Possibility of S=1 spin liquids with fermionic spinons on triangular lattices

In this paper we generalize the fermionic representation for $S=1/2$ spins to arbitrary spins. Within a mean field theory we obtain several spin liquid states for spin $S=1$ antiferromagnets on triangular lattices, including gapless f-wave spin liquid and topologically nontrivial $p_x+ip_y$ spin liquid. After considering different competing orders, we construct a phase diagram for the $J_1$-$J_3$-$K$ model. The application to recently discovered material $\mathrm{NiGa_2S_4}$ is discussed.Comment: 5 pages, 3 figure

Mechanisms of cognitive impairment in epilepsy

Cognitive impairment and dementia are increasingly reported as people with epilepsy grow older, with major impact on quality of life. The underlying mechanisms of cognitive dysfunction, however, and the magnitude of associated dementia risk in epilepsy remains unclear. This thesis will explore how cardiovascular risk factors and hippocampal dysfunction are two important mechanistic links between epilepsy and dementia. Using data from a large population-based cohort, the studies in this thesis demonstrate that cardiovascular risk factors are closely related to impairment of executive function. One finding highlighted a continuous dose-response relation of cognition with blood pressure, even in non-hypertensive individuals. The relationship between cardiovascular risk and cognition was mediated through changes in both frontoparietal white and grey matter structural networks. In the same cohort, people with epilepsy and a high cardiovascular risk were over 13 times more likely to develop dementia compared to healthy controls with low cardiovascular risk. People with epilepsy had a greater risk of developing dementia even compared with individuals with a history of stroke, with associated changes to hippocampal volume. To examine specific hippocampal-related cognitive mechanisms that may underlie memory difficulties in epilepsy, I examined two processes believed to be central to encoding and retrieval in the hippocampus: pattern separation and pattern completion. I devised a novel computer-based behavioural paradigm called the Memory Pinhole Task to distinguish them. Impairment of these two cognitive operations have been identified in ageing and other conditions such as Alzheimer’s disease. Compared to healthy controls, pattern separation deficits were observed in people with epilepsy while reduced pattern completion was seen in healthy older individuals. I then mapped these findings from the Memory Pinhole task onto potential brain mechanisms through computational modelling using a neural network. The work in this thesis describes how modifiable cardiovascular risk factors significantly contribute to cognitive ageing and dementia risk in healthy individuals and people with epilepsy. This has important implications for personal health practices and clinical guidelines, especially in people with epilepsy as there is no current guidance to mitigate dementia risk. Further, I describe a framework for testing encoding and retrieval of information into memory which may allow us to better understand difficulties seen in both health and disease

Fermionic theory for quantum antiferromagnets with spin S > 1/2

The fermion representation for S = 1/2 spins is generalized to spins with arbitrary magnitudes. The symmetry properties of the representation is analyzed where we find that the particle-hole symmetry in the spinon Hilbert space of S =1/2 fermion representation is absent for S > 1/2. As a result, different path integral representations and mean field theories can be formulated for spin models. In particular, we construct a Lagrangian with restored particle-hole symmetry, and apply the corresponding mean field theory to one dimensional (1D) S = 1 and S = 3/2 antiferromagnetic Heisenberg models, with results that agree with Haldane's conjecture. For a S = 1 open chain, we show that Majorana fermion edge states exist in our mean field theory. The generalization to spins with arbitrary magnitude S is discussed. Our approach can be applied to higher dimensional spin systems. As an example, we study the geometrically frustrated S = 1 AFM on triangular lattice. Two spin liquids with different pairing symmetries are discussed: the gapped px + ipy-wave spin liquid and the gapless f-wave spin liquid. We compare our mean field result with the experiment on NiGa2S4, which remains disordered at low temperature and was proposed to be in a spin liquid state. Our fermionic mean field theory provide a framework to study S > 1/2 spin liquids with fermionic spinon excitations.Comment: 16 pages, 4 figure

Raman signature of the U(1) Dirac spin-liquid state in spin-1/2 kagome system

We followed the Shastry--Shraiman formulation of Raman scattering in Hubbard systems and considered the Raman intensity profile in the spin-1/2 "perfect" kagome lattice herbertsmithite ZnCu_3(OH)_6Cl_2, assuming the ground state is well-described by the U(1) Dirac spin-liquid state. In the derivation of the Raman T-matrix, we found that the spin chirality term appears in the A_{2g} channel in the kagome lattice at the t^4/(\omega_i-U)^3 order, but (contrary to the claims by Shastry and Shraiman) vanishes in the square lattice to that order. In the ensuing calculations on the spin-1/2 kagome lattice, we found that the Raman intensity profile in the E_g channel is invariant under an arbitrary rotation in the kagome plane, and that in all (A_{1g}, E_g, and A_{2g}) symmetry channels the Raman intensity profile contains broad continua that display power-law behaviors at low energy, with exponent approximately equal to 1 in the A_{2g} channel and exponent approximately equal to 3 in the E_g and the A_{1g} channels. For the A_{2g} channel, the Raman profile also contains a characteristic 1/\omega singularity, which arose in our model from an excitation of the emergent U(1) gauge field.Comment: 17 pages, 19 figures; Minor revisions, updated to be consistent with the published versio

Phase diagram of doped BaFe2_2As2_2 superconductor under broken C4C_4 symmetry

We develop a minimal multiorbital tight-binding model with realistic hopping parameters. The model breaks the symmetry of the tetragonal point group by lowering it from $C_4$ to $D_{2d}$, which accurately describes the Fermi surface evolution of the electron-doped BaFe$_{2-x}$Co$_x$As$_2$ and hole-doped Ba$_{1-y}$K$_y$Fe$_2$As$_2$ compounds. An investigation of the phase diagram with a mean-field $t$-$U$-$V$ Bogoliubov-de Gennes Hamiltonian results in agreement with the experimentally observed electron- and hole-doped phase diagram with only one set of $t$, $U$ and $V$ parameters. Additionally, the self-consistently calculated superconducting order parameter exhibits $s^\pm$-wave pairing symmetry with a small d-wave pairing admixture in the entire doping range, % The superconducting $s^\pm + d$-wave order parameter which is the subtle result of the weakly broken symmetry and competing interactions in the multiorbital mean-field Hamiltonian