A systematic interpolatory method for an impurity in a one-dimensional fermionic background

We explore a new numerical method for studying one-dimensional quantum systems in a trapping potential. We focus on the setup of an impurity in a fermionic background, where a single distinguishable particle interacts through a contact potential with a number of identical fermions. We can accurately describe this system, for various particle numbers, different trapping potentials and arbitrary finite repulsion, by constructing a truncated basis containing states at both zero and infinite repulsion. The results are compared with matrix product states methods and with the analytical result for two particles in a harmonic well.

Sorting Fermionization from Crystallization in Many-Boson Wavefunctions

Fermionization is what happens to the state of strongly interacting repulsive bosons interacting with contact interactions in one spatial dimension. Crystallization is what happens for sufficiently strongly interacting repulsive bosons with dipolar interactions in one spatial dimension. Crystallization and fermionization resemble each other: in both cases – due to their repulsion – the bosons try to minimize their spatial overlap. We trace these two hallmark phases of strongly correlated one-dimensional bosonic systems by exploring their ground state properties using the one- and two-body density matrix. We solve the N-body Schrödinger equation accurately and from first principles using the multiconfigurational time-dependent Hartree for bosons (MCTDHB) and for fermions (MCTDHF) methods. Using the one- and two-body density, fermionization can be distinguished from crystallization in position space. For N interacting bosons, a splitting into an N-fold pattern in the one-body and two-body density is a unique feature of both, fermionization and crystallization. We demonstrate that this splitting is incomplete for fermionized bosons and restricted by the confinement potential. This incomplete splitting is a consequence of the convergence of the energy in the limit of infinite repulsion and is in agreement with complementary results that we obtain for fermions using MCTDHF. For crystalline bosons, in contrast, the splitting is complete: the interaction energy is capable of overcoming the confinement potential. Our results suggest that the spreading of the density as a function of the dipolar interaction strength diverges as a power law. We describe how to distinguish fermionization from crystallization experimentally from measurements of the one- and two-body density.

STRUCTURAL DISTORTION IN LUDWIGITES

Structural distortion in a three-leg-ladder is studied in connection with Ludwigites, in particular the Fe and Co homometallic ones. Static impurities in t2g-orbitals as infinite repulsion potentials randomly located in the three-leg-ladder and a Su–Schrieffer–Heeger like tight-binding Hamiltonian are proposed and discussed. It is found that such potentials block itinerant electrons and diminish a structural staggered order parameter, related with structural distortion, as 3-M being M the number of impurities. This diminution is in detriment of Peierls like distortion that occurs in these ladders as in the case of Fe -Ludwigite. On the other hand, this diminution could explain the lack of structural distortion as in the case of Co -Ludwigite.

On the Ground State of Hubbard Model with Strong Repulsion

For square (cubic) Hubbard lattice with infinite repulsion energy U exact result has been obtained: the ferromagnetic state with maximum total spin is not the ground state of system, if the hole number is equal to two.