Elementary excitations in one-dimensional spin-orbital models: neutral and charged solitons and their bound states

We study, both numerically and variationally, the interplay between different types of elementary excitations in the model of a spin chain with anisotropic spin-orbit coupling, in the vicinity of the "dimer line" with an exactly known dimerized ground state. Our variational treatment is found to be in a qualitative agreement with the exact diagonalization results. Soliton pairs are shown to be the lowest excitations only in a very narrow region of the phase diagram near the dimer line, and the phase transitions are always governed by magnon-type excitations which can be viewed as soliton-antisoliton bound states. It is shown that when the anisotropy exceeds certain critical value, a new phase boundary appears. In the doped model on the dimer line, the exact elementary charge excitation is shown to be a hole bound to a soliton. Bound states of those "charged solitons" are studied; exact solutions for N-hole bound states are presented.Comment: 11 pages revtex, 6 figure

Spin-orbital gapped phase with least symmetry breaking in the one-dimensional symmetrically coupled spin-orbital model

To describe the spin-orbital energy gap formation in the one-dimensional symmetrically coupled spin-orbital model, we propose a simple mean field theory based on an SU(4) constraint fermion representation of spins and orbitals. A spin-orbital gapped phase is formed due to a marginally relevant spin-orbital valence bond pairing interaction. The energy gap of the spin and orbital excitations grows extremely slowly from the SU(4) symmetric point up to a maximum value and then decreases rapidly. By calculating the spin, orbital, and spin-orbital tensor static susceptibilities at zero temperature, we find a crossover from coherent to incoherent magnetic excitations as the spin-orbital coupling decreasing from large to small values.Comment: 10 pages, Revtex file, 5 figure

Phase Diagram of a Spin Ladder with Cyclic Four Spin Exchange

We present the phase diagram of the $S=1/2$ Heisenberg model on the two leg ladder with cyclic four spin exchange, determined by a combination of Exact Diagonalization and Density Matrix Renormalization Group techniques. We find six different phases and regimes: the rung singlet phase, a ferromagnetic phase, two symmetry broken phases with staggered dimers and staggered scalar chiralities, and a gapped region with dominant vector chirality or collinear spin correlations. We localize the phase transitions and investigate their nature.Comment: 4 pages, 6 figures, REVTeX 4, published versio

Series study of the One-dimensional S-T Spin-Orbital Model

We use perturbative series expansions about a staggered dimerized ground state to compute the ground state energy, triplet excitation spectra and spectral weight for a one-dimensional model in which each site has an S=\case 1/2 spin ${\bf S}_i$ and a pseudospin ${\bf T}_i$, representing a doubly degenerate orbital. An explicit dimerization is introduced to allow study of the confinement of spinon excitations. The elementary triplet represents a bound state of two spinons, and is stable over much of the Brillouine zone. A special line is found in the gapped spin-liquid phase, on which the triplet excitation is dispersionless. The formation of triplet bound states is also investigated.Comment: 9 pages, 9 figure

Plasma Aβ42/40 ratio, p‐tau181, GFAP, and NfL across the Alzheimer's disease continuum: A cross‐sectional and longitudinal study in the AIBL cohort

Introduction Plasma amyloid beta (Aβ)1-42/Aβ1-40 ratio, phosphorylated-tau181 (p-tau181), glial fibrillary acidic protein (GFAP), and neurofilament light (NfL) are putative blood biomarkers for Alzheimer's disease (AD). However, head-to-head cross-sectional and longitudinal comparisons of the aforementioned biomarkers across the AD continuum are lacking. Methods Plasma Aβ1-42, Aβ1-40, p-tau181, GFAP, and NfL were measured utilizing the Single Molecule Array (Simoa) platform and compared cross-sectionally across the AD continuum, wherein Aβ-PET (positron emission tomography)–negative cognitively unimpaired (CU Aβ−, n = 81) and mild cognitive impairment (MCI Aβ−, n = 26) participants were compared with Aβ-PET–positive participants across the AD continuum (CU Aβ+, n = 39; MCI Aβ+, n = 33; AD Aβ+, n = 46) from the Australian Imaging, Biomarker & Lifestyle Flagship Study of Ageing (AIBL) cohort. Longitudinal plasma biomarker changes were also assessed in MCI (n = 27) and AD (n = 29) participants compared with CU (n = 120) participants. In addition, associations between baseline plasma biomarker levels and prospective cognitive decline and Aβ-PET load were assessed over a 7 to 10-year duration. Results Lower plasma Aβ1-42/Aβ1-40 ratio and elevated p-tau181 and GFAP were observed in CU Aβ+, MCI Aβ+, and AD Aβ+, whereas elevated plasma NfL was observed in MCI Aβ+ and AD Aβ+, compared with CU Aβ− and MCI Aβ−. Among the aforementioned plasma biomarkers, for models with and without AD risk factors (age, sex, and apolipoprotein E (APOE) ε4 carrier status), p-tau181 performed equivalent to or better than other biomarkers in predicting a brain Aβ−/+ status across the AD continuum. However, for models with and without the AD risk factors, a biomarker panel of Aβ1-42/Aβ1-40, p-tau181, and GFAP performed equivalent to or better than any of the biomarkers alone in predicting brain Aβ−/+ status across the AD continuum. Longitudinally, plasma Aβ1-42/Aβ1-40, p-tau181, and GFAP were altered in MCI compared with CU, and plasma GFAP and NfL were altered in AD compared with CU. In addition, lower plasma Aβ1-42/Aβ1-40 and higher p-tau181, GFAP, and NfL were associated with prospective cognitive decline and lower plasma Aβ1-42/Aβ1-40, and higher p-tau181 and GFAP were associated with increased Aβ-PET load prospectively. Discussion These findings suggest that plasma biomarkers are altered cross-sectionally and longitudinally, along the AD continuum, and are prospectively associated with cognitive decline and brain Aβ-PET load. In addition, although p-tau181 performed equivalent to or better than other biomarkers in predicting an Aβ−/+ status across the AD continuum, a panel of biomarkers may have superior Aβ−/+ status predictive capability across the AD continuum

Phase Diagram of the Heisenberg Spin Ladder with Ring Exchange

We investigate the phase diagram of a generalized spin-1/2 quantum antiferromagnet on a ladder with rung, leg, diagonal, and ring-exchange interactions. We consider the exactly soluble models associated with the problem, obtain the exact ground states which exist for certain parameter regimes, and apply a variety of perturbative techniques in the regime of strong ring-exchange coupling. By combining these approaches with considerations related to the discrete Z_4 symmetry of the model, we present the complete phase diagram.Comment: 17 pages, 10 figure

Solution of a two-leg spin ladder system

A model for a spin-1/2 ladder system with two legs is introduced. It is demonstrated that this model is solvable via the Bethe ansatz method for arbitrary values of the rung coupling J. This is achieved by a suitable mapping from the Hubbard model with appropriate twisted boundary conditions. We determine that a phase transition between gapped and gapless spin excitations occurs at the critical value J(c) = 1/2 of the rung coupling