where (1) finite-size properties of Ising-ordered phases -- specifically, ground state level crossings -- were observed and (2) continuous phase transitions related to the p-state chiral clock model were probed, with interesting but only partially conclusive results regarding the nature of the phase transitions and the possible existence of a chiral universality class.For (1), the relation of the level crossings to topologically protected edge modes of Majorana fermion models is discussed, and the implication is made explicit that the auto-correlation time of the edge spins may be infinite even for non-integrable albeit finite systems, and independently of temperature. The level crossings are then reinterpreted in the context of degenerate perturbation theory as being a consequence of destructive quantum interference between tunneling processes involving different numbers of spin-flip operations. It is shown that this phenomenon is independent of the lattice geometry, as long as this one is not geometrically frustrated, and is ubiquitous to TFI-like models, being also found in single spin-S systems, the latter having already been observed in the field of magnetic molecules. The effect of disorder on the crossings is studied in lowest order.For (2), we perform density matrix renormalization group simulations on open chains to investigate the experimentally observed quantum phase transitions and we conclude that isolated conformal critical points exist along the p=3 and p=4 critical boundaries: we accurately locate such points and characterize their universality classes by determining critical exponents numerically, where we find that the p=3 agrees with a 3-state Potts universality class and the p=4 point agrees with an Ashkin-Teller universality class with Îœ â 0.80 (Î» â 0.5). Our results are in favor of the existence of chiral transition lines surrounding the conformal points, beyond which a gapless intermediate phase is expected.

Dimerization and exotic criticality in spin-S chains

Natalia Chepiga

In this thesis we have studied the emergence of spontaneously dimerized phases in frustrated spin-S chains, with emphasis on the nature of the critical lines between the dimerized and non-dimerized phases. The main numerical method used in this thesis is the Density Matrix Renormalization Group (DMRG). The DMRG algorithm is a relatively old and well established method for the investigation of the ground-state. In this thesis, we show how to use this algorithm to calculate the excitation spectra of one-dimensional critical systems, known in the context of conformal field theory as conformal towers of states. We have demonstrated that the method works very well for two simple minimal models (the transverse-field Ising model and the three-state Potts model), and we have used it systematically to identify the universality classes and the underlying conformal field theories of various one-dimensional spin systems. It has been known for a long time that the transition to a spontaneously dimerized phase in a spin-1 chain can be either continuous, in the Wess-Zumino-Witten (WZW) SU(2) level 2 universality class, or first order. By combining a careful numerical investigation with a conformal field theory analysis, we were able to detect in a frustrated spin-1 chain with competing next-nearest-neighbor and three-site interactions the presence of yet another type of continuous phase transition that belongs to the Ising universality class. In contrast to the WZW SU(2) level 2 critical line, at which the singlet-triplet gap closes, the Ising transition occurs entirely in the singlet sector, while the singlet-triplet gap remains open. The use of the standard DMRG approach, along the lines mentioned above, has allowed us to provide explicit numerical evidence for the presence of a conformal tower of singlets inside the spin gap. Moreover, according to field theory, a WZW SU(2) level k critical line can turn into a first order transition due to the presence of a marginal operator in the WZW SU(2) level k model. A careful investigation of the conformal towers along the critical lines has allowed us to find the precise location of this point in both S=1 and S=3/2 chains. We have also shown that the nature of the continuous dimerization transitions is related to the topological properties of the corresponding phases, and that the phase diagrams of various frustrated spin chains can be effectively extracted by looking at the local topological order parameter - the degeneracy of the lowest state in the entanglement spectrum. When coupled with the conformal field theory of open systems, DMRG appears to be an extremely powerful tool to characterize not only the phase diagram and the ground-state correlations of quantum one-dimensional systems, but also the excitation spectrum and the conformal structure along critical lines.

EPFL2017

Etude par microscopie électronique à transmission à haute résolution de l'élargissement thermique des parois de domaines ferroélectriques dans un système de premier ordre

The macroscopic properties of ferroelectric materials depend directly on the domain configuration and the structure of the domain boundaries. For this reason, their study is of great scientific and technological interest. Several models have been developed to describe the properties of domain walls (structure, thickness, stress at the interface, mobility, …). However, few quantitative experimental observations of ferroelectric domain walls at an atomic scale have been reported, and even less results exist at higher temperatures. The ferroelectric domain-wall thickness is an important parameter whose behavior as a function of temperature is directly related to the order of the phase transition. In a second-order system, the temperature dependence of the domain-wall thickness follows a power law L ~ (Tc - T)-ω where ω is the critical exponent characterizing the divergence of L near the critical temperature Tc The predictions concerning the numerical value of are different depending on the theoretical model considered. Nevertheless, the majority of ferroelectric materials are known to undergo a first-order transition. In these systems the domain-wall thickness increases when the transition temperature is approached, but without diverging as for a second-order phase transition. The major objective of this work was to measure this broadening predicted by the theory for the first time at the approach of the phase transition temperature. We have shown that high resolution transmission electron microscopy is powerful technique for the study of ferroelectric domain walls not only at room temperature but also at higher temperatures. This method allows a direct and local observation of interfaces at an atomic scale which is a considerable advantage over diffraction techniques (X-ray, neutron, electron) and most of the other electron microscopy methods. However, the requirements of this method concerning the performance of the optical system of the microscope, the quality of the specimen and its stability in the column are very high, and today high resolution microscopy at high temperature remains a major challenge. The domain-wall thickness is obtained from the measurement of the crystal lattice distortion near the interface using two different numerical techniques of image analysis. The first method is based on the accurate determination of the center of bright peaks which appear on high resolution images for a judicious choice of the experimental parameters (delocalization and crystal thickness) and which represent the crystal lattice nodes. The second technique consists in selecting a circular region of the power spectrum around a reflection peak, centering the Fourier space on this reflection and performing the inverse Fourier transform. The information about the local displacement of atomic planes corresponding to the selected reflection is extracted form the phase component of the obtained complex image. Both techniques have been successfully applied to the measurement of the thickness of the 90° ferroelectric domain walls in PbTiO3 single crystals. This perovskite presents a first order phase transition at Tc = 492.2°C. which corresponds to the transformation of the crystal from the high-temperature paraelectric cubic phase to the low-temperature ferroelectric tetragonal phase. For the first time, the thermal broadening of domain walls has been measured quantitatively using HRTEM. The results are compared with the predictions made by phenomenological theories. We find that the domain wall thickness increases continuously from 0.7 nm at room temperature up to 5.5 nm near the transition temperature. Our results are consistent with those obtained by other authors at room temperature and those of a very recent study performed at higher temperatures using weak-beam microscopy. The measured domain-wall broadening is greater than the one predicted by a three-dimensional Ginzburg-Landau model where the polarization which is the primary order parameter is coupled to the elastic strain which plays the role of secondary order parameter. Our results are better described by a one-dimensional Ginzburg-Landau model without secondary order parameter. In this case the gradient coupling coefficient κ of the Ginzburg-Landau free energy is found to be 1.3 · 10-10 m3F-1. The methods developed for the measurement of the domain-wall thickness can by applied not only to other first-order ferroelectric crystals but also to ferroelectric systems presenting a second-order phase transition thus allowing the determination of the critical exponent ω. Characteristics only present in 2-D systems could also be detected by studying very thin specimens. Moreover, the same techniques can be adapted to the study of domain walls in purely ferroelastic materials.

EPFL2000

Classical and Quantum Critical Phenomena in the Dipolar Antiferromagnet LiErF4

Neda Nikseresht Ghanepour

The collective behavior of systems consisting of interacting dipoles is a subject of considerable studies. The anisotropic nature of such interactions opens an arena to explore fundamental questions in correlated electron physics, ranging from quantum entanglement, phase transitions, spin glass states to disorder and fluctuations. LiHoF4 is a textbook example of a ferromagnetic Ising-dipolar model, offering a simple and well-understood Hamiltonian. The system undergoes a quantum phase transition (QPT) in a field transverse to the easy axis, which induces quantum fluctuations between the ground state doublet. Dilution of Ho sites with non-magnetic Yttrium ions lowers only the transition temperature (Tc), and eventually lead to spin-glass state. While Tc decreases in a linear fashion, as expected from simple mean-field (MF) calculation, critical field decreases much faster. The behavior upon dilution has been pointed out to be related to randomness and off-diagonal dipolar interactions. In chapter 5 of this thesis I quantify the deviation of experimental results from neutron scattering studies from MF prediction, with the aim that this analysis can be used in future theoretical efforts towards a quantitative description. The aim of this thesis, however, deals with LiErF4 which is an unexplored planar dipolar antiferromagnetic member of LiReF4 family, with TN ≃ 370 mK. The system undergoes a QPT in an applied field H∥c = 4.0±0.1 kOe, confirmed by a softening of the characteristic excitations at Hc. A combined neutron scattering, specific heat, and magnetic susceptibility study reveals a novel non-MF critical scaling of the classical phase transition, belonging to the 2DXY /h4 universality class. In accord with this, the quantum phase transition at Hc exhibits a three-dimensional classical behavior. The effective dimensional reduction may be a consequence of the intrinsic anisotropic nature of the dipolar interaction. Four-fold anisotropy and degeneracy breaking could be due to the "order-by-disorder" phenomena, which could open a gap in dispersion of the magnetic excitations.

EPFL2012