We first present a simple proof that for any bipartite lattice at half filling the RKKY interaction is antiferromagnetic between impurities on opposite (i.e., A and B) sublattices and is ferromagnetic between impurities on the same sublattices. This result is valid on all length scales. We then focus on the honeycomb lattice and examine the theorem in the long distance limit by performing the low energy calculation using Dirac electrons. To find the universal (cutoff free) result we perform the calculation in smooth cutoff schemes, as we show that the calculation based on a sharp cutoff leads to wrong results. We also find the long distance behavior of the RKKY interaction between "plaquette" impurities in both coherent and incoherent regimes.
Carrier-mediated Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction plays an important role in itinerant magnetism. There have been intense interest on its general trend on bipartite lattice with particle-hole symmetry. In particular, recently fabricated graphene is well described by the honeycomb lattice within tight-binding approximation. We use SUSY quantum mechanics to study the RKKY interaction on bipartite lattices. The SUSY structure naturally differentiate the zero modes and those paired states at finite energies. The significant role of zero modes is largely ignored in previous literatu…
The 2D half-filled Kondo lattice model with exchange J and nearest neighbor hopping t is considered. It is shown that this model belongs to a class of Hamiltonians for which zero-temperature auxiliary field Monte Carlo methods may be efficiently applied. We compute the staggered moment, spin and quasiparticle gaps on lattice sizes up to 12 X 12. The competition between the RKKY interaction and Kondo effect leads to a continuous quantum phase transition between antiferromagnetic and spin-gaped insulators. This transition occurs at J/t = 1.45 \pm 0.05.
Carrier-mediated exchange coupling, known as Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, plays a fundamental role in itinerant ferromagnetism and has great application potentials in spintronics. A recent theorem based on the imaginary-time method shows that the oscillatory RKKY interaction becomes commensurate on bipartite lattice and predicts that the effective exchange coupling is always ferromagnetic for the same sublattice but antiferromagnetic for opposite sublattices. We revisit this important problem by real- and imaginary-time methods and find the theorem misses important contrib…
The emerging and screening of local magnetic moments in solids has been investigated for more than 60 years. Local vacancies as in graphene or in Heavy Fermions can induce decoupled bound states that lead to the formation of local moments. In this paper, we address the puzzling question how these local moments can be screened and what determines the additionally emerging low temperature scale. We review the initial problem for half-filled conduction bands from two complementary perspectives: By a single-particle supercell analysis in the uncorrelated limit and by the Lieb-Mathis theorem for sy…
As a prototype model of antiferromagnetism, we propose a repulsive Hubbard Hamiltonian defined on a graph $Ł={\cal A}\cup{\cal B}$ with ${\cal A}\cap {\cal B}=\emptyset$ and bonds connecting any element of ${\cal A}$ with all the elements of ${\cal B}$. Since all the hopping matrix elements associated with each bond are equal, the model is invariant under an arbitrary permutation of the ${\cal A}$-sites and/or of the ${\cal B}$-sites. This is the Hubbard model defined on the so called $(N_{A},N_{B})$-complete-bipartite graph, $N_{A}$ ($N_{B}$) being the number of elements in ${\cal A}$ (${\cal…
We investigate the finite-temperature properties of an Anderson lattice with regularly depleted impurities. The physics of this model is ruled by two different magnetic exchange mechanisms: conventional Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction at weak hybridization strength V and a novel inverse indirect magnetic exchange (IIME) at strong V, both favoring a ferromagnetic ground state. The stability of ferromagnetic order against thermal fluctuations is systematically studied by static mean-field theory for an effective low-energy spin-only model emerging perturbatively in the strong-co…
As a prototype model of antiferromagnetism, we propose a repulsive Hubbard Hamiltonian defined on a graph $Ł={\cal A}\cup{\cal B}$ with ${\cal A}\cap {\cal B}=\emptyset$ and bonds connecting any element of ${\cal A}$ with all the elements of ${\cal B}$. Since all the hopping matrix elements associated with each bond are equal, the model is invariant under an arbitrary permutation of the ${\cal A}$-sites and/or of the ${\cal B}$-sites. This is the Hubbard model defined on the so called $(N_{A},N_{B})$-complete-bipartite graph, $N_{A}$ ($N_{B}$) being the number of elements in ${\cal A}$ (${\cal…
We present a detailed numerical study of spin and charge dynamics of the two-dimensional Kondo lattice model with hopping t and exchange J. At T=0 and J > 0, the competition between the RKKY interaction and Kondo effect triggers a quantum phase transition between magnetically ordered and disordered insulators: J_c/t = 1.45(5). The quasiparticle gap scales as |J|. S(q,ω), evolves smoothly from its strong coupling form with spin gap at q = (π,π) to a spin wave form. At J>0, A(\vec{k},ω) shows a dispersion relation following that of hybridized bands. For J < J_c this feature is supplemented by sh…
We study a one-dimensional SU(N) Hubbard model with an attractive on-site interaction and $N>2$ at half-filling on the bipartite lattice using density-matrix renormalization-group method and a perturbation theory. We find that the ground state of the SU(N) Hubbard model is a charge density wave state with two-fold degeneracy. All the excitations are found to be gapful, resulting in an insulating ground state, on contrary to that in the SU(2) case. Moreover, the charge gap is equal to the Cooperon gap, which behaves as $-2Nt^2/(N-1)U$ in the strong coupling regime. However, the spin gap $Δ_{s}$…
We solve the sign problem in a particle-hole symmetric spin-polarized fermion model on bipartite lattices using the idea of fermion bags. The solution can be extended to a class of models at half filling but without particle-hole symmetry. Attractive Hubbard models with an odd number of fermion species can also be solved. The new solutions should allow us to study quantum phase transitions that have remained unexplored so far due to sign problems.
We present an exact diagonalization study of the half-filled Hubbard model on bipartite quasi-one-dimensional lattices. In particular, we emphasize the dependence of the ferrimagnetic ground state properties, and its associated magnetic excitations, on the Coulomb repulsion U.
We investigate the existence of quantum disentangled liquid (QDL) states in the half-filled Hubbard model on bipartite lattices. In the one dimensional case we employ a combination of integrability and strong coupling expansion methods to argue that there are indeed finite energy-density eigenstates that exhibit QDL behaviour in the sense of J. Stat. Mech. P10010 (2014). The states exhibiting the QDL property are atypical in the sense that while their entropy density is non-zero, it is smaller than that of thermal states at the same energy density. We argue that for U >> t these latter thermal…
In order to study the interplay between Kondo and Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, we calculate the spin-spin correlation functions between two Kondo impurities coupled to different sites of a half-filled open Hubbard chain. Using the density-matrix renormalization group (DMRG), we re-examine the exponents for the power-law decay of the correlation function between the two impurity spins as a function of the antiferromagnetic coupling J, the Hubbard interaction U, and the distance R between the impurities. The exponents for finite systems obtained in this work deviate from pre…
In 1989, Lieb proved two theorems about the Hubbard model. One showed that the ground state of the attractive model was a spin singlet state ($S=0$), was unique, and was positive definite. The other showed that the ground state of the repulsive model on a bipartite lattice at half-filling has a total spin given by $|(N_A-N_B)/2|$, corresponding to the difference of the number of lattice sites on the two sublattices divided by two. In the mid to late 1990's, Shen extended these proofs to show that the pseudospin of the attractive model was minimal until the electron number equaled $2N_A$ where …
With current research efforts shifting towards the 4$d$ and 5$d$ transition metal oxides, understanding the evolution of the electronic and magnetic structure as one moves away from 3$d$ materials is of critical importance. Here we perform X-ray spectroscopy and electronic structure calculations on $A$-site ordered perovskites with Cu in the $A$-site and the $B$-sites descending along the 9th group of the periodic table to elucidate the emerging properties as $d$-orbitals change from partially filled 3$d$, 4$d$, to 5$d$. The results show that when descending from Co to Ir the charge transfers …
We have studied the Hubbard model with bond-charge interaction on a triangular lattice for a half-filled band. At the point of particle-hole symmetry the model could be analyzed in detail in two opposite regimes of the parameter space. Using a real space renormalization group we calculate the ground state energy and the local moment over the whole parameter space. The RG results obey the exact results in the respective limits. In the intermediate region of the parameter space the RG results clearly show the effects of the non-bipartite geometry of the lattice as well as the absence of symmetry…
We describe here a quantum simulator of extended bipartite Hubbard model with broken sublattice symmetry. The simulator consists of a structured lateral gate confining two dimensional electrons in a quantum well into artificial minima arranged in a hexagonal lattice. The sublattice symmetry breaking is generated by forming an artificial triangular graphene quantum dot (ATGQD) with zigzag edges. The resulting extended Hubbard model generates tunable ratio of tunneling strength to electron-electron interactions and of sublattice symmetry with control over shape. The validity of the simulator is …
We introduce a half-filled Hamiltonian of spin-half lattice fermions that can be studied with the efficient meron-cluster algorithm in any dimension. As with the usual bipartite half-filled Hubbard models, the naïve $U(2)$ symmetry is enhanced to $SO(4)$. On the other hand our model has a novel spin-charge flip ${\mathbb Z}^C_2$ symmetry which is an important ingredient of free massless fermions. In this work we focus on one spatial dimension, and show that our model can be viewed as a lattice-regularized two-flavor chiral-mass Gross-Neveu model. Our model remains solvable in the presence of t…
