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Register a new userThe phase diagram of the extended anisotropic ferromagnetic-antiferromagnetic Heisenberg chain
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By using Density Matrix Renormalization Group (DMRG) technique we study the phase diagram of 1D extended anisotropic Heisenberg model with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. We analyze the static correlation functions for the spin operators both in- and out-of-plane and classify the zero-temperature phases by the range of their correlations. On clusters of $64,100,200,300$ sites with open boundary conditions we isolate the boundary effects and make finite-size scaling of our results. Apart from the ferromagnetic phase, we identify two gapless spin-fluid phases and two ones with massive excitations. Based on our phase diagram and on estimates for the coupling constants known from literature, we classify the ground states of several edge-sharing materials.
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We consider a modified extended Hubbard model (EHM) which, in addition to the on-site repulsion U and nearest-neighbor repulsion V, includes polarization effects in second-order perturbation theory. The model is equivalent to an EHM with renormalized U plus a next-nearest-neighbor repulsion term. Using a method based on topological quantum numbers (charge and spin Berry phases), we generalize to finite hopping t the quantum phase diagram in one dimension constructed by van den Brink et al. (Phys. Rev. Lett. 75, 4658 (1995)). At hopping t=0 there are two charge density-wave phases, one spin density-wave phase and one intermediate phase with charge and spin ordering, depending on the parameter values. At t eq 0 the nature of each phase is confirmed by studying correlation functions. However, in addition to the strong-coupling phases, a small region with bond ordering appears. The region occupied by the intermediate phase first increases and then decreases with increasing t, until it finally disappears for t of the order but larger than U. For small t, the topological transitions agree with the results of second order perturbation theory.
A central question on Kitaev materials is the effects of additional couplings on the Kitaev model which is proposed to be a candidate for realizing topological quantum computations. However, two spatial dimension typically suffers the difficulty of lacking controllable approaches. In this work, using a combination of powerful analytical and numerical methods available in one dimension, we perform a comprehensive study on the phase diagram of a one-dimensional version of the spin-1/2 Kitaev-Heisenberg-Gamma model in its full parameter space. A strikingly rich phase diagram is found with nine distinct phases, including four Luttinger liquid phases, a ferromagnetic phase, a Neel ordered phase, an ordered phase of distorted-spiral spin alignments, and two ordered phase which both break a $D_3$ symmetry albeit in different ways, where $D_3$ is the dihedral group of order six. Our work paves the way for studying one-dimensional Kitaev materials and may provide hints to the physics in higher dimensional situations.
We successfully synthesized the zinc-verdazyl complex [Zn(hfac)$_2$]$cdot$($o$-Py-V) [hfac = 1,1,1,5,5,5-hexafluoroacetylacetonate; $o$-Py-V = 3-(2-pyridyl)-1,5-diphenylverdazyl], which is an ideal model compound with an $S$ = 1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain (F-AF AHC). $Ab$ $initio$ molecular orbital (MO) calculations indicate that two dominant interactions $J_{rm{F}}$ and $J_{rm{AF}}$ form the $S=1/2$ F-AF AHC in this compound. The magnetic susceptibility and magnetic specific heat of the compound exhibit thermally activated behavior below approximately 1 K. Furthermore, its magnetization curve is observed up to the saturation field and directly indicates a zero-field excitation gap of 0.5 T. These experimental results provide evidence for the existence of a Haldane gap. We successfully explain the results in terms of the $S=1/2$ F-AF AHC through quantum Monte Carlo calculations with $|J_{rm{AF}}/J_{rm{F}}|$ = 0.22. The $ab$ $initio$ MO calculations also indicate a weak AF interchain interaction $J$ and that the coupled F-AF AHCs form a honeycomb lattice. The $J$ dependence of the Haldane gap is calculated, and the actual value of $J$ is determined to be less than 0.01$|J_{rm{F}}|$.
We study the Kitaev-Heisenberg-$Gamma$ model with antiferromagnetic Kitaev exchanges in the strong anisotropic (toric code) limit to understand the phases and the intervening phase transitions between the gapped $Z_2$ quantum spin liquid and the spin-ordered (in the Heisenberg limit) as well as paramagnetic phases (in the pseudo-dipolar, $Gamma$, limit). We find that the paramagnetic phase obtained in the large $Gamma$ limit has no topological entanglement entropy and is proximate to a gapless critical point of a system described by an equal superposition of differently oriented stacked one-dimensional $Z_2times Z_2$ symmetry protected topological phases. Using a combination of exact diagonalization calculations and field-theoretic analysis we map out the phases and phase transitions to reveal the complete phase diagram as a function of the Heisenberg, the Kitaev, and the pseudo-dipolar interactions. Our work shows a rich plethora of unconventional phases and phase transitions and provides a comprehensive understanding of the physics of anisotropic Kitaev-Heisenberg-$Gamma$ systems along with our recent paper [Phys. Rev. B 102, 235124 (2020)] where the ferromagnetic Kitaev exchange was studied.
By using Density Matrix Renormalization Group (DMRG) technique we study the 1D extended anisotropic Heisenberg model. We find that starting from the ferromagnetic phase, the system undergoes two quantum phase transitions (QPTs) induced by frustration. By increasing the next-nearest-neighbor (NNN) interaction, the ground state of the system changes smoothly from a completely polarized state to a NNN correlated one. On the contrary, letting the in-plane interaction to be greater than the out-of-plane one, the ground state changes abruptly.
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