We investigate the energy spectrum for hybrid mechanical systems described by non-parity-symmetric quantum Rabi models. A set of analytical solutions in terms of the confluent Heun functions and their analytical energy spectrum is obtained. The analytical energy spectrum includes regular and exceptional parts, which are both confirmed by direct numerical simulation. The regular part is determined by the zeros of the Wronskian for a pair of analytical solutions. The exceptional part is relevant to the isolated exact solutions and its energy eigenvalues are obtained by analyzing the truncation conditions for the confluent Heun functions. By analyzing the energy eigenvalues for exceptional points, we obtain the analytical conditions for the energy-level crossings, which correspond to two-fold energy degeneracy.
We investigate the thermal and magnetic properties of the integrable su(4) ladder model by means of the quantum transfer matrix method. The magnetic susceptibility, specific heat, magnetic entropy and high field magnetization are evaluated from the free energy derived via the recently proposed method of high temperature expansion for exactly solved models. We show that the integrable model can be used to describe the physics of the strong coupling ladder compounds.Excellent agreement is seen between the theoretical results and the experimental data for the known ladder compounds (5IAP) 2 CuBr 4 ·2H 2 O, Cu 2 (C 5 H 12 N 2 ) 2 Cl 4 etc.
Ultracold atoms confined to periodic potentials have proven to be a powerful tool for quantum simulation of complex many-body systems. We confine fermions to one dimension to realize the Tomonaga-Luttinger liquid model, which describes the highly collective nature of their low-energy excitations. We use Bragg spectroscopy to directly excite either the spin or charge waves for various strengths of repulsive interaction. We observe that the velocity of the spin and charge excitations shift in opposite directions with increasing interaction, a hallmark of spin-charge separation. The excitation spectra are in quantitative agreement with the exact solution of the Yang-Gaudin model and the Tomonaga-Luttinger liquid theory. Furthermore, we identify effects of nonlinear corrections to this theory that arise from band curvature and back-scattering.
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