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تسجيل مستخدم جديدHubbard Model on the Pyrochlore Lattice: a 3D Quantum Spin Liquid
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We demonstrate that the insulating one-band Hubbard model on the pyrochlore lattice contains, for realistic parameters, an extended quantum spin-liquid phase. This is a three-dimensional spin liquid formed from a highly degenerate manifold of dimer-based states, which is a subset of the classical dimer coverings obeying the ice rules. It possesses spinon excitations, which are both massive and deconfined, and on doping it exhibits spin-charge separation. We discuss the realization of this state in effective S = 1/2 pyrochlore materials with and without spin-orbit coupling.
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Spin liquids are highly correlated yet disordered states formed by the entanglement of magnetic dipoles$^1$. Theories typically define such states using gauge fields and deconfined quasiparticle excitations that emerge from a simple rule governing th
e local ground state of a frustrated magnet. For example, the 2-in-2-out ice rule for dipole moments on a tetrahedron can lead to a quantum spin ice in rare-earth pyrochlores - a state described by a lattice gauge theory of quantum electrodynamics$^{2-4}$. However, f-electron ions often carry multipole degrees of freedom of higher rank than dipoles, leading to intriguing behaviours and hidden orders$^{5-6}$. Here we show that the correlated ground state of a Ce$^{3+}$-based pyrochlore, Ce$_2$Sn$_2$O$_7$, is a quantum liquid of magnetic octupoles. Our neutron scattering results are consistent with the formation of a fluid-like state of matter, but the intensity distribution is weighted to larger scattering vectors, which indicates that the correlated degrees of freedom have a more complex magnetization density than that typical of magnetic dipoles in a spin liquid. The temperature evolution of the bulk properties in the correlated regime below 1 Kelvin is well reproduced using a model of dipole-octupole doublets on a pyrochlore lattice$^{7-8}$. The nature and strength of the octupole-octupole couplings, together with the existence of a continuum of excitations attributed to spinons, provides further evidence for a quantum ice of octupoles governed by a 2-plus-2-minus rule. Our work identifies Ce$_2$Sn$_2$O$_7$ as a unique example of a material where frustrated multipoles form a hidden topological order, thus generalizing observations on quantum spin liquids to multipolar phases that can support novel types of emergent fields and excitations.
The mathematics of gauge theories lies behind many of the most profound advances in physics in the last 200 years, from Maxwells theory of electromagnetism to Einsteins theory of general relativity. More recently it has become clear that gauge theori
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the density matrix renormalization group with SU(2)$_{rm{spin}} otimes $U(1)$_{rm{charge}}$ symmetries implemented, we study the TLU model defined on the long cylinder geometry with circumference $W=4$. A gapped quantum spin liquid, with on-site interaction $9 lesssim U / t lesssim 10.75$, is identified between the metallic and the antiferromagnetic Mott insulating phases. In particular, we find that this spin liquid develops a robust long-range spin scalar-chiral correlation as the system length $L$ increases, which unambiguously unveils the spontaneous time-reversal symmetry breaking. In addition, the large degeneracy of the entanglement spectrum supports symmetry fractionalization and spinon edge modes in the obtained ground state. The possible origin of chiral order in this intermediate spin liquid and its relation to the rotonlike excitations have also been discussed.
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