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 topological natures are encoded not into the flat band itself but into the dispersive bands touching the flat band. Such a band structure may become a source of exotic phenomena arising from the combination of flat bands, topology and correlations.
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 resolved nonlinear response distinguishes interacting integrable systems from noninteracting ones, exemplifying this for the Lieb-Liniger gas. We give a prescription for computing finite-temperature Drude weights of arbitrary order, which is in excellent agreement with numerical evaluation of the third-order response of the XXZ spin chain. We identify intrinsically nonperturbative regimes of the nonlinear response of integrable systems.
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 recently proposed phenomenological expression for the effective mass. Our results apply to such models as the repulsive Lieb-Liniger model and the hyperbolic Calogero-Sutherland model.
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 probabilistic model. The unitary transformation is implemented as a quantum counterpart of neural canonical transformation, which incorporates correlation effects via a flow of fermion coordinates. As the first application, we study electrons in a two-dimensional quantum dot with an interaction-induced crossover from Fermi liquid to Wigner molecule. The present approach provides accurate results in the low-temperature regime, where conventional quantum Monte Carlo methods face severe difficulties due to the fermion sign problem. The approach is general and flexible for further extensions, thus holds the promise to deliver new physical results on strongly correlated fermions in the context of ultracold quantum gases, condensed matter, and warm dense matter physics.
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 thermalization in a periodically-driven generalized Sachdev-Ye-Kitaev (SYK)-model, which realizes a crossover from a heavy Fermi liquid (FL) to a non-Fermi liquid (NFL) at a tunable energy scale. Developing an exact field theoretic approach, we determine two distinct regimes in the heating dynamics. While the NFL heats exponentially and thermalizes rapidly, we report that the presence of quasi-particles in the heavy FL obstructs heating and thermalization over comparatively long time scales. Prethermal high-frequency dynamics and possible experimental realizations of non-equilibrium SYK physics are discussed as well.