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That’s most definitely not the case anymore. All graphs are drawn in the first Brillouin zone with interaction u = 1 and the parameters (a) B = 0, μ = − 0.6619, density n = 0.9801 (near half-filled band), (b) B = 0, μ = − 3.8508, density n = 0.1389 (dilute limit), (c) B = 0.555, μ = − 1, and (d) B = 0.555, μ = − 1.32.Once upon a time, not so long ago, the art of contouring-using shadows and darker colors to define and reshape your face-was a makeup technique almost solely reserved for the pros. (d) Gapped excitation spectra for length-1 k − Λ string and a length-2 Λ string. (c) Fractional antiholon-spinon excitations ( 1 2, − 1 2 ), i.e., adding an extra spin-down electron to create an antiholon and a spinon. The inset in (a) shows the excitation for small momentum, while the inset in (b) shows the excitation for the momentum within the first Brillouin zone, whose zero energy modes are situated at 0, 2 π n c, 2 π ( 1 − n c ), 2 π. The orange areas in (a) and (b) represent particle-hole excitations of charge, whereas the green parts show the two-spinon excitations with quantum numbers ( Δ η z, Δ S z ) = ( 0, 1 ) induced from spin flipping. As an application of these concepts, which hold true for higher-dimensional systems, we propose a quantum cooling scheme based on the interaction-driven refrigeration cycle.Įlementary fractional spin and charge excitations. (2) We study the interaction-driven phase transition and the associated criticality, and build up an essential connection between the contact susceptibilities and the variations of density, magnetization, and entropy with respect to the interaction strength. We investigate the universal properties and the asymptotic of correlation functions of the SILL. (1) We calculate the fractional excitations of the system in various phases, from which we identify the parameter regime featuring the spin-incoherent Luttinger liquid (SILL).
In this work, based on the solutions to the thermodynamic Bethe ansatz equations, we provide a rigorous study on the following. Although the one-dimensional repulsive Fermi-Hubbard model has been intensively studied over many decades, a rigorous understanding of many aspects of the model is still lacking.
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