Spin-spin Correlation Research Articles

A Combined Selected Configuration Interaction and Many-Body Treatment of Static and Dynamical Correlation in Oligoacenes.

We have combined our adaptive configuration interaction (ACI) [J. B. Schriber and F. A. Evangelista, J. Chem. Phys. 2016, 144, 161106] with a density-fitted implementation of the second-order perturbative multireference-driven similarity renormalization group (DSRG-MRPT2) [K. P. Hannon, C. Li, and F. A. Evangelista, J. Chem. Phys. 2016, 144, 204111]. We use ACI reference wave functions to recover static correlation for active spaces larger than the conventional limit of 18 orbitals. The dynamical correlation is computed using the DSRG-MRPT2 method to yield a complete treatment of electron correlation. We apply the resulting method, ACI-DSRG-MRPT2, to predict singlet-triplet gaps, metrics of open-shell character, and spin-spin correlation functions for the oligoacene series (2-7 rings). Our computations employ active spaces with as many as 30 electrons in 30 orbitals and up to 1350 basis functions, yielding gaps that are in good agreement with available experimental results. Large bases and reference relaxation lead to a significant reduction in the estimated radical character of the oligoacenes, with respect to previous valence-only treatments of correlation effects.

Pinch point singularities of tensor spin liquids

Recently, a new class of three-dimensional spin liquid models have been theoretically discovered, which feature generalized Coulomb phases of emergent symmetric tensor $U(1)$ gauge theories. These ``higher rank'' tensor models are particularly intriguing due to the presence of quasiparticles with restricted mobility, such as fractons. We investigate universal experimental signatures of tensor Coulomb phases. Most notably, we show that tensor Coulomb spin liquids (both quantum and classical) feature characteristic pinch point singularities in their spin-spin correlation functions, accessible via neutron scattering, which can be readily distinguished from pinch points in conventional $U(1)$ spin liquids. These pinch points can thus serve as a crisp experimental diagnostic for such phases. We also tabulate the low-temperature heat capacity of various tensor Coulomb phases, which serves as a useful additional diagnostic in certain cases.

Properties of the spin-liquid phase in the vicinity of the Lifshitz transition from Néel to spin-spiral state in frustrated magnets

Three decades ago Ioffe and Larkin pointed out a generic mechanism for the formation of a gapped spin liquid. In the case when a classical two-dimensional (2D) frustrated Heisenberg magnet undergoes a Lifshitz transition between a collinear N\'eel phase and a spin spiral phase, quantum effects usually lead to the development of a spin-liquid phase sandwiched between the N\'eel and spin spiral phases. In the present work, using field theory techniques, we study properties of this universal spin liquid phase. We examine the phase diagram near the Lifshitz point and calculate the positions of critical points, excitation spectra, and spin-spin correlations functions. We argue that the spin liquid in the vicinity of 2D Lifshitz point (LP) is similar to the gapped Haldane phase in integer-spin 1D chains. We also consider a specific example of a frustrated system with the spiral-N\'eel LP, the $J_1-J_3$ antiferromagnet on the square lattice that manifests the spin liquid behavior. We present numerical series expansion calculations for this model and compare results of the calculations with predictions of the developed field theory.

Ground-State Properties for Bilayer Kitaev Model: Dimer Expansion Study

We study ground state properties in the bilayer Kitaev model by means of the dimer expansion. The existence of parity symmetries in the system reduces the computational cost significantly. This allows us to expand the ground state energy and interlayer spin-spin correlation up to 30th order in the interdimer Kitaev coupling. The numerical calculations clarify that the dimer singlet state is indeed realized in the wide parameter region.

Finite-temperature dynamical correlations for the dimerized spin- 12 chain

We use the density matrix renormalization group method (DMRG) to compute the frequency and momentum resolved spin-spin correlation functions of a dimerized spin-1/2 chain under a magnetic field at finite temperature. The spectral features strongly depend on the regime of the magnetic field. For increasing magnetic fields, the transitions from a gapped spin liquid phase to a Tomonaga-Luttinger liquid, and then to a totally polarized phase, can be identified in the spectra. Compared to the zero temperature case, the finite temperature excitations give rise to additional spectral features that we compute numerically and identify analytically as transitions from thermally excited states. We compute quantitatively the broadening of the dispersion of a single spin-flip excitation due to the temperature and find a strong asymmetric broadening. We discuss the consequences of these findings for neutron experiments on dimerized one dimensional quantum chains.

Cluster mean-field study of the Heisenberg model for CuInVO5

Motivated by the experimental report of unusual low-temperature magnetism in the quasi-one-dimensional magnet ${\mathrm{CuInVO}}_{5}$, we present results of a cluster mean-field study on a spin-$1/2$ Heisenberg model with alternating ferromagnetic and antiferromagnetic nearest-neighbor coupling. We map out the ground-state phase diagrams with varying model parameters, including the effect of an external magnetic field. An unexpected competition between different spin-spin correlations is uncovered. Multiple spin-flop transitions are identified with the help of component-resolved correlation functions. For the material-specific choice of model parameters we discuss the temperature dependence of specific heat and magnetic susceptibility and compare our results with the available experimental data. A detailed account of spin-spin correlations allows us to present a microscopic understanding of the low-temperature magnetic ordering in ${\mathrm{CuInVO}}_{5}$. Most notably, we identify the origin of an extra peak in the low-temperature specific heat data of ${\mathrm{CuInVO}}_{5}$ reported by Hase et al. [Phys. Rev. B 94, 174421 (2016)].

Tests of the standard model in neutron β decay with a polarized neutron and electron and an unpolarized proton

We analyse the electron--energy and angular distribution of the neutron beta decay with polarized neutron and electron and unpolarized proton, calculated in Phys. Rev. C 95, 055502 (2017) within the Standard Model (SM), by taking into account the contributions of interactions beyond the SM. After the absorption of vector and axial vector contributions by the axial coupling constant and Cabibbo-Kobayashi-Maskawa (CKM) matrix element (Bhattacharya et al., Phys. Rev. D 85, 054512 (2012) and so on) these are the contributions of scalar and tensor interactions only. The neutron lifetime, correlation coefficients and their averaged values, and asymmetries of the neutron beta decay with polarized neutron and electron are adapted to the analysis of experimental data on searches of contributions of interactions beyond the SM. Using the obtained results we propose some estimates of the values of the scalar and tensor coupling constants of interactions beyond the SM. We use the estimate of the Fierz interference term "b_F = - 0.0028 +/- 0.0026" by Hardy and Towner (Phys. Rev. C 91, 025501 (2015)), the neutron lifetime "tau_n = 880.2(1.0)s"(Particle Data Group, Chin. Phys. C 40, 100001 (2016)) and the experimental data "N_{\exp} = 0.067 +/- 0.011_{\rm stat.} +/- 0.004_{\rm syst.}" for the averaged value of the correlation coefficient of the neutron-electron spin-spin correlations, measured by Kozela et al. (Phys. Ref. C 85, 045501 (2012)). The contributions of G-odd correlations are calculated and found at the level of 10^{-5} in agreement with the results obtained by Gardner and Plaster (Phys. Rev. C 87, 065504 (2013)).

Unraveling the complex magnetic structure of multiferroic pyroxene NaFeGe2O6 : A combined experimental and theoretical study

Magnetic order and the underlying magnetic model of the multiferroic pyroxene NaFeGe2O6 are systematically investigated by neutron powder diffraction, thermodynamic measurements, density-functional bandstructure calculations, and Monte-Carlo simulations. Upon cooling, NaFeGe2O6 first reveals one-dimensional spin-spin correlations in the paramagnetic state below about 50 K, revealed by magnetic diffuse scattering. The sinusoidal spin-density wave with spins along the a-direction sets in at 13 K, followed by the cycloidal configuration with spins lying in the (ac) plane below 11.6 K. Microscopically, the strongest magnetic coupling runs along the structural chains, J1 ' 12 K, which is likely related to the one-dimensional spin-spin correlations. The interchain couplings J2 ' 3:8K and J3 ' 2:1K are energetically well balanced and compete, thus giving rise to the incommensurate order in sharp contrast to other transition-metal pyroxenes, where one type of the interchain couplings prevails. The magnetic model of NaFeGe2O6 is further completed by the weak single-ion anisotropy along the a-direction. Our results resolve the earlier controversies regarding the magnetic order in NaFeGe2O6 and establish relevant symmetries of the magnetic structures. These results, combined with symmetry analysis, enable us to identify the possible mechanisms of the magnetoelectric coupling in this compound. We also elucidate microscopic conditions for the formation of incommensurate magnetic order in pyroxenes.

Effective low-energy description of the two-impurity Anderson model: RKKY interaction and quantum criticality

We show that the RKKY interaction in the two-impurity Anderson model comprise two contributions: a ferromagnetic part stemming from the symmetrized hybridization functions and an anti-ferromagnetic part. We demonstrate that this anti-ferromagnetic contribution can also be generated by an effective local tunneling term between the two impurities. This tunneling can be analytically calculated for particle-hole symmetric impurities. Replacing the full hybridization functions by the symmetric part and this tunneling term leads to the identical low-temperature fixed point spectrum in the numerical renormalization group. Compensating this tunneling term is used to restore the Varma-Jones quantum critical point between a strong coupling phase and a local singlet phase even in the absence of particle-hole symmetry in the hybridization functions. We analytically investigate the spatial frequencies of the effective tunneling term based on the combination of the band dispersion and the shape of the Fermi surface. Numerical renormalization group calculations provide a comparison of the distance dependent tunneling term and the local spin-spin correlation function. Derivations between the spatial dependency of the full spin-spin correlation function and the textbook RKKY interaction are reported.

Quenches near Ising quantum criticality as a challenge for artificial neural networks

The near-critical unitary dynamics of quantum Ising spin chains in transversal and longitudinal magnetic fields is studied using an artificial neural network representation of the wave function. A focus is set on strong spatial correlations which build up in the system following a quench into the vicinity of the quantum critical point. We compare correlations observed following reinforcement learning of the network states with analytical solutions in integrable cases and tDMRG simulations, as well as with predictions from a semi-classical discrete Truncated Wigner analysis. While the semi-classical approach excells mainly at short times and for small transverse fields, the neural-network representation provides accurate results for a much wider range of parameters. Where long-range spin-spin correlations build up in the long-time dynamics we find qualitative agreement with exact results while quantitative deviations are of similar size as for the semi-classically predicted correlations, and slow convergence is observed when increasing the number of hidden neurons.

Generalized Langevin equation formulation for anomalous diffusion in the Ising model at the critical temperature.

We consider the two- (2D) and three-dimensional (3D) Ising models on a square lattice at the critical temperature T_{c}, under Monte Carlo spin flip dynamics. The bulk magnetization and the magnetization of a tagged line in the 2D Ising model, and the bulk magnetization and the magnetization of a tagged plane in the 3D Ising model, exhibit anomalous diffusion. Specifically, their mean-square displacements increase as power laws in time, collectively denoted as ∼t^{c}, where c is the anomalous exponent. We argue that the anomalous diffusion in all these quantities for the Ising model stems from time-dependent restoring forces, decaying as power laws in time-also with exponent c-in striking similarity to anomalous diffusion in polymeric systems. Prompted by our previous work that has established a memory-kernel based generalized Langevin equation (GLE) formulation for polymeric systems, we show that a closely analogous GLE formulation holds for the Ising model as well. We obtain the memory kernels from spin-spin correlation functions, and the formulation allows us to consistently explain anomalous diffusion as well as anomalous response of the Ising model to an externally applied magnetic field in a consistent manner.

Thermodynamics of the kagome-lattice Heisenberg antiferromagnet with arbitrary spin S

We use a second-order rotational invariant Green's function method (RGM) and the high-temperature expansion (HTE) to calculate the thermodynamic properties, of the kagome-lattice spin-$S$ Heisenberg antiferromagnet with nearest-neighbor exchange $J$. While the HTE yields accurate results down to temperatures of about $T/S(S+1) \sim J$, the RGM provides data for arbitrary $T \ge 0$. For the ground state we use the RGM data to analyze the $S$-dependence of the excitation spectrum, the excitation velocity, the uniform susceptibility, the spin-spin correlation functions, the correlation length, and the structure factor. We found that the so-called $\sqrt{3}\times\sqrt{3}$ ordering is more pronounced than the $q=0$ ordering for all values of $S$. In the extreme quantum case $S=1/2$ the zero-temperature correlation length is only of the order of the nearest-neighbor separation. Then we study the temperature dependence of several physical quantities for spin quantum numbers $S=1/2,1,\dots,7/2$. As increasing $S$ the typical maximum in the specific heat and in the uniform susceptibility are shifted towards lower values of $T/S(S+1)$ and the height of the maximum is growing. The structure factor ${\cal S}(\mathbf{q})$ exhibits two maxima at magnetic wave vectors $\mathbf{q}={\mathbf{Q}_i}, i=0,1,$ corresponding to the $q=0$ and $\sqrt{3}\times\sqrt{3}$ state. We find that the $\sqrt{3}\times \sqrt{3}$ short-range order is more pronounced than the $q=0$ short-range order for all temperatures $T \ge 0$. For the spin-spin correlation functions, the correlation lengths and the structure factors, we find a finite low-temperature region $0 \le T < T^*\approx a/S(S+1)$, $a \approx 0.2$, where these quantities are almost independent of $T$.

Interhole correlation and phase separation in t-J model

Interhole and interelectron correlations as well as a transition to phase separation in the t-J model near half filling are reconsidered using a variational Monte Carlo method. As a trial wave function, we use a state that can simultaneously represent a d-wave superconducting and antiferromagnetic (AF) orders and allows for nearest-neighbor hole-hole and spin-spin correlation factors and band renormalization effects. It is found that a transition occurs at J = JPS ∼ 2.5t for the doping rates δ = 0.08 and 0.20 from a seemingly uniform state to phase separation (J > JPS) of singly occupied sites and empty sites. For J < JPS, where the values used for cuprate superconductors (0.25 ≲ J/t ≲ 0.5) are included, the interhole correlation is always repulsive. This result is negative to an intuitive picture for cuprates: Two holons coherently move in the background of AF orders.

Importance of orbital fluctuations for the magnetic dynamics in the heavy-fermion compound SmB6

The emergent dynamical processes associated with magnetic excitations in heavy-fermion SmB$_6$ are investigated. By imposing multiorbital interactions on a first-principles model, we find the interplay between spin and orbital fluctuations in the $f$ manifold is highly sensitive to local correlations. The magnetic phase diagram constructed at zero temperature reveals quantum critical features with the existence of several competing phases. Within the random phase approximation, we perform a comprehensive study of the spin-spin correlation function, and our results agree with neutron scattering experiments. Spectral weight analysis shows the low energy spin excitations are selectively accompanied by orbital fluctuations, indicating a non-trivial entanglement between the spin and orbital degree of freedom driven by relativistic couplings.

Coupled charge and spin dynamics in a photoexcited doped Mott insulator

Using a nonequilibrium implementation of the extended dynamical mean field theory (EDMFT) we simulate the relaxation after photo excitation in a strongly correlated electron system with antiferromagnetic spin interactions. We consider the $t$-$J$ model and focus on the interplay between the charge- and spin-dynamics in different excitation and doping regimes. The appearance of string states after a weak photo excitation manifests itself in a nontrivial scaling of the relaxation time with the exchange coupling and leads to a correlated oscillatory evolution of the kinetic energy and spin-spin correlation function. A strong excitation of the system, on the other hand, suppresses the spin correlations and results in a relaxation that is controlled by hole scattering. We discuss the possibility of detecting string states in optical and cold atom experiments.

Dynamic Spin-Lattice Coupling and Nematic Fluctuations in NaFeAs

We use inelastic neutron scattering to study acoustic phonons and spin excitations in single crystals of NaFeAs, a parent compound of iron pnictide superconductors. NaFeAs exhibits a tetragonal-to-orthorhombic structural transition at $T_s\approx 58$ K and a collinear antiferromagnetic (AF) order at $T_N\approx 45$ K. While longitudinal and out-of-plane transverse acoustic phonons behave as expected, the in-plane transverse acoustic phonons reveal considerable softening on cooling to $T_s$, and then harden on approaching $T_N$ before saturating below $T_N$. In addition, we find that spin-spin correlation lengths of low-energy magnetic excitations within the FeAs layer and along the $c$-axis increase dramatically below $T_s$, and show weak anomaly across $T_N$. These results suggest that the electronic nematic phase present in the paramagnetic tetragonal phase is closely associated with dynamic spin-lattice coupling, possibly arising from the one-phonon-two-magnon mechanism.

Isoscalar and isovector spin response in sd -shell nuclei

The spin magnetic dipole transitions and the neutron-proton spin-spin correlations in $sd-$shell even-even nuclei with $N=Z$ are investigated using shell model wave functions taking into accout enhanced isoscalar (IS) spin-triplet pairing as well as the effective spin operators. It was shown that the IS pairing and the effective spin operators gives a large quenching effect on the IV spin transitions to be consistent with observed data by $(p,p')$ experiments. On the other hand, the observed IS spin strength show much smaller quenching effect than expected by the calculated results. The IS pairing gives a substantial quenching effect on the spin magnetic dipole transitions, especially on the isovector (IV) ones. Consequently, an enhanced isoscalar spin-triplet pairing interaction enlarges the proton-neutron spin-spin correlation deduced from the difference between the isoscalar (IS) and the IV sum rule strengths. The beta-decay rates and the IS magnetic moments of $sd-$shell are also examined in terms of the IS pairing as well as the effective spin operators.

Spin-Ice Thin Films: Large- N Theory and Monte Carlo Simulations

We explore the physics of highly frustrated magnets in confined geometries, focusing on the Coulomb phase of pyrochlore spin ices. As a specific example, we investigate thin films of nearest-neighbor spin ice, using a combination of analytic large-N techniques and Monte Carlo simulations. In the simplest film geometry, with surfaces perpendicular to the [001] crystallographic direction, we observe pinch points in the spin-spin correlations characteristic of a two-dimensional Coulomb phase. We then consider the consequences of crystal symmetry breaking on the surfaces of the film through the inclusion of orphan bonds. We find that when these bonds are ferromagnetic, the Coulomb phase is destroyed by the presence of fluctuating surface magnetic charges, leading to a classical Z_2 spin liquid. Building on this understanding, we discuss other film geometries with surfaces perpendicular to the [110] or the [111] direction. We generically predict the appearance of surface magnetic charges and discuss their implications for the physics of such films, including the possibility of an unusual Z_3 classical spin liquid. Finally, we comment on open questions and promising avenues for future research.

Measurement of entanglement entropy in the two-dimensional Potts model using wavelet analysis.

A method is introduced to measure the entanglement entropy using a wavelet analysis. Using this method, the two-dimensional Haar wavelet transform of a configuration of Fortuin-Kasteleyn (FK) clusters is performed. The configuration represents a direct snapshot of spin-spin correlations since spin degrees of freedom are traced out in FK representation. A snapshot of FK clusters loses image information at each coarse-graining process by the wavelet transform. It is shown that the loss of image information measures the entanglement entropy in the Potts model.

Complex-network description of thermal quantum states in the Ising spin chain

We use network analysis to describe and characterize an archetypal quantum system - an Ising spin chain in a transverse magnetic field. We analyze weighted networks for this quantum system, with link weights given by various measures of spin-spin correlations such as the von Neumann and Renyi mutual information, concurrence, and negativity. We analytically calculate the spin-spin correlations in the system at an arbitrary temperature by mapping the Ising spin chain to fermions, as well as numerically calculate the correlations in the ground state using matrix product state methods, and then analyze the resulting networks using a variety of network measures. We demonstrate that the network measures show some traits of complex networks already in this spin chain, arguably the simplest quantum many-body system. The network measures give insight into the phase diagram not easily captured by more typical quantities, such as the order parameter or correlation length. For example, the network structure varies with transverse field and temperature, and the structure in the quantum critical fan is different from the ordered and disordered phases.