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We calculate correlation functions of exactly-solvable one-dimensional flat-band models by utilizing the molecular-orbital representation. The models considered in this paper have a gapped ground state with flat-band being fully occupied, even in the presence of the interaction. The remarkable feature of such models is that the correlation functions are obtained without deriving explicit forms of the flat-band wave functions. Rather, they can be calculated by using the molecular-orbitals. As a demonstration, several one-dimensional models and their correlation functions are presented.
On the basis of the molecular-orbital representation which describes generic flat-band models, we propose a systematic way to construct a class of flat-band models with finite-range hoppings that have topological natures. In these models, the topolog
We develop a formalism for computing the non-linear response of interacting integrable systems. Our results are asymptotically exact in the hydrodynamic limit where perturbing fields vary sufficiently slowly in space and time. We show that spatially
We study low-energy excitations of one-dimensional Galilean-invariant models integrable by Bethe ansatz and characterized by nonsingular two-particle scattering phase shifts. We prove that the curvature of the excitation spectra is described by the r
We present a variational density matrix approach to the thermal properties of interacting fermions in the continuum. The variational density matrix is parametrized by a permutation equivariant many-body unitary transformation together with a discrete
Periodically driven quantum matter can realize exotic dynamical phases. In order to understand how ubiquitous and robust these phases are, it is pertinent to investigate the heating dynamics of generic interacting quantum systems. Here we study the t