Spin-spin Correlation Function Research Articles

Quantum phases of spin-1/2 extended XY model in transverse magnetic field

In this study, a spin-1/2 extended anisotropic XY chain has been introduced in which both time reversal and SU(2) symmetries are broken but Z 2 symmetry is preserved. Magnetic and topological phase diagrams in the parameter space have been drawn in the presence of transverse magnetic field. Entanglement measures like mutual information and quantum discord are also evaluated and it indicates that these transitions are second order in nature. Quantum phase transition is noted at zero magnetic field, as well as magnetic long range order is found to withstand magnetic field of any strength. Exact analytic results for spin-spin correlation functions have been obtained in terms of Jordan-Wigner fermionization. Existence of long range magnetic order has been investigated numerically by finding correlation functions as well as the Binder cumulant in the ground state. Dispersion relation, ground state energy, and energy gap are obtained analytically. In order to find the topologically nontrivial phase, sign of Pfaffian invariant and value of winding number have been evaluated. Both magnetic and topological phases are robust against the magnetic field and found to move coercively in the parameter space with the variation of its strength. Long range orders along two orthogonal directions and two different topological phases are found and their one-to-one correspondence has been found. Finally casting the spinless fermions onto Majorana fermions, properties of zero energy edge states are studied. Three different kinds of Majorana pairings are noted. In the trivial phase, next-nearest-neighbor Majorana pairing is found, whereas two different types of nearest-neighbor Majorana pairings are identified in the topological superconducting phase.

Thermodynamics of resonating-valence-bond states toward the understanding of quantum spin liquid phenomena.

A quantum spin liquid (QSL) is a state of matter in which spins do not exhibit magnetic order. In contrast to paramagnets, the spins in a QSL interact strongly, similar to conventional ordered magnets; however the thermodynamic stability of QSLs is rarely studied. Here, the thermodynamic properties of centered hexagon nanoclusters were investigated using the Hubbard model, which was solved using exact numerical diagonalization. The total spin, spin-spin correlation functions, local magnetic moments, charge and spin gaps, and magnetocaloric effect were analyzed for a half-filled band as a function of the ratio between the on-site Coulomb repulsion and electronic hopping (U/t). The centered hexagon nanocluster exhibited an antiferromagnetic (AFM) behavior with exotic magnetic ordering. Resonating-valence-bond (RVB) states were observed for intermediate values of U/t, in which short-range spin-spin correlation functions were suppressed to minimize spin frustration. The AFM order was examined in terms of the Néel-like temperature derived from the temperature dependence of the magnetic susceptibility. An interesting result is that the systems under external magnetic fields exhibited an inverse magnetocaloric effect, which was remarkable for intermediate values of U/t, where the RVB state was observed. Owing to the novel discovery of exotic magnetic ordering in triangular moiré patterns in twisted bilayer graphene (TBLG) systems, these results provide insights into the onset of magnetism and the possible spin liquid states in these graphene moiré materials.

Nonlocal Spin Correlation as a Signature of Ising Anyons Trapped in Vacancies of the Kitaev Spin Liquid.

In the Kitaev chiral spin liquid, Ising anyons are realized as Z_{2} fluxes binding Majorana zero modes, which, however, are thermal excitations with finite decay rates. On the other hand, a lattice vacancy traps a Z_{2} flux even in the ground state, resulting in the stable realization of a Majorana zero mode in a vacancy. We demonstrate that spin-spin correlation functions between two vacancy sites exhibit long-range correlation arising from the fractionalized character of Majorana zero modes, in spite of the strong decay of bulk spin correlations. Remarkably, this nonlocal spin correlation does not decrease as the distance between two vacancy sites increases, signaling Majorana teleportation. Furthermore, we clarify that the nonlocal correlation can be detected electrically via the measurement of nonlocal conductance between two vacancy sites, which is straightforwardly utilized for the readout of Majorana qubits. These findings pave the way to the measurement-based quantum computation with Ising anyons trapped in vacancies of the Kitaev spin liquid.

A plane defect in the 3d O(N) model

It was recently found that the classical 3d O(N)(N) model in the semi-infinite geometry can exhibit an “extraordinary-log” boundary universality class, where the spin-spin correlation function on the boundary falls off as \langle \vec{S}(x) \cdot \vec{S}(0)\rangle \sim \frac{1}{(\log x)^q}〈S→(x)⋅S→(0)⟩∼1(logx)q. This universality class exists for a range 2 ≤N <N_c2≤N<Nc and Monte-Carlo simulations and conformal bootstrap indicate N_c > 3Nc>3. In this work, we extend this result to the 3d O(N)(N) model in an infinite geometry with a plane defect. We use renormalization group (RG) to show that in this case the extraordinary-log universality class is present for any finite N ≥2N≥2. We additionally show, in agreement with our RG analysis, that the line of defect fixed points which is present at N = ∞N=∞ is lifted to the ordinary, special (no defect) and extraordinary-log universality classes by 1/N1/N corrections. We study the “central charge” aa for the O(N)O(N) model in the boundary and interface geometries and provide a non-trivial detailed check of an aa-theorem by Jensen and O’Bannon. Finally, we revisit the problem of the O(N)(N) model in the semi-infinite geometry. We find evidence that at N = N_cN=Nc the extraordinary and special fixed points annihilate and only the ordinary fixed point is left for N > N_cN>Nc.

On the renormalization group fixed point of the two-dimensional Ising model at criticality

We analyze the renormalization group fixed point of the two-dimensional Ising model at criticality. In contrast with expectations from tensor network renormalization (TNR), we show that a simple, explicit analytic description of this fixed point using operator-algebraic renormalization (OAR) is possible. Specifically, the fixed point is characterized in terms of spin-spin correlation functions. Explicit error bounds for the approximation of continuum correlation functions are given.

Finite temperature spin diffusion in the Hubbard model in the strong coupling limit

We investigate finite temperature spin transport in one spatial dimension by considering the spin-spin correlation function of the Hubbard model in the limiting case of infinitely strong repulsion. We find that in the absence of a magnetic field the transport is diffusive, and derive the spin diffusion constant. Our approach is based on asymptotic analysis of a Fredholm determinant representation. The obtained results are in agreement with Generalized Hydrodynamics approach.

A high-performance implementation of atomistic spin dynamics simulations on x86 CPUs

Atomistic spin dynamics simulations provide valuable information about the energy spectrum of magnetic materials in different phases, allowing one to identify instabilities and the nature of their excitations. However, the time cost of evaluating the spin-spin correlation functions in real space increases quadratically as the number of spins N, leading to significant computational effort, making the simulation of large spin systems very challenging. In this work, we propose to use a highly optimized general matrix multiply (GEMM) subroutine to calculate the dynamical spin-spin correlation function that can achieve near-optimal hardware utilization. Furthermore, we fuse the element-wise operations in the calculation of S(q,t) into the in-house GEMM kernel, which results in further performance improvements of 44% - 71% on several relatively large lattice sizes when compared to the implementation that uses the GEMM subroutine in OpenBLAS, which is the state-of-the-art open source library for Basic Linear Algebra Subroutine (BLAS).

Coulomb correlations in a germanide iron-based superconductor: The example of YFe2Ge2

We report results of a detailed theoretical study of the effect of Coulomb correlations on the structural, electronic, and magnetic properties of the non-pnictide iron-based superconductor ${\mathrm{YFe}}_{2}{\mathrm{Ge}}_{2}$. In particular, by employing the density functional theory plus dynamical mean-field theory method ($\mathrm{DFT}+\mathrm{DMFT}$) we perform a structural optimization of the unit-cell volume and the internal coordinate ${z}_{\mathrm{Ge}}$ of Ge. Our results for the lattice parameters obtained by $\mathrm{DFT}+\mathrm{DMFT}$ show a much better agreement with experiment as compared to those calculated by DFT implying the importance of correlation effects. We show that ${\mathrm{YFe}}_{2}{\mathrm{Ge}}_{2}$ is a moderately correlated system with electron-electron correlations being strong enough to renormalize the low-energy band structure but not sufficient to form Hubbard bands, in close analogy to the iron-based pnictides and chalcogenides. The analysis of the local spin-spin correlation function and momentum-dependent spin susceptibility $\ensuremath{\chi}(\mathbf{q})$ indicates the correlation induced formation of short-lived local moments in the Fe ${t}_{2g}$ states and the presence of competing spin fluctuations, in agreement with experiment.

Tunable correlation effects of magnetic impurities by cubic Rashba spin-orbit coupling

We theoretically study the influence of the $k$-cubic Rashba spin-orbit coupling (SOC) on the correlation effects of magnetic impurities by combining the variational method and the Hirsch-Fye quantum Monte Carlo (HFQMC) simulations. Markedly different from the normal $k$-linear Rashba SOC, even a small cubic Rashba term can greatly alter the band structure and induce a Van Hove singularity in a wide range of energy; thus, the single impurity local moment becomes largely tunable. The cubic Rashba SOC adopted in this paper breaks the rotational symmetry, but the host material is still invariant under the operations ${\mathcal{R}}^{z}(\ensuremath{\pi}), {\mathcal{IR}}^{z}(\ensuremath{\pi}/2), {\mathcal{M}}_{xz}, {\mathcal{M}}_{yz}$, where ${\mathcal{R}}^{z}(\ensuremath{\theta})$ is the rotation of angle $\ensuremath{\theta}$ about the $z$ axis, $\mathcal{I}$ is the inversion operator, and ${\mathcal{M}}_{xz}$ (${\mathcal{M}}_{yz}$) is the mirror reflection about the $x\text{\ensuremath{-}}z$ ($y\text{\ensuremath{-}}z$) principal plane. Saliently, various components of spin-spin correlation between the single magnetic impurity and the conduction electrons show three- or sixfold rotational symmetry. This unique feature is due to the triple winding of the spins with a $2\ensuremath{\pi}$ rotation of $\mathbf{k}$, which is a hallmark of the cubic Rashba effect, and can possibly be an identifier to distinguish the cubic Rashba SOC from the normal $k$-linear Rashba term in experiments. Although the cubic Rashba term drastically alters the electronic properties of the host, we find that the spatial decay rate of the spin-spin correlation function remains essentially unchanged. Moreover, the carrier-mediated Ruderman-Kittel-Kasuya-Yosida interactions between two magnetic impurities show twisted features, the ferromagnetic diagonal terms dominate when two magnetic impurities are very close, but the off-diagonal terms become important at long distances.

Quasiparticle dynamics in a quasiperiodic Ising model with temporally fluctuating transverse fields

We study quasiparticle dynamics in a quasiperiodic Ising model with temporally fluctuating transverse fields. Specifically, we calculate the dynamical exponents of the standard deviation of a quasiparticle spreading under a field chosen randomly from binary values $\ifmmode\pm\else\textpm\fi{}h$ at every time interval. We find that the short-time behavior of the dynamical exponents depends on the interval of the temporally fluctuating fields. We also reveal how the quasiparticle dynamics affects the relaxation of spin-spin correlation functions. The dynamics can be explained via the overlap between the eigenvectors of a Hamiltonian with $\ifmmode\pm\else\textpm\fi{}h$.

U(1)-symmetric Gaussian fermionic projected entangled paired states and their Gutzwiller projection

We develop a formalism for constructing particle-number-conserving Gaussian fermionic projected entangled pair states [U(1)-GfPEPS] and show that these states can describe ground states of band insulators and gapless fermions with band touching points. When using them as variational Ans\"{a}tze for two Dirac fermion systems ($\pi$-flux model on the square lattice and $[0,\pi]$-flux model on the kagome lattice), we find that the U(1)-GfPEPS, even with a relatively small bond dimension, can accurately approximate the Dirac Fermi sea ground states. By applying Gutzwiller projectors on top of these U(1)-GfPEPS, we obtain PEPS representation of U(1)-Dirac spin liquid states for spin-1/2 systems. With state-of-the-art tensor network numerics, the critical exponent in the spin-spin correlation function of the Gutzwiller-projected $\pi$-flux state is estimated to be $\eta \approx 1.7$.

Transition from Pauli paramagnetism to Curie-Weiss behavior in vanadium

We study electron correlations and their impact on magnetic properties of bcc vanadium by a combination of density functional and dynamical mean-field theory. The calculated uniform magnetic susceptibility {in bcc structure} is of Pauli type at low temperatures, while it obeys the Curie-Weiss law at higher temperatures. Thus, we qualitatively reproduce the experimental temperature dependence of magnetic susceptibility without introducing the martensitic phase transition. Our results for local spin-spin correlation function and local susceptibility reveal that the Curie-Weiss behavior appears due to partial formation of local magnetic moments, which originate from $t_{2g}$ states and occur due to local spin correlations caused by Hund's rule coupling. At the same time, the fermionic quasiparticles remain well-defined, while the formation of local moments is accompanied by a deviation from the Fermi-liquid behavior. In particular, the self-energy of the $t_{2g}$ states shows the non-analytic frequency dependence, which is a characteristic of the spin-freezing behavior, while the quasiparticle damping changes approximately linearly with temperature in the intermediate temperature range $200$--$700$~K. By analyzing the momentum dependence of static magnetic susceptibility, we find incommensurate magnetic correlations, which may provide a mechanism for unconventional superconductivity at low temperatures.

Many-body theory of phonon-induced spin relaxation and decoherence

First-principles calculations enable accurate predictions of electronic interactions and dynamics. However, computing the electron spin dynamics remains challenging. The spin-orbit interaction causes various dynamical phenomena that couple with phonons, such as spin precession and spin-flip e-ph scattering, which are difficult to describe with current first-principles calculations. In this work, we show a rigorous framework to study phonon-induced spin relaxation and decoherence, by computing the spin-spin correlation function and its vertex corrections due to e-ph interactions. We apply this approach to a model system and develop corresponding first-principles calculations of spin relaxation in GaAs. Our vertex-correction formalism is shown to capture the Elliott-Yafet, Dyakonov-Perel, and strong-precession mechanisms - three independent spin decoherence regimes with distinct physical origins - thereby unifying their theoretical treatment and calculation. Our method is general and enables quantitative studies of spin relaxation, decoherence, and transport in a wide range of materials and devices.

Predicting Phonon-Induced Spin Decoherence from First Principles: Colossal Spin Renormalization in Condensed Matter.

Developing a microscopic understanding of spin decoherence is essential to advancing quantum technologies. Electron spin decoherence due to atomic vibrations (phonons) plays a special role as it sets an intrinsic limit to the performance of spin-based quantum devices. Two main sources of phonon-induced spin decoherence-the Elliott-Yafet and Dyakonov-Perel mechanisms-have distinct physical origins and theoretical treatments. Here, we show calculations that unify their modeling and enable accurate predictions of spin relaxation and precession in semiconductors. We compute the phonon-dressed vertex of the spin-spin correlation function with a treatment analogous to the calculation of the anomalous electron magnetic moment in QED. We find that the vertex correction provides a giant renormalization of the electron spin dynamics in solids, greater by many orders of magnitude than the corresponding correction from photons in vacuum. Our Letter demonstrates a general approach for quantitative analysis of spin decoherence in materials, advancing the quest for spin-based quantum technologies.

Spatial spin-spin correlations of the single-impurity Anderson model with a ferromagnetic bath

We investigate the interplay between the Kondo effect and the ferromagnetism by an one dimension Anderson impurity model with a spin partially polarized bath, using the projective truncation approximation under Lacroix basis.The equal-time spatial spin-spin correlation function (SSCF) is calculated. For the case of spin-unpolarized conduction electrons, it agrees qualitatively with the results from density matrix renormalization group (DMRG). For system with partially spin-polarized conduction electrons, an oscillation in the envelope of SSCF emerges due to the beating of two Friedel oscillations associated to two spin-split Fermi surfaces of conduction electrons. The period is proportional to the inverse of magnetic field $h$. A fitting formula is proposed to perfectly fits the numerical results of SSCF in both the short- and long-range regions. For large enough bath spin polarization, a bump appears in the curve of the integrated SSCF. It marks the boundary between the suppressed Kondo cloud and the polarized bath sites.

Incommensurate phases in the two-dimensional XY model with Dzyaloshinskii-Moriya interactions.

The two-dimensional XY model with Dzyaloshinskii-Moriya interaction has been studied through extensive Monte Carlo simulations. A hybrid algorithm consisting of single-spin Metropolis and Swendsen-Wang cluster-spin updates has been employed. Single histogram techniques have been used to obtain the thermodynamic variables of interest and finite-size-scaling analysis has led to the phase transition behavior in the thermodynamic limit. Fluctuating boundary conditions have been utilized in order to match the incommensurability between the spin structures and the finite lattice sizes due to the Dzyaloshinskii-Moriya interaction. The effects of the fluctuating boundary conditions have been analyzed in detail in both commensurate and incommensurate cases. The Berezinskii-Kosterlitz-Thouless transition temperature has been obtained as a function of the Dzyaloshinskii-Moriya interaction and the results are in excellent agreement with the exact equationfor the transition line. The spin-spin correlation function critical exponent has been computed as a function of the Dzyaloshinskii-Moriya interaction and temperature. In the incommensurate cases, optimal sizes for the finite lattices and the distribution of the boundary shift angle have been extracted. Analysis of the low temperature configurations and the corresponding vortex-antivortex pairs have also been addressed in some regions of the phase diagram.

Exact nonequilibrium hole dynamics, magnetic polarons, and string excitations in antiferromagnetic Bethe lattices

We investigate a rare instance of an exactly solvable nonequilibrium many-body problem. In particular, we derive an exact solution for the nonequilibrium dynamics of an initially localized single hole in a fully anisotropic antiferromagnetic Bethe lattice, described by the $t$-$J_z$ model. The solvability of the model relies on the fractal self-similarity of Bethe lattices, making it possible to compute the full motion of the hole as it moves through the lattice, as well as exactly characterizing the resulting effect on spin-spin correlation functions. We find that the hole remains bound to its initial position with large aperiodic oscillations in the hole density distribution. We track this back to the irregular pattern of the eigenenergies of the magnetic polaron ground state and string excitations, which we also determine exactly.

Decoherence and maintenance of an entangled state in three-spin system coupled to ferromagnetic electrodes

We study the model of three-spin system by using Born-Markov master equation for density matrix. Three-spin system consists of a spin-1/2 quantum dot and two spin-1 magnetic particles arranged in triangular geometry and a quantum dot is also tunnel-coupled to ferromagnetic electrodes, respectively. In this case, we are interested in decoherence of entangled state of the system. Decoherence occurs due to tunneling of electrons through coupling to ferromagnetic electrodes. Therefore, an entangled state undergoes decoherence dependent on the spin polarization as well as magnetization orientations of electrodes. We have established master-equation formalism for the density matrix of three-spin system and calculated spin-spin correlation function between two magnetic particles corresponding to entangled state. The results show that with the increase of spin polarization, spin-spin correlation function for parallel configuration of electrodes’ magnetizations decays more rapidly, while spin-spin correlation function for antiparallel configuration decays more slowly.

Benchmark calculations of multiloop pseudofermion fRG

The pseudofermion functional renormalization group (pffRG) is a computational method for determining zero-temperature phase diagrams of frustrated quantum magnets. In a recent methodological advance, the commonly employed Katanin truncation of the flow equations was extended to include multiloop corrections, thereby capturing additional contributions from the three-particle vertex (Thoenniss et al. https://arxiv.org/abs/2011.01268; Kiese et al. https://arxiv.org/abs/2011.01269). This development has also stimulated significant progress in the numerical implementation of pffRG, allowing one to track the evolution of pseudofermion vertices under the renormalization group flow with unprecedented accuracy. However, cutting-edge solvers differ in their integration algorithms, heuristics to discretize Matsubara frequency grids, and more. To lend confidence in the numerical robustness of state-of-the-art multiloop pffRG codes, we present and compare results produced with two independently developed and algorithmically distinct solvers for Heisenberg models on three-dimensional lattice geometries. Using the cubic lattice Heisenberg (anti)ferromagnet with nearest and next-nearest neighbor interactions as a generic benchmark model, we find the two codes to quantitatively agree, often up to several orders of magnitude in digital precision, both on the level of spin-spin correlation functions and renormalized fermionic vertices for varying loop orders. These benchmark calculations further substantiate the usage of multiloop pffRG solvers to tackle unconventional forms of quantum magnetism.Graphic abstract

Combined unitary and symmetric group approach applied to low-dimensional Heisenberg spin systems

A novel combined unitary and symmetric group approach is used to study the spin-$\frac{1}{2}$ Heisenberg model and related Fermionic systems in a total spin-adapted representation, using a linearly-parameterised Ansatz for the many-body wave function. We show that a more compact ground-state wave function representation---indicated by a larger leading ground-state coefficient---is obtained when combining the symmetric group ${\mathcal{S}}_{n}$, in the form of permutations of the underlying lattice site ordering, with the cumulative spin coupling based on the unitary group $\mathrm{U}(n)$. In one-dimensional systems the observed compression of the wave function is reminiscent of block-spin renormalization group approaches, and allows us to study larger lattices (here taken up to 80 sites) with the spin-adapted full configuration interaction quantum Monte Carlo method, which benefits from the sparsity of the Hamiltonian matrix and the corresponding sampled eigenstates that emerge from the reordering. We find that in an optimal lattice ordering the configuration state function with highest weight already captures with high accuracy the spin-spin correlation function of the exact ground-state wave function. This feature is found for more general lattice models, such as the Hubbard model, and ab initio quantum chemical models, exemplified by one-dimensional hydrogen chains. We also provide numerical evidence that the optimal lattice ordering for the unitary group approach is not generally equivalent to the optimal ordering obtained for methods based on matrix-product states, such as the density-matrix renormalization group approach.