We have used exact numerical diagonalization to study the excitation spectrum and the dynamic spin correlations in the
s=1/2 next-next-nearest-neighbor Heisenberg antiferromagnet on the square lattice, with additional four-spin ring exchange from higher-order terms in the Hubbard expansion. We have varied the ratio between Hubbard model parameters
t/U to obtain different relative strengths of the exchange parameters, while keeping electrons localized. The Hubbard model parameters have been parametrized via an effective ring exchange coupling
Jr, which have been varied between
0J and 1.
5J. We find that ring exchange induces a quantum phase transition from a $(\ensuremath{\pi},\ensuremath{\pi})$ ordered state to a $(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$ ordered state. This quantum critical point is reduced by quantum fluctuations from its mean-field value of
Jr/J=2 to a value of $\ensuremath{\sim}1.1$. At the quantum critical point, the dynamical correlation function shows a pseudocontinuum at
q values between the two competing ordering vectors.
The system of several
(N) quantum dots coupled in parallel to the same single-mode conduction channel can be modeled as a single-channel
N-impurity Anderson model. Using the generalized Schrieffer-Wolff transformation we show that near the particle-hole symmetric point, the effective Hamiltonian in the local moment regime is the
N-impurity
S=1∕2 Kondo model. The conduction-band-mediated RKKY exchange interaction between the dots is ferromagnetic and at intermediate temperatures locks the moments into a maximal spin
S=N∕2 ground state. We provide an analytical estimate for the RKKY interaction. At low temperatures the spin is partially screened by the conduction electrons to $N∕2\ensuremath{-}1∕2$ due to the Kondo effect. By comparing accurate numerical renormalization group results for magnetic susceptibility of the
N-impurity Anderson model to the exact Bethe ansatz results of a
S=N∕2 SU(2) Kondo system we show that at low-temperature the quantum dots can be described by the effective
S=N∕2 Kondo model. Moreover, the Kondo temperature is independent of the number of impurities
N. We demonstrate the robustness of the spin
N∕2 ground state as well as of the associated
S=N∕2 Kondo effect by studying the stability of the system with respect to various experimentally relevant perturbations. We finally explore various quantum phase transitions driven by these perturbations.
The goal of this book is the investigation of physical effects at low energies caused by magnetic impurity adatoms, coupled to a small non-magnetic metallic substrate surface. Such systems can be understood with help of multi-impurity Kondo models, describing the substrate as a tight-binding model of finite-size and the impurities as quantum spins, which are antiferromagnetically coupled locally to their respective substrate sites. Focusing on one-dimensional finite-size systems with open boundary conditions at half-filling numerical exact diagonalisation and the variation of matrix product states (VMPS) method are used for the investigation. It is the aim to study finite-size effects in different regimes of the magnetic exchange interaction. For example due to the finite size of the system, the interplay of the Kondo effect and the indirect magnetic Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction between impurity spins is site dependent and non-trivial for at least three impurity Kondo systems. Furthermore evidence for an unconventional and novel magnetic coupling mechanism, causing magnetic order in the actually non-magnetic substrate, due to inverse indirect magnetic exchange, will be given.
The four-spin operators are suspected to have a significant amplitude and an impact on the collective properties in spin ladders and magnetic two-dimensional lattices. They originate from cyclic circulation of electrons (ring currents). Starting from a simple Hubbard Hamiltonian one may establish their form from a fourth order expansion of quasidegenerate perturbation theory. This form slightly deviates from the generally assumed biquadratic expression. From a quantitative point of view, their amplitude can be assessed from accurate ab initio explicitly correlated wave functions and energies on embedded clusters. The present work shows that symmetry-broken density functional theory calculations may also provide estimates of the four-body operator amplitudes, but reliable results require the use of a large Fock component in the exchange functional.
We consider a finite two dimensional XY spin model. The model consists of a set of seven localized spin- 12 particles in a two dimensional triangular lattice coupled through nearest neighbor exchange interaction in presence of an external magnetic field. We study the effect of a single impurity spin coupled to its nearest neighbor through an exchange interaction J′ on the pairwise entanglement between the different spins in the lattice. We found that when the spin is located at a border site the entanglement between the impurity and its nearest neighbors increases monotonically with J′ reaching a saturation value that depends on the magnetic field strength h. On the other hand the entanglement with the next nearest spins shows a critical behavior where the entanglement increases and then decreases rapidly until it vanishes. The critical coupling value at which the entanglement vanishes increases as h increases. Studying the entanglement between two spins excluding the impurity show that while the entanglement between two spins coupled to the impurity reach a saturation value as J′ increases, it vanishes for spins not coupled to the impurity. Furthermore studying the effect of a central impurity show that the entanglement between nearest neighbor and next nearest neighbor spins reaches an asymptotic value as J′ increases. Interestingly it was demonstrated that the impurity can be used as a switch to control the entanglement between different spins in the lattice turning it on and off.
We study the emergence of magnetic order in localized spins that interact solely through their coupling to a Kitaev-type spin liquid. Using three toy models – the Kitaev model, the Yao–Lee model, and a square-lattice generalization of the Kitaev model – we calculate the effective exchange Hamiltonians mediated by the fractionalized excitations of these spin liquids. This setup is analogous to a Kondo lattice model, where conduction electrons are replaced by itinerant Majorana fermions. In the Kitaev model, our results show that the lowest-order perturbation theory generates short-range interactions with modified couplings and extending to sixth order introduces longer-range interactions while preserving the quantum spin-liquid ground state . Models involving more Majorana flavors on honeycomb and square lattices exhibit more complex behavior. The honeycomb Yao–Lee model with three flavors of itinerant Majorana fermions generates long-range RKKY-type interactions, leading to antiferromagnetic order and partial gapping of the Majorana fermion spectrum. In contrast, the square-lattice model produces a combination of anisotropic short- and long-range interactions, which can give rise to either a dimerized quantum paramagnetic state or an Ising antiferromagnet, depending on the parameters. These results illustrate the rich variety of magnetic orders that can be mediated by Kitaev-type spin liquids.