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Glucan oligomers obtained from cellulose hydrolysis in molten salt hydrate can be separated using anti-solvent precipitation with a high efficiency.
We generalize Babelon's approach to equations in dual variables so as to be able to treat new types of operators which we build out of the sub-constituents of the model's monodromy matrix. Further, we also apply Sklyanin's recent monodromy matrix identities so as to obtain equations in dual variables for yet other operators. The schemes discussed in this paper appear to be universal and thus, in principle, applicable to many models solvable through the quantum separation of variables.
In this work, we derive an exact renormalization group recursion relation for the Loschmidt amplitude of the quantum Q-state clock model and the quantum Q-state Potts model in one dimension. The renormalization group flow is discussed in detail. The fixed points of the renormalization group flow are found to be complex in general. These fixed points control the dynamical phases of the two models, giving rise to nonanalyticities in its Loschmidt rate function, for both the pure and the disordered system. For the quench protocols studied, dynamical quantum phase transitions are found to occur in the clock model for all Qs considered, while in the Potts model, they only occur when Q < 4 .
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We study the doping evolution of spin excitations in a one-dimensional (1D) Hubbard model and its downfolded spin Hamiltonians, by using exact diagonalization combined with cluster perturbation theory. In all models we observe hardening (softening) of spin excitations upon electron (hole) doping, which are reminiscent of recent experiments on two-dimensional (2D) cuprate materials. We also find that the three-site and even higher-order terms are crucial for the low-energy effective spin models to reproduce the magnetic spectra of doped Hubbard systems at a quantitative level. To interpret the numerical results, we further employ a strong coupling slave-boson mean-field theory. The mean-field theory provides an intuitive understanding of the overall compact support of dynamic spin structure factors, including the shift of zero-energy modes and change of spin excitation bandwidth with doping. Our results can serve as predictive benchmarks for future inelastic x-ray or neutron scattering experiments on doped 1D antiferromagnetic Mott insulators.
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