By removing one empty site between two occupied sites, we map the ground states of chains of hardcore bosons and spinless fermions with infinite nearest-neighbor repulsion to ground states of chains of hardcore bosons and spinless fermions without nearest-neighbor repulsion, respectively, and ultimately in terms of the one-dimensional Fermi sea. We then introduce the intervening-particle expansion, where we write correlation functions in such ground states as a systematic sum over conditional expectations, each of which can be ultimately mapped to a one-dimensional Fermi-sea expectation. Various ground-state correlation functions are calculated for the bosonic and fermionic chains with infinite nearest-neighbor repulsion, as well as for a ladder model of spinless fermions with infinite nearest-neighbor repulsion and correlated hopping in three limiting cases. We find that the decays of these correlation functions are governed by surprising power-law exponents.
We develop a procedure which systematically generates all conserved operators in the disordered models of interacting fermions. Among these operators, we identify and count the independent and local integrals of motion (LIOM), which represent the hallmark of the many-body localization (MBL). The method is tested first on the prototype disordered chain of interacting spinless fermions. As expected for full MBL, we find for large enough disorder ${N}_{M}={2}^{M}\ensuremath{-}1$ independent and quasilocal LIOM with support on
M consecutive sites. On the other hand, the study of the disordered Hubbard chain reveals that ${3}^{M}\ensuremath{-}1<{N}_{M}\ensuremath{\lesssim}{4}^{M}/2$, which is less than required for full MBL but much more than in the case of spinless fermions.
We study spinless fermions in a flux threaded AB
2 chain taking into account nearest-neighbor Coulomb interactions. The exact diagonalization of the spinless AB
2 chain is presented in the limiting cases of infinite or zero nearest-neighbor Coulomb repulsion for any filling. Without interactions, the AB
2 chain has a flat band even in the presence of magnetic flux. We show that the respective localized states can be written in the most compact form as standing waves in one or two consecutive plaquettes. We show that this result is easily generalized to other frustrated lattices such as the Lieb lattice. A restricted Hartree-Fock study of the
V/t versus filling phase diagram of the AB
2 chain has also been carried out. The validity of the mean-field approach is discussed taking into account the exact results in the case of infinite repulsion. The ground-state energy as a function of filling and interaction
V is determined using the mean-field approach and exactly for infinite or zero
V. In the strong coupling limit, two kinds of localized states occur: one-particle localized states due to geometry and two-particle localized states due to interaction and geometry. These localized fermions create open-boundary regions for itinerant carriers. At filling $\ensuremath{\rho}=2/9$ and in order to avoid the existence of itinerant fermions with positive kinetic energy, phase separation occurs between a high-density phase ($\ensuremath{\rho}=2/3$) and a low-density phase ($\ensuremath{\rho}=2/9$) leading to a metal-insulator transition. The ground-state energy reflects such phase separation by becoming linear on filling above
2/9. We argue that for filling near or larger than 2/9, the spectrum of the t-V AB
2 chain can be viewed as a mix of the spectra of Luttinger liquids (LL) with different fillings, boundary conditions, and LL velocities.