Fractional quantum Hall effect

The fractional quantum Hall effect (FQHE) is a physical phenomenon in which the Hall conductance of 2-dimensional (2D) electrons shows precisely quantized plateaus at fractional values of e^2/h. It is a property of a collective state in which electrons bind magnetic flux lines to make new quasiparticles, and excitations have a fractional elementary charge and possibly also fractional statistics. The 1998 Nobel Prize in Physics was awarded to Robert Laughlin, Horst Störmer, and Daniel Tsui "for their discovery of a new form of quantum fluid with fractionally charged excitations" The microscopic origin of the FQHE is a major research topic in condensed matter physics. Descriptions The fractional quantum Hall effect (FQHE) is a collective behavior in a 2D system of electrons. In particular magnetic fields, the electron gas condenses into a remarkable liquid state, which is very delicate, requiring high quality material with a low carrier concentration, and extr

Spinon-like excitations in spin-1/2 quantum antiferromagnets

Irina Safiulina

Quantum magnetism remains a hot topic in condensed matter physics due to its complexity and possible powerful and significant applications in data storage and memory. To understand how the materials can achieve these goals, one should have a clear idea about the fundamentals behind it. In this thesis, we focus on three examples that can help us deepen the knowledge in many-body effects, which stand to be crucial for quantum magnetism.(1) The well-known \textbf{CuSO

_4\cdot

_2

O} material has already demonstrated the model behaviour as one-dimensional Heisenberg antiferromagnet in zero and high (

H>H_{sat}

) fields. The fully-polarized magnetic ground state is described by linear spin-wave theory with magnons, whereas at zero field, the excitations are pairs of topological excitations called spinons. In an intermediate field, the dynamic properties are even more complicated. The inelastic spectrum cannot be reproduced without considering exotic elementary excitations and bound states such as psinons and Bethe strings. Although Bethe in 1931 provided an exact solution for 1D Heisenberg systems, there is still no quantitative comparison between theory and experiment.(2) The magnetic ground state and hence the dynamic properties of the gemstone mineral green dioptase, \textbf{Cu

_6[

_6

_{18}]\cdot6

_2

O} are under debate: starting from controversial theories and continuing with non-explained experimental observations. Dioptase is a quasi-one-dimensional spin chain with dominant antiferromagnetic interactions. Recent studies claim the classical spin chain behaviour and absence of any quantum fluctuations in the system. In contrast, our experimental findings indicate the presence of continuous excitations above and below T

_N

.(3) Newly synthesized material \textbf{CuSb

_2

_6

} of rosiaite-type structure tends to become a quantum spin-liquid (QSL) candidate since the magnetic cations Cu

^{2+}

are arranged in trigonal layers, and no long-range order is observed down to 2~K. The idea of QSL on the triangular lattice was proposed by P. Anderson in 1973. Since his work, a lot of efforts have been made to explore deeper, both theoretically and experimentally, this state. As for now, there are several requirements needed to be met -- small spin number, absence of long-range order or spin freezing, long-range entanglement, and the associated fractional spin excitations. We aim to establish whether or not CuSb

_2

_6

can be considered as a potential quantum spin-liquid candidate employing different techniques suitable for a powder sample.

EPFL2022

Static and dynamic properties of non-collinear quantum antiferromagnets explored by neutron scattering

Luc Testa

This thesis is devoted to the investigation of static and dynamic properties of two different sets of quantum magnets with neutron scattering techniques and the help of linear spin wave theory. Both systems are copper-based with spin-1/2, which makes them ideal to study the interplay between purely quantum and semi-classical effects. I start with the analysis of the antiferromagnet SeCuO3, which has a canted spins structure. Through careful inelastic neutron scattering experiments on thermal and cold triple-axis spectrometers, I demonstrate that this compound exhibits three primary types of excitations that are intrinsically opposite : spin waves (magnons), singlet to triplet excitations (triplons), and fractional spins excitations (spinons). Such a strong coexistence and interdependence of these collective excitations has not been observed yet, thereby the quantification and description of the excitations in SeCuO3 leads the way to further theoretical work on multi-excitation spin systems, as well as the existence of quantum effects in high dimensional systems.\ My second project is on the extraction of the magnetic structure of three members of the A(BO)Cu4(PO4)4 chiral family, namely (A; B) = (Ba; Ti), (Sr; Ti) and (Pb; Ti), from spherical neutron polarimetry measurements. I prove that the first two compounds exhibit a highly non-collinear magnetic structure, with the Cu spins forming clusters of 'two-in--two-out' arrangements on each structural unit. This structure is stabilised by the presence of a strong Dzyaloshinskii-Moriya interaction, and explains the observation of magnetoelectric effects as emerging from quadrupole moments. The analysis of the latter compound did not lead to the confirmation of its magnetic structure due to strong nuclear-magnetic interference. I conclude this thesis by the investigation of the magnetic excitation spectrum of some members of the (A; B) family, probed by inelastic neutron scattering measurements. Indeed, its particular crystallographic structure makes it an ideal playground to study tetramerisation effects on the two dimensional square lattice. Additionally, the aforementioned Dzyaloshinskii-Moriya interaction ensures the presence of a structural gap, which competes with the quantum one emerging from tetramerisation effects. Using linear spin wave theory, I describe (Ba; Ti) as a chequerboard system with almost equal intra- and inter-plaquette couplings, with weak quantum effects. I also provide a qualitative description of (Pb; Ti), which exhibits similar physics, and conclude by presenting the first results on the highly symmetric compound (K; Nb), which shows hints of a strong quantum behaviour.

EPFL2021

Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study

Abelian and non-Abelian topological phases exhibiting protected chiral edge modes are ubiquitous in the realm of the fractional quantum Hall (FQH) effect. Here, we investigate a spin-1 Hamiltonian on the square lattice which could, potentially, host the spin liquid analog of the (bosonic) non-Abelian Moore-Read FQH state, as suggested by exact diagonalization of small clusters. Using families of fully SU(2)-spin symmetric and translationally invariant chiral projected entangled pair states (PEPS), variational energy optimization is performed using infinite-PEPS methods, providing good agreement with density matrix renormalization group (DMRG) results. A careful analysis of the bulk spin-spin and dimer-dimer correlation functions in the optimized spin liquid suggests that they exhibit long-range "gossamer tails". From the investigation of the entanglement spectrum, we observe sharply defined chiral edge modes following the prediction of the SU(2)(2) Wess-Zumino-Witten theory and exhibiting a conformal field theory (CFT) central charge c = 3/2, as expected for a Moore-Read chiral spin liquid. Using the PEPS bulk-edge correspondence, we argue the "weak" criticality of the bulk is in fact a finite-D artifact of the chiral PEPS, which quickly becomes (practically) irrelevant as the PEPS bond dimension D is increased. We conclude that the PEPS formalism offers an unbiased and efficient method to investigate non-Abelian chiral spin liquids in quantum antiferromagnets.

2018