We study the momentum distribution of the electrons in an extended periodic Anderson model, where the interaction, $U_{cf}$, between itinerant and localized electrons is taken into account. In the symmetric half-filled model, due to the increase of t
he interorbital interaction, the $f$ electrons become more and more delocalized, while the itinerancy of conduction electrons decreases. Above a certain value of $U_{cf}$ the $f$ electrons become again localized together with the conduction electrons. In the less than half-filled case, we observe that $U_{cf}$ causes strong correlations between the $f$ electrons in the mixed valence regime.
Tensor network states and specifically matrix-product states have proven to be a powerful tool for simulating ground states of strongly correlated spin models. Recently, they have also been applied to interacting fermionic problems, specifically in t
he context of quantum chemistry. A new freedom arising in such non-local fermionic systems is the choice of orbitals, it being far from clear what choice of fermionic orbitals to make. In this work, we propose a way to overcome this challenge. We suggest a method intertwining the optimisation over matrix product states with suitable fermionic Gaussian mode transformations. The described algorithm generalises basis changes in the spirit of the Hartree-Fock method to matrix-product states, and provides a black box tool for basis optimisation in tensor network methods.
We study the ground-state properties of an extended periodic Anderson model to understand the role of Hunds coupling between localized and itinerant electrons using the density-matrix renormalization group algorithm. By calculating the von Neumann en
tropies we show that two phase transitions occur and two new phases appear as the hybridization is increased in the symmetric half-filled case due to the competition between Kondo-effect and Hunds coupling. In the intermediate phase, which is bounded by two critical points, we found a dimerized ground state, while in the other spatially homogeneous phases the ground state is Haldane-like and Kondo-singlet-like, respectively. We also determine the entanglement spectrum and the entanglement diagram of the system by calculating the mutual information thereby clarifying the structure of each phase.
We investigate the effect of the Coulomb interaction, $U_{cf}$, between the conduction and f electrons in the periodic Anderson model using the density-matrix renormalization-group algorithm. We calculate the excitation spectrum of the half-filled sy
mmetric model with an emphasis on the spin and charge excitations. In the one-dimensional version of the model it is found that the spin gap is smaller than the charge gap below a certain value of $U_{cf}$ and the reversed inequality is valid for stronger $U_{cf}$. This behavior is also verified by the behavior of the spin and density correlation functions. We also perform a quantum information analysis of the model and determine the entanglement map of the f and conduction electrons. It is revealed that for a certain $U_{cf}$ the ground state is dominated by the configuration in which the conduction and f electrons are strongly entangled, and the ground state is almost a product state. For larger $U_{cf}$ the sites are occupied alternatingly dominantly by two f electrons or by two conduction electrons.
The system of ultracold atoms with hyperfine spin $F=3/2$ might be unstable against the formation of quintet pairs if the interaction is attractive in the quintet channel. We have investigated the behavior of correlation functions in a model includin
g only s-wave interactions at quarter filling by large-scale density-matrix renormalization-group simulations. We show that the correlations of quintet pairs become quasi-long-ranged, when the system is partially polarized, leading to the emergence of various mixed superfluid phases in which BCS-like pairs carrying different magnetic moment coexist.
Quantum impurity models describe interactions between some local degrees of freedom and a continuum of non-interacting fermionic or bosonic states. The investigation of quantum impurity models is a starting point towards the understanding of more com
plex strongly correlated systems, but quantum impurity models also provide the description of various correlated mesoscopic structures, biological and chemical processes, atomic physics and describe phenomena such as dissipation or dephasing. Prototypes of these models are the Anderson impurity model, or the single- and multi-channel Kondo models. The numerical renormalization group method (NRG) proposed by Wilson in mid 70s has been used in its original form for a longtime as one of the most accurate and powerful methods to deal with quatum impurity problems. Recently, a number of new developments took place: First, a spectral sum-conserving density matrix NRG approach (DM-NRG) has been developed, which has also been generalized for non-Abelian symmetries. In this manual we introduce some of the basic concepts of the NRG method and present recently developed Flexible DM-NRG code. This code uses user-defined non-Abelian symmetries dynamically, computes spectral functions, expectation values of local operators for user-defined impurity models. The code can also use a uniform density of states as well as a user-defined density of states. The current version of the code assumes fermionic baths and it uses any number of U(1), SU(2) charge SU(2) or Z(2) symmetries. The Flexible DM-NRG code can be downloaded from http://www.phy.bme.hu/~dmnrg
The commensurate $p/q$-filled $n$-component Hubbard chain was investigated by bosonization and high-precision density-matrix renormalization-group analysis. It was found that depending on the relation between the number of components $n$, and the fil
ling parameter $q$, the system shows metallic or insulating behavior, and for special fillings bond-ordered (dimerized, trimerized, tetramerized etc.) ground state develops in the insulating phase. A mean-field analysis shows that this bond ordering is a direct consequence of the spin-exchange interaction, which plays a crucial role in the one-parameter Hubbard model -- not only for infinite Coulomb repulsion, but for intermediate values as well.
The one-dimensional repulsive SU$(n)$ Hubbard model is investigated analytically by bosonization approach and numerically using the density-matrix renormalization-group (DMRG) method for $n=3,4$, and 5 for commensurate fillings $f=p/q$ where $p$ and
$q$ are relatively prime. It is shown that the behavior of the system is drastically different depending on whether $q>n$, $q=n$, or $q<n$. When $q>n$, the umklapp processes are irrelevant, the model is equivalent to an $n$-component Luttinger liquid with central charge $c=n$. When $q=n$, the charge and spin modes are decoupled, the umklapp processes open a charge gap for finite $U>0$, whereas the spin modes remain gapless and the central charge $c=n-1$. The translational symmetry is not broken in the ground state for any $n$. On the other hand, when $q<n$, the charge and spin modes are coupled, the umklapp processes open gaps in all excitation branches, and a spatially nonuniform ground state develops. Bond-ordered dimerized, trimerized or tetramerized phases are found depending on the filling.
