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تسجيل مستخدم جديدTwo-step gap opening across the quantum critical point in a Kitaev honeycomb magnet
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Quantum spin liquid involves fractionalized quasipariticles such as spinons and visons. They are expressed as itinerant Majorana fermions and $Z_2$ fluxes in the Kitaev model with bond-dependent exchange interactions on a honeycomb spin lattice. The observation has recently attracted attention for a candidate material $alpha$-RuCl$_3$, showing spin liquid behaviour induced by a magnetic field. Since the observable spin excitation is inherently composed of the two quasiparticles, which further admix each other by setting in the magnetic field as well as non-Kitaev interactions, their individual identification remains challenging. Here we report an emergent low-lying spin excitation through nuclear magnetic and quadrupole resonance measurements down to $sim 0.4$ K corresponding to $1/500$ of the exchange energy under the finely tuned magnetic field across the quantum critical point. We determined the critical behaviour of low-lying excitations and found evolution of two kinds of the spin gap at high fields. The two excitations exhibit repulsive magnetic field dependence, suggesting anti-crossing due to the hybridization between fractionalized quasiparticles.
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Quantum spin liquid is a disordered magnetic state with fractional spin excitations. Its clearest example is found in an exactly solved Kitaev honeycomb model where a spin flip fractionalizes into two types of anyons, quasiparticles that are neither
fermions nor bosons: a pair of gauge fluxes and a Majorana fermion. Here we demonstrate this kind of fractionalization in the Kitaev paramagnetic state of the honeycomb magnet $alpha$-RuCl$_3$. The spin-excitation gap measured by nuclear magnetic resonance consists of the predicted Majorana fermion contribution following the cube of the applied magnetic field, and a finite zero-field contribution matching the predicted size of the gauge-flux gap. The observed fractionalization into gapped anyons survives in a broad range of temperatures and magnetic fields despite inevitable non-Kitaev interactions between the spins, which are predicted to drive the system towards a gapless ground state. The gapped character of both anyons is crucial for their potential application in topological quantum computing.
We show that the topological Kitaev spin liquid on the honeycomb lattice is extremely fragile against the second-neighbor Kitaev coupling $K_2$, which has recently been shown to be the dominant perturbation away from the nearest-neighbor model in iri
date Na$_2$IrO$_3$, and may also play a role in $alpha$-RuCl$_3$ and Li$_2$IrO$_3$. This coupling naturally explains the zigzag ordering (without introducing unrealistically large longer-range Heisenberg exchange terms) and the special entanglement between real and spin space observed recently in Na$_2$IrO$_3$. Moreover, the minimal $K_1$-$K_2$ model that we present here holds the unique property that the classical and quantum phase diagrams and their respective order-by-disorder mechanisms are qualitatively different due to the fundamentally different symmetries of the classical and quantum counterparts.
We describe the phase diagram of electrons on a fully connected lattice with random hopping, subject to a random Heisenberg spin exchange interactions between any pair of sites and a constraint of no double occupancy. A perturbative renormalization g
roup analysis yields a critical point with fractionalized excitations at a non-zero critical value $p_c$ of the hole doping $p$ away from the half-filled insulator. We compute the renormalization group to two loops, but some exponents are obtained to all loop order. We argue that the critical point $p_c$ is flanked by confining phases: a disordered Fermi liquid with carrier density $1+p$ for $p>p_c$, and a metallic spin glass with carrier density $p$ for $p<p_c$. Additional evidence for the critical behavior is obtained from a large $M$ analysis of a model which extends the SU(2) spin symmetry to SU($M$). We discuss the relationship of the vicinity of this deconfined quantum critical point to key aspects of cuprate phenomenology.
The Kitaev model is a rare example of an analytically solvable and physically instantiable Hamiltonian yielding a topological quantum spin liquid ground state. Here we report signatures of Kitaev spin liquid physics in the honeycomb magnet $Li_3Co_2S
bO_6$, built of high-spin $it{d^7}$ ($Co^{2+}$) ions, in contrast to the more typical low-spin $it{d^5}$ electron configurations in the presence of large spin-orbit coupling. Neutron powder diffraction measurements, heat capacity, and magnetization studies support the development of a long-range antiferromagnetic order space group of $it{C_C}2/it{m}$, below $it{T_N}$ = 11 K at $it{mu_0H}$ = 0 T. The magnetic entropy recovered between $it{T}$ = 2 K and 50 K is estimated to be 0.6Rln2, in good agreement with the value expected for systems close to a Kitaev quantum spin liquid state. The temperature-dependent magnetic order parameter demonstrates a $beta$ value of 0.19(3), consistent with XY anisotropy and in-plane ordering, with Ising-like interactions between layers. Further, we observe a spin-flop driven crossover to ferromagnetic order with space group of $it{C}2/it{m}$ under an applied magnetic field of $it{mu_0H}$ $approx$ 0.7 T at $it{T}$ = 2 K. Magnetic structure analysis demonstrates these magnetic states are competing at finite applied magnetic fields even below the spin-flop transition. Both the $it{d^7}$ compass model, a quantitative comparison of the specific heat of $Li_3Co_2SbO_6$, and related honeycomb cobaltates to the anisotropic Kitaev model further support proximity to a Kitaev spin liquid state. This material demonstrates the rich playground of high-spin $it{d^7}$ systems for spin liquid candidates, and complements known $it{d^5}$ Ir- and Ru-based materials.
We show that the defect density $n$, for a slow non-linear power-law quench with a rate $tau^{-1}$ and an exponent $alpha>0$, which takes the system through a critical point characterized by correlation length and dynamical critical exponents $ u$ an
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