Spin-spin Correlation Function Research Articles

Magnetic impurity in a Weyl semimetal

We utilize the variational method to study the Kondo screening of a spin-$1/2$ magnetic impurity in a three-dimensional (3D) Weyl semimetal with two Weyl nodes along the $k_z$-axis. The model reduces to a 3D Dirac semimetal when the separation of the two Weyl nodes vanishes. When the chemical potential lies at the nodal point, $\mu=0$, the impurity spin is screened only if the coupling between the impurity and the conduction electron exceeds a critical value. For finite but small $\mu$, the impurity spin is weakly bound due to the low density of state, which is proportional to $\mu^2$, contrary to that in a 2D Dirac metal such as graphene and 2D helical metal where the density of states is proportional to $|\mu|$. The spin-spin correlation function $J_{uv}(\mathbf{r})$ between the spin $v$-component of the magnetic impurity at the origin and the spin $u$-component of a conduction electron at spatial point $\mathbf{r}$, is found to be strongly anisotropic due to the spin-orbit coupling, and it decays in the power-law. The main difference of the Kondo screening in 3D Weyl semimetals and in Dirac semimetals is in the spin $x$- ($y$-) component of the correlation function in the spatial direction of the $z$-axis.

Fractional Wigner Crystal in the Helical Luttinger Liquid.

The properties of the strongly interacting edge states of two dimensional topological insulators in the presence of two-particle backscattering are investigated. We find an anomalous behavior of the density-density correlation functions, which show oscillations that are neither of Friedel nor of Wigner type: they, instead, represent a Wigner crystal of fermions of fractional charge e/2, with e the electron charge. By studying the Fermi operator, we demonstrate that the state characterized by such fractional oscillations still bears the signatures of spin-momentum locking. Finally, we compare the spin-spin correlation functions and the density-density correlation functions to argue that the fractional Wigner crystal is characterized by a nontrivial spin texture.

Universal single-frequency oscillations in a quantum impurity system after a local quench

Long-lived single-frequency oscillations in the local non-equilibrium dynamics of a quantum many-body system is an exceptional phenomenon. In fact, till now, it has never been observed, nor predicted, for the physically relevant case where a system is prepared to be quenched from one quantum phase to another. Here we show how the quench dynamics of the entanglement spectrum may reveal the emergence of such oscillations in a correlated quantum system with Kondo impurities. The oscillations we find are characterized by a single frequency. This frequency is independent of the amount of energy released by the local quench, and scales with the inverse system size. Importantly, the quench-independent frequency manifests itself also in local observables, such as the spin-spin correlation function of the impurities.

Slope-reversed Mott transition in multiorbital systems

We examine finite-temperature phase transitions in the two-orbital Hubbard model with different bandwidths by means of the dynamical mean-field theory combined with the continuous-time quantum Monte Carlo method. It is found that there emerges a peculiar slope-reversed first-order Mott transition between the orbital-selective Mott phase and the Mott insulator phase in the presence of Ising-type Hund's coupling. The origin of the slope-reversed phase transition is clarified by the analysis of the temperature dependence of the energy density. It turns out that the increase of Hund's coupling lowers the critical temperature of the slope-reversed Mott transition. Beyond a certain critical value of Hund's coupling the first-order transition turns into a finite-temperature crossover. We also reveal that the orbital-selective Mott phase exhibits frozen local moments in the wide orbital, which is demonstrated by the spin-spin correlation functions.

Magnetism of ordered and disorderedNi2MnAlfull Heusler compounds

Based on ab initio calculations and Monte Carlo simulations, we present a systematic study of the magnetic ground state and finite temperature magnetism of ordered and disordered ${\mathrm{Ni}}_{2}\mathrm{MnAl}$ full Heusler compounds. By increasing the degree of the long-range chemical disorder between the Mn and Al sublattices, the magnetic order progressively changes from the ferromagnetic state in the ordered $L{2}_{1}$ phase toward a fully compensated antiferromagnetic state in the disordered $B2$ phase and we also conclude that the Ni atoms exhibit induced moments. We determine the Mn-Mn interactions by using the magnetic force theorem and find dominating, but rather weak ferromagnetic couplings in the ordered $L{2}_{1}$ phase. We used a recently proposed renormalization technique to include the weak Ni moments into the spin model, which indeed remarkably increased the nearest-neighbor Mn-Mn interaction. In accordance with the total energy calculations, in the disordered compounds, strong antiferromagnetic site-antisite Mn-Mn interactions appear. Determining the spin-spin correlation functions from Monte Carlo simulations, we conclude that above the transition temperature, short-range antiferromagnetic correlations prevail between the Mn atoms. In view of the potential application of disordered ${\mathrm{Ni}}_{2}\mathrm{MnAl}$ as a room temperature antiferromagnet, we calculate the magnetic anisotropy energies of tetragonally distorted samples in the $B2$ phase and find that they are smaller by two orders in magnitude than in the frustrated antiferromagnet ${\mathrm{IrMn}}_{3}$.

Evidence of quantum dimer excitations inSr3Ir2O7

The magnetic excitation spectrum in the bilayer iridate Sr$_3$Ir$_2$O$_7$ has been investigated using high-resolution resonant inelastic x-ray scattering (RIXS) performed at the iridium L$_3$ edge and theoretical techniques. A study of the systematic dependence of the RIXS spectrum on the orientation of the wavevector transfer, $\mathbf{Q}$, with respect to the iridium-oxide bilayer has revealed that the magnon dispersion is comprised of two branches well separated in energy and gapped across the entire Brillouin zone. Our results contrast with those of an earlier study which reported the existence of a single dominant branch. While these earlier results were interpreted as two overlapping modes within a spin-wave model of weakly coupled iridium-oxide planes, our results are more reminiscent of those expected for a system of weakly coupled dimers. In this latter approach the lower and higher energy modes find a natural explanation as those corresponding to transverse and longitudinal fluctuations, respectively. We have therefore developed a bond-operator theory which describes the magnetic dispersion in Sr$_3$Ir$_2$O$_7$ in terms of quantum dimer excitations. In our model dimerisation is produced by the leading Heisenberg exchange, $J_c$, which couples iridium ions in adjacent planes of the bilayer. The Hamiltonian also includes in plane exchange, $J$, as well as further neighbour couplings and relevant anisotropies. The bond-operator theory provides an excellent account of the dispersion of both modes, while the measured $\mathbf{Q}$ dependence of the RIXS intensities is in reasonable qualitative accord with the spin-spin correlation function calculated from the theory. We discuss our results in the context of the quantum criticality of bilayer dimer systems in the presence of anisotropic interactions derived from strong spin-orbit coupling.

Signatures of pairing and spin-orbit coupling in correlation functions of Fermi gases

We derive expressions for spin and density correlation functions in the (greatly enhanced) pseudogap phase of spin-orbit coupled Fermi superfluids. Density-density correlation functions are found to be relatively insensitive to the presence of these Rashba effects. To arrive at spin-spin correlation functions we derive new $f$-sum rules, valid even in the absence of a spin conservation law. Our spin-spin correlation functions are shown to be fully consistent with these $f$-sum rules. Importantly, they provide a clear signature of the Rashba band-structure and separately help to establish the presence of a pseudogap.

An Exact Closed Formula of a Spin-spin Correlation Function of the Two-Dimensional Ising Model with Finite Size

Some expressions of spin-spin correlation functions of the two-dimensional Ising model in the thermodynamic limit have been obtained, however, so far, no one correlation function that can show long range order of the model with finite size has been obtained. The purpose of this paper is to fill this gap. We present an exact closed formula for the correlation functions of the farthest pairs of spins in a column of the two-dimensional rectangular Ising model with periodic-free boundary condition and finite size by the spinor analysis method. The concrete expression correct to \(\mathrm {e}^{-LC_{0} }\) order of magnitude of such correlation functions is presented, from which it is shown clearly how long range order emerges as the decrease of the temperature. Some properties are discussed.

Simplex valence-bond crystal in the spin-1 kagome Heisenberg antiferromagnet

We investigate the ground state properties of a spin-1 kagome antiferromagnetic Heisenberg model using tensor-network (TN) methods. We obtain the energy per site {$e_0=-1.41090(2)$ with $D^*=8$ multiplets retained (i.e., a bond dimension of $D=24$), and $e_0=-1.4116(4)$ from large-$D$ extrapolation,} by accurate TN calculations directly in the thermodynamic limit. The symmetry between the two kinds of triangles is spontaneously broken, with a relative energy difference of $\delta \approx$ 19\%, i.e, there is a trimerization (simplex) valence-bond order in the ground state. The spin-spin, dimer-dimer, and chirality-chirality correlation functions are found to decay exponentially with a rather short correlation length, showing that the ground state is gapped. We thus identify the ground state be a simplex valence-bond crystal (SVBC). We also discuss the spin-1 bilinear-biquadratic Heisenberg model on a kagome lattice, and determine its ground state phase diagram. Moreover, we implement non-abelian symmetries, here spin SU(2), in the TN algorithm, which improves the efficiency greatly and provides insight into the tensor structures.

Spin-wave multiple excitations in nanoscale classical Heisenberg antiferromagnets

Monte Carlo and spin dynamics techniques have been used to perform large-scale simulations of the dynamic behavior of a nanoscale, classical, Heisenberg antiferromagnet on a simple-cubic lattice with linear sizes $L\ensuremath{\leqslant}40$ at a temperature below the N\'eel temperature. Nanoparticles are modeled with completely free boundary conditions, i.e., six free surfaces, and nanofilms are modeled with two free surfaces in the spatial $z$ direction and periodic boundaries parallel to the surfaces in the $xy$ direction, which are compared to the ``infinite'' system with periodic boundary conditions. The temporal evolutions of spin configurations were determined numerically from coupled equations of motion for individual spins using a fast spin dynamics algorithm with the fourth-order Suzuki-Trotter decomposition of exponential operators, with initial spin configurations generated by Monte Carlo simulations. The local dynamic structure factor $S(q,\ensuremath{\omega})$ was calculated from the local space- and time-displaced spin-spin correlation function. Multiple excitation peaks for wave vectors within the first Brillouin zone appear in the spin-wave spectra of the transverse component of dynamic structure factor ${S}^{T}(q,\ensuremath{\omega})$ in the nanoscale classical Heisenberg antiferromagnet, which are lacking if periodic boundary conditions are used. With the assumption of $q$-space spin-wave reflections with broken momentum conservation due to free-surface confinements, we successfully explained those spectra quantitatively in the linear dispersion region. Meanwhile, we also observed two unexpected quantized spin-wave excitation modes in the spatial $z$ direction in nanofilms for ${S}^{T}(q,\ensuremath{\omega})$ not expected in bulk systems. The results of this study indicate the presence of unexpected forms of spin-wave excitation behavior that have yet to be observed experimentally but could be directly tested through neutron scattering experiments on nanoscale ${\mathrm{RbMnF}}_{3}$ particles or films.

Quantum Spin Liquid in Spin 1/2J1–J2Heisenberg Model on Square Lattice: Many-Variable Variational Monte Carlo Study Combined with Quantum-Number Projections

The nature of quantum spin liquids is studied for the spin-$1/2$ antiferromagnetic Heisenberg model on a square lattice containing exchange interactions between nearest-neighbor sites, $J_1$, and those between next-nearest-neighbor sites, $J_2$. We perform variational Monte Carlo simulations together with the quantum-number-projection technique and clarify the phase diagram in the ground state together with its excitation spectra. We obtain the nonmagnetic phase in the region $0.4< J_2/J_1\le 0.6$ sandwiched by the staggered and stripe antiferromagnetic (AF) phases. Our direct calculations of the spin gap support the notion that the triplet excitation from the singlet ground state is gapless in the range of $0.4 < J_2/J_1 \le 0.5$, while the gapped valence-bond-crystal (VBC) phase is stabilized for $0.5 < J_2/J_1 \le 0.6$. The VBC order is likely to have the columnar symmetry with a spontaneous symmetry breaking of the $C_{4v}$ symmetry. The power-law behaviors of the spin-spin and dimer-dimer correlation functions in the gapless region are consistent with the emergence of the algebraic quantum-spin-liquid phase (critical phase). The exponent of the spin correlation $\langle S(0)S(r)\rangle \propto 1/r^{z+\eta}$ at a long distance $r$ appears to increase from $z+\eta\sim 1$ at $J_2/J_1\sim0.4$ toward the continuous transition to the VBC phase at $J_1/J_1\sim0.5$. Our results, however, do not fully exclude the possibility of a direct quantum transition between the staggered AF and VBC phases with a wide critical region and deconfined criticality.

Density-matrix renormalization group study of the extended Kitaev-Heisenberg model

We study an extended Kitaev-Heisenberg model including additional anisotropic couplings by using two-dimensional density-matrix renormalization group method. Calculating the gound-state energy, entanglement entropy, and spin-spin correlation functions, we make a phase diagram of the extended Kitaev-Heisenberg model around spin-liquid phase. We find a zigzag antiferromagnetic phase, a ferromagnetic phase, a 120-degree antiferromagnetic phase, and two kinds of incommensurate phases around the Kitaev spin-liquid phase. Furthermore, we study the entanglement spectrum of the model and find that entanglement levels in the Kitaev spin-liquid phase are degenerate forming pairs but those in the magnetically ordered phases are non-degenerate. The Schmidt gap defined as the energy difference between the lowest two levels changes at the phase boundary adjacent to the Kitaev spin-liquid phase. However, we find that phase boundaries between magnetically ordered phases do not necessarily agree with the change of the Schmidt gap.

Upper Bounds on the Critical Temperature of the Ising Model on the Pyrochlore Lattice

A procedure, based on exact relations for the spin-spin correlation function and on rigorous correlation inequalities, is presented and used to obtain upper bounds for the critical temperature of the Ising model on the three dimensional pyrochlore lattice. The exact relations for the correlation functions are constructed from clusters of spins that retain the characteristics of the full model

Magnetic order without tetragonal-symmetry-breaking in iron arsenides: Microscopic mechanism and spin-wave spectrum

Most iron-based superconductors undergo a transition to a magnetically ordered state characterized by staggered stripes of parallel spins. With ordering vectors $(\pi,0)$ or $(0,\pi)$, this magnetic state breaks the high-temperature tetragonal symmetry of the system, which is manifested by a splitting of the lattice Bragg peaks. Remarkably, recent experiments in hole-doped iron arsenides reported an ordered state that displays magnetic Bragg peaks at $(\pi,0)$ and $(0,\pi)$ but remains tetragonal. Despite being inconsistent with a magnetic stripe configuration, this unusual magnetic phase can be described in terms of a double-$\mathbf{Q}$ magnetic structure consisting of an equal-weight superposition of the ordering vectors $(\pi,0)$ and $(0,\pi)$. Here we show that a non-collinear double-$\mathbf{Q}$ magnetic configuration, dubbed \emph{orthomagnetic}, arises naturally within an itinerant three-band microscopic model for the iron pnictides. In particular, we find that strong deviations from perfect nesting and residual interactions between the electron pockets favor the orthomagnetic over the stripe magnetic state. Using an effective low-energy model, we also calculate the spin-wave spectrum of the orthomagnetic state. In contrast to the stripe state, there are three Goldstone modes, manifested in all diagonal and one off-diagonal component of the spin-spin correlation function. The total magnetic structure factor displays two anisotropic spin-wave branches emerging from both $(\pi,0)$ and $(0,\pi)$ momenta, in contrast to the case of domains of stripe order, where only one spin-wave branch emerges from each momentum. We propose that these unique features of the orthomagnetic state can be used to unambiguously distinguish it from the stripe state via neutron scattering experiments, and discuss the implications of its existence to the nature of the magnetism of the iron arsenides.

Phase separation induced by density-spin interaction in one-dimensional extended t-J model

t-J model is one of important theoretical models in the study of high temperature superconductivity. Recent cold molecule experiments indicate that t-J model can be simulated by ultracold polar molecules. In the simulated t-J model, besides long-range dipolar interaction, density-spin interaction has also been introduced. In the present we study the effect of density-spin interaction in the one-dimensional extended t-J model by using the density matrix renormalization group method. We choose three sets of representative parameters, which correspond to three different phases in the ground state phase diagram of t-J model, to calculate the charge and spin density distribution in real space and the structure factor of density-density and spin-spin correlation functions. The results indicate that the nature of the system will not change if the intensity of the density-spin interaction is small, however if the intensity is large enough, the system enters the phase separation, in which the character is quiet different form that of the phase separation in the traditional t-J model.

Variational description of the ground state of the repulsive two-dimensional Hubbard model in terms of nonorthogonal symmetry-projected Slater determinants

The few determinant (FED) methodology, introduced in our previous works for 1D lattices, is here adapted for the repulsive two-dimensional Hubbard model at half-filling and with finite doping fractions. Within this configuration mixing scheme, a given ground state with well defined spin and space group quantum numbers, is expanded in terms of a nonorthogonal symmetry-projected basis determined through chains of variation-after projection calculations. The results obtained for the ground state and correlation energies of half-filled and doped 4$\times$4, 6$\times$6, 8$\times$8, and 10$\times$10 lattices, as well as momentum distributions and spin-spin correlation functions in small lattices, compare well with those obtained using other state-of-the-art approximations. The structure of the intrinsic determinants resulting from the variational strategy is interpreted in terms of defects that encode information on the basic units of quantum fluctuations in the considered 2D systems. The varying nature of the underlying quantum fluctuations, reflected in a transition to a stripe regime for increasing onsite repulsions, is discussed using the intrinsic determinants belonging to a 16$\times$4 lattice with 56 electrons. Such a transition is further illustrated by computing spin-spin and charge-charge correlation functions with the corresponding multireference FED wave functions. In good agreement with previous studies, the analysis of the pairing correlation functions reveals a weak enhancement of the extended $s$-wave and d$_{x^2-y^2}$ pairing modes. Given the quality of results here reported together with those previously obtained for 1D lattices and the parallelization properties of the FED scheme, we believe that symmetry projection techniques are very well suited for building ground state wave functions of correlated electronic systems, regardless of their dimensionality.

Block Lanczos density-matrix renormalization group method for general Anderson impurity models: Application to magnetic impurity problems in graphene

We introduce a block Lanczos (BL) recursive technique to construct quasi-one-dimensional models, suitable for density-matrix renormalization group (DMRG) calculations, from single- as well as multiple-impurity Anderson models in any spatial dimensions. This new scheme, named BL-DMRG method, allows us to calculate not only local but also spatially dependent static and dynamical quantities of the ground state for general Anderson impurity models without losing elaborate geometrical information of the lattice. We show that the BL-DMRG method can be easily extended to treat a multiorbital Anderson impurity model where not only inter- and intraorbital Coulomb interactions but also Hund's coupling and pair hopping interactions are included. We also show that the symmetry adapted BL bases can be utilized, when it is appropriate, to reduce the computational cost. As a demonstration, we apply the BL-DMRG method to three different models for graphene with a structural defect and with a single hydrogen or fluorine absorbed, where a single Anderson impurity is coupled to conduction electrons in the honeycomb lattice. These models include (i) a single adatom on the honeycomb lattice, (ii) a substitutional impurity in the honeycomb lattice, and (iii) an effective model for a single carbon vacancy in graphene. Our analysis of the local dynamical magnetic susceptibility and the local density of states at the impurity site reveals that, for the particle-hole symmetric case at half-filling of electron density, the ground state of model (i) behaves as an isolated magnetic impurity with no Kondo screening, while the ground state of the other two models forms a spin-singlet state where the impurity moment is screened by the conduction electrons. We also calculate the real-space dependence of the spin-spin correlation functions between the impurity site and the conduction sites for these three models. Our results clearly show that, reflecting the presence or absence of unscreened magnetic moment at the impurity site, the spin-spin correlation functions decay as $\ensuremath{\propto}$ ${r}^{\ensuremath{-}3}$, differently from the noninteracting limit ($\ensuremath{\propto}$ ${r}^{\ensuremath{-}2}$), for model (i) and as $\ensuremath{\propto}$ ${r}^{\ensuremath{-}4}$, exactly the same as the noninteracting limit, for models (ii) and (iii) in the asymptotic $r$, where $r$ is the distance between the impurity site and the conduction site. Finally, based on our results, we shed light on recent experiments on graphene where the formation of local magnetic moments as well as the Kondo-like behavior have been observed.

Exact diagonalization study of the spin-1 two-dimensional J1–J3 Heisenberg model on a triangular lattice

The spin-1 Heisenberg model on a triangular lattice with the ferromagnetic nearest- and antiferromagnetic third-nearest-neighbor exchange interactions, $J_1=-(1-p)J$ and $J_2=pJ$, $J>0$ $ (0 \leq p \leq 1)$, is studied with the use of the SPINPACK code. This model is applicable for the description of the magnetic properties of NiGa$_2$S$_4$. The ground, low-lying excited state energies and spin-spin correlation functions have been found for lattices with N=16 and N=20 sites with the periodic boundary conditions. These results are in qualitative agreement with earlier authors' results obtained with Mori's projection operator technique.

Quantum impurity in a Tomonaga-Luttinger liquid: Continuous-time quantum Monte Carlo approach

We develop a continuous-time quantum Monte Carlo (CTQMC) method for quantum impurities coupled to interacting quantum wires described by a Tomonaga-Luttinger liquid. The method is negative-sign free for any values of the Tomonaga-Luttinger parameter, which is rigorously proved, and thus, efficient low-temperature calculations are possible. Duality between electrons and bosons in one dimensional systems allows us to construct a simple formula for the CTQMC algorithm in these systems. We show that the CTQMC for Tomonaga-Luttinger liquids can be implemented with only minor modifications of previous CTQMC codes developed for impurities coupled to non-interacting fermions. We apply this method to the Kane-Fisher model of a potential scatterer in a spin-less quantum wire and to a single spin coupled with the edge state of a two-dimensional topological insulator assuming an anisotropic XXZ coupling. Various dynamical response functions such as the electron Green's function and spin-spin correlation functions are calculated numerically and their scaling properties are discussed.

Continuous Mott transition in a two-dimensional Hubbard model

We investigate nonmagnetic metal-insulator transition in the 1/5-depleted square lattice Hubbard model at half-filling within the 8-site cellular dynamical mean field theory. We find that a metal-insulator transition without any signatures of the first order transition, a continuous Mott transition, takes place in a certain range of parameters. The nature of the continuous Mott transition is nothing but a Lifshitz transition driven by the on-site Coulomb interaction. The renormalized matrix elements of hoppings and the spin-spin correlation functions reveal that physics of this transition is strong enhancement of the dimerization due to the non-local effects of electron-electron interaction.