Simple approach for the two-terminal conductance through interacting clusters

We present a new method for the determination of the two-terminal differential conductance through an interacting cluster, where one maps the interacting cluster into a non-interacting cluster of $M$ independent sites (where $M$ is the number of cluster states with one particle more or less than the ground state of the cluster), with different onsite energy and connected to the leads with renormalized hoppings constants. The onsite energies are determined from the one-particle (one-hole) excitations of the interacting cluster and the hopping terms are given by the overlap between the interacting $N$ particle ground state and the one-particle (one-hole) excitations of the interacting cluster with $N$-1 ($N$+1) particles. The conductance is obtained from the solution of a system of $M$+2 coupled linear equations. We apply this method to the case of the conductance of spinless fermions through an AB$_2$ ring taking into account nearest neighbors interactions. We discuss the effects of interactions on the zero frequency dipped conductance peak characteristic of the non-interacting AB$_2$ ring as well as the consequences of a particle number jump that occurs as the gate potential is varied

Generalization of Zak's phase for lattice models with non-centered inversion symmetry axis

We show how the presence of inversion symmetry in a one-dimensional (1D) lattice model is not a sufficient condition for a quantized Zak's phase. This is only the case when the inversion axis is at the center of the unit cell. When the inversion axis is not at the center, the modified inversion operator within the unit cell gains a k-dependence in some of its matrix elements which adds a correction term to the usual Zak's phase expression1, making it in general deviate from its quantized value. A general expression that recovers a quantized Zak's phase in a lattice model with a unit cell of arbitrary size and arbitrarily positioned inversion axis is provided in this paper, which relates the quantized value with the eigenvalues of a modified parity operator at the inversion invariant momenta.Comment: 4 pages, 2 figures, 2 table

Magnetic phase diagram of the Hubbard model in the Lieb lattice

We study the mean-field phase diagram of the repulsive Hubbard model in the Lieb lattice. Far from half-filling, the most stable phases are paramagnetism for low on-site interaction $U/t$ and ferromagnetism for high $U/t$, as in the case of the mean-field phase diagram of the square lattice Hubbard model obtained by Dzierzawa [\onlinecite{Dzierzawa1992}]. At half-filling, the ground state was found to be ferrimagnetic [a $(\pi,\pi)$ spiral phase], in agreement with a theorem by Lieb [\onlinecite{Lieb1989}]. The total magnetization approaches Lieb's prediction as $U/t$ becomes large. As we move away from half-filling, this ferrimagnetic phase becomes a $(q_1,q_1)$ spiral phase with $q_1 \approx \pi$ and then undergoes a series of first-order phase transitions, $(q_1,q_1) \rightarrow (q_1,q_2) \rightarrow (q_1,0)$, with $q_2 \approx \pi/2$, before becoming ferromagnetic at large $U/t$ or paramagnetic at low $U/t$.Comment: 6 pages, 5 figure

Interacting spinless fermions in a diamond chain

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 $\rho=2/9$ and in order to avoid the existence of itinerant fermions with positive kinetic energy, phase separation occurs between a high-density phase ($\rho=2/3$) and a low-density phase ($\rho=2/9$) 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.Comment: 17 pages, 17 figure

Topological bound states in interacting Su-Schrieffer-Heeger rings

We study two-particle states in a Su-Shrieffer-Heeger (SSH) chain with periodic boundary conditions and nearest-neighbor (NN) interactions. The system is mapped into a problem of a single particle in a two-dimensional (2D) SSH lattice with potential walls along specific edges. The 2D SSH model has a trivial Chern number but a non-trivial Zak's phase, the one-dimensional (1D) topological invariant, along specific directions of the lattice, which allow for the presence of topological edge states. Using center-of-mass and relative coordinates, we calculate the energy spectrum of these two-body states for strong interactions and find that, aside from the expected appearance of doublon bands, two extra in-gap bands are present. These are identified as bands of topological states localized at the edges of the internal coordinate, the relative distance between the two particles. As such, the topological states reported here are intrinsically many-body in what concerns their real space manifestation, having no counterpart in single-particle states derived from effective models. Finally, we compare the effect of Hubbard interactions with that of NN interactions to show how the presence of the topological bound states is specific to the latter case.Comment: 12 pages, 8 figures, 1 tabl

Spin and charge density waves in the Lieb lattice

We study the mean-field phase diagram of the two-dimensional (2D) Hubbard model in the Lieb lattice allowing for spin and charge density waves. Previous studies of this diagram have shown that the mean-field magnetization surprisingly deviates from the value predicted by Lieb's theorem \cite{Lieb1989} as the on-site repulsive Coulomb interaction ($U$) becomes smaller \cite{Gouveia2015}. Here, we show that in order for Lieb's theorem to be satisfied, a more complex mean-field approach should be followed in the case of bipartite lattices or other lattices whose unit cells contain more than two types of atoms. In the case of the Lieb lattice, we show that, by allowing the system to modulate the magnetization and charge density between sublattices, the difference in the absolute values of the magnetization of the sublattices, $m_{\text{Lieb}}$, at half-filling, saturates at the exact value $1/2$ for any value of $U$, as predicted by Lieb. Additionally, Lieb's relation, $m_{\text{Lieb}}=1/2$, is verified approximately for large $U$, in the $n \in [2/3,4/3]$ range. This range includes not only the ferromagnetic region of the phase diagram of the Lieb lattice (see Ref.~\onlinecite{Gouveia2015}), but also the adjacent spiral regions. In fact, in this lattice, below or at half-filling, $m_{\text{Lieb}}$ is simply the filling of the quasi-flat bands in the mean-field energy dispersion both for large and small $U$

Spiral ferrimagnetic phases in the two-dimensional Hubbard model

We address the possibility of spiral ferrimagnetic phases in the mean-field phase diagram of the two-dimensional (2D) Hubbard model. For intermediate values of the interaction $U$ ($6 \lesssim U/t \lesssim 11$) and doping $n$, a spiral ferrimagnetic phase is the most stable phase in the $(n,U)$ phase diagram. Higher values of $U$ lead to a non-spiral ferrimagnetic phase. If phase separation is allowed and the chemical potential $\mu$ replaces the doping $n$ as the independent variable, the $(\mu,U)$ phase diagram displays, in a considerable region, a spiral (for $6 \lesssim U/t \lesssim 11$) and non-spiral (for higher values of $U$) ferrimagnetic phase with fixed particle density, $n=0.5$, reflecting the opening of an energy gap in the mean-field quasi-particle bands.Comment: 8 pages, 3 figure

Edge currents in frustrated Josephson junction ladders

We present a numerical study of quasi-1D frustrated Josephson junction ladders with diagonal couplings and open boundary conditions, in the large capacitance limit. We derive a correspondence between the energy of this Josephson junction ladder and the expectation value of the Hamiltonian of an analogous tight-binding model, and show how the overall superconducting state of the chain is equivalent to the minimum energy state of the tight-binding model in the subspace of one-particle states with uniform density. To satisfy the constraint of uniform density, the superconducting state of the ladder is written as a linear combination of the allowed k-states of the tight-binding model with open boundaries. Above a critical value of the parameter t (ratio between the intra-rung and inter-rung Josephson couplings), the ladder spontaneously develop currents at the edges which spread to the bulk as t is increased until complete coverage is reached. Above a certain value of t, which varies with ladder size (t = 1 for an infinite-sized ladder), the edge currents are destroyed. The value t = 1 corresponds, in the tight-binding model, to the opening of a gap between two bands. We argue that the disappearance of the edge currents with this gap opening is not coincidental, and that this points to a topological origin for these edge current states.Comment: 11 pages, 6 figure

Critical hybridization for the Kondo resonance in gapless systems

We study the Kondo resonance in a spin-1/2 single impurity Anderson model with a gapless conduction band using the equation of motion approach in order to obtain the impurity spectral function. We study two different scenarios for gapless systems: a purely power-law energy dependence of the density of states or a constant density of states with a gapless behavior near the Fermi level. We demonstrate that strong electron-electron correlations lead to a sharp peak in the impurity spectral function in the case of a large exchange coupling ($J>J_{c}$) or equivalently, a strong hybridization ($V>V_{c}$). This Kondo-like peak emerges much below the Fermi level in the case of a strongly depleted density of states. These results are compared with the ones from renormalization group approaches.Comment: 7 pages, 7 figure

Time evolution of localized states in Lieb lattices

We study the slow time evolution of localized states of the open-boundary Lieb lattice when a magnetic flux is applied perpendicularly to the lattice and increased linearly in time. In this system, Dirac cones periodically disappear, reappear and touch the flat band as the flux increases. We show that the slow time evolution of a localized state in this system is analogous to that of a zero-energy state in a three-level system whose energy levels intersect periodically and that this evolution can be mapped into a classical precession motion with a precession axis that rotates as times evolves. Beginning with a localized state of the Lieb lattice, as the magnetic flux is increased linearly and slowly, the evolving state precesses around a state with a small itinerant component and the amplitude of its localized component oscillates around a constant value (below but close to 1), except at multiples of the flux quantum where it may vary sharply. This behavior reflects the existence of an electric field (generated by the time-dependent magnetic field) which breaks the C4 symmetry of the constant flux Hamiltonian.Comment: 7 pages, 2 figure