Spin-spin Correlation Function Research Articles

Quantum criticality in dimerised anisotropic spin-1 chains

Applying the (infinite) density-matrix renormalisation group technique, we explore the effect of an explicit dimerisation on the ground-state phase diagram of the spin-1 XXZ chain with single-ion anisotropy D. We demonstrate that the Haldane phase between large-D and antiferromagnetic phases survives up to a critical dimerisation only. As a further new characteristic the dimerisation induces a direct continuous Ising quantum phase transition between the large-D and antiferromagnetic phases with central charge c=1/2, which terminates at a critical end-point where c=7/10. Calculating the critical exponents of the order parameter, neutral gap and spin–spin-correlation function, we find beta =1/8 (1/24), nu =1 (5/9), and eta =1/4 (3/20), respectively, which proves the Ising (tricritical Ising) universality class in accordance with field-theoretical predictions.

Staggered flux state for rectangular-lattice spin- 12 Heisenberg antiferromagnets

We investigate the spin-1/2 Heisenberg model on a rectangular lattice, using the Gutzwiller projected variational wave function known as the staggered flux state. Using Monte Carlo techniques, the variational parameters and static spin-structure factor for different coupling anisotropies $\gamma=J_y/J_x$ are calculated. We observe a gradual evolution of the ground state energy towards a value which is very close to the 1D estimate provided by the Bethe ansatz and a good agreement between the finite size scaling of the energies. The spin-spin correlation functions exhibit a power-law decay with varying exponents for different anisotropies. Though the lack of N\'eel order makes the staggered flux state energetically unfavorable in the symmetric case $\gamma=1$, it appears to capture the essence of the system close to 1D. Hence we believe that the staggered flux state provides an interesting starting point to explore the crossover from quantum disordered chains to the N\'eel ordered 2D square lattices.

Construction of variational matrix product states for the Heisenberg spin-1 chain

We propose a simple variational wave function that captures the correct ground state energy of the spin-1 Heisenberg chain model to within 0.04\%. The wave function is written in the matrix product state (MPS) form with the bond dimension $D=8$, and characterized by three fugacity parameters. The proposed MPS generalizes the Affleck-Kennedy-Lieb-Tasaki (AKLT) state by dressing it with dimers, trimers, and general $q$-dimers. The fugacity parameters control the number and the average size of the $q$-mers. Furthermore, the $D=8$ variational MPS state captures the ground states of the entire family of bilinear-biquadratic Hamiltonian belonging to the Haldane phase to high accuracy. The 2-4-2 degeneracy structure in the entanglement spectrum of our MPS state is found to match well with the results of density matrix renormalization group (DMRG) calculation, which is computationally much heavier. Spin-spin correlation functions also find excellent fit with those obtained by DMRG.

Mean-field theory of interacting triplons in a two-dimensional valence-bond solid: Stability and properties of many-triplon states

We study a system of interacting triplons (the elementary excitations of a valence-bond solid) described by an effective interacting boson model derived within the bond-operator formalism. In particular, we consider the square lattice spin-1/2 $J_1$-$J_2$ antiferromagnetic Heisenberg model, focus on the intermediate parameter region, where a quantum paramagnetic phase sets in, and consider the columnar valence-bond solid phase. Within the bond-operator theory, the Heisenberg model is mapped into an effective boson model in terms of triplet operators $t$. The effective boson model is studied at the harmonic approximation and the energy of the triplons and the expansion of the triplon operators $b$ in terms of the triplet operators $t$ are determined. Such an expansion allows us to performed a second mapping, and therefore, determine an effective interacting boson model in terms of the triplon operators $b$. We then consider systems with a fixed number of triplons and determined the ground-state energy and the spectrum of elementary excitations within a mean-field approximation. We show that many-triplon states are stable, the lowest-energy ones are constituted by a small number of triplons, and the excitation gaps are finite. For $J_2=0.48 J_1$ and $J_2=0.52 J_1$, we also calculate spin-spin and dimer-dimer correlation functions, dimer order parameters, and the bipartite von Neumann entanglement entropy within our mean-field formalism in order to determine the properties of the many-triplon state as a function of the triplon number. We find that the spin and the dimer correlations decay exponentially and that the entanglement entropy obeys an area law, regardless the triplon number. Moreover, only for $J_2=0.48 J_1$, the spin correlations indicate that the many-triplon states with large triplon number might display a more homogeneous singlet pattern than the columnar valence-bond solid.

Tuning the optical band gap and magnetization of oleic acid coated CoFe2O4 NPs synthesized by facile hydrothermal route

The high-quality oleic acid coated cobalt ferrite (OCF) nanopowders were prepared by hydrothermal route at 60 °C, 120 °C and 180 °C temperatures. The average crystallite sizes of 5.2 ± 0.07 nm, 13.3 ± 0.19 nm and 18.9 ± 0.23 nm were evaluated for OCF-60, OCF-120 and OCF-180. The SEM images of OCF exhibits agglomerated nanoparticles of roughly spherical shape. Optical energy gap was estimated and found to be enhanced from 1.8 to 2.3 eV with decreasing particle size. The area ratio Av2 of phonon modes occurred at 447 and 600–613 cm−1 are correspond to octahedral and tetrahedral sites, respectively. The enhancement in saturation magnetization MS was observed from 44.64 to 76.66 (emu/g) owing to decrease in area ratio Av2. Value of spin-spin correlation function was found to be decreased from 1.60 to 0.93 with increase in MS/size. A strong correlation between magnetic and optical properties with particle size was observed.

Superconducting properties of the hole-doped three-band d−p model studied with minimal-size real-space d -wave pairing operators

The three-band \emph{d-p} model is investigated by means of Variational Monte-Carlo (VMC) method with the BCS-like wave-function supplemented by the Gutzwiller and Jastrow correlators. The VMC optimization leads to $d$-$wave$ superconducting state with a characteristic dome-like shape of the order parameter for hole doping $\delta \lesssim 0.4$, in a good agreement with the experimental observations. Also, the off-diagonal pair-pair correlation functions, calculated within VMC, vindicates the results obtained very recently within the diagrammatic expansion of the Gutzwiller wave function method (DE-GWF) [cf. Phys. Rev. B \textbf{99}, 104511 (2019)]. Subsequently, the nature of the $d$-$wave$ pairing is investigated by means of recently proposed \emph{minimal-size real-space d-wave pairing operators} [Phys. Rev. B \textbf{100}, 214502 (2019)]. An emergence of the long-range superconducting ordering for both $d$ and $p$ orbitals is reported by analysing the corresponding off-diagonal pair-pair correlation functions. The dominant character of \emph{d-wave} pairing on $d$ orbitals is confirmed. Additionally, the trial wave-function is used to investigate the magnetic properties of the system. The analysis of spin-spin correlation functions is carried out and shows antiferromagnetic $\mathbf{q}=(\pi,\pi)$, short-range order, as expected. For the sake of completeness, the charge gap has been estimated, which for the parent compound takes the value $\Delta_{CG}\approx1.78\pm0.51\text{ eV}$, and agrees with values reported experimentally for the cuprates.

Self-averaging in many-body quantum systems out of equilibrium: Chaotic systems

Despite its importance to experiments, numerical simulations, and the development of theoretical models, self-averaging in many-body quantum systems out of equilibrium remains underinvestigated. Usually, in the chaotic regime, self-averaging is taken for granted. The numerical and analytical results presented here force us to rethink these expectations. They demonstrate that self-averaging properties depend on the quantity and also on the time scale considered. We show analytically that the survival probability in chaotic systems is not self-averaging at any time scale, even when evolved under full random matrices. We also analyze the participation ratio, R\'enyi entropies, the spin autocorrelation function from experiments with cold atoms, and the connected spin-spin correlation function from experiments with ion traps. We find that self-averaging holds at short times for the quantities that are local in space, while at long times, self-averaging applies for quantities that are local in time. Various behaviors are revealed at intermediate time scales.

Phase Diagram of the Spin-1/2 Kitaev-Gamma Chain and Emergent SU(2) Symmetry.

We study the phase diagram of a one-dimensional version of the Kitaev spin-1/2 model with an extra "Γterm," using analytical, density matrix renormalization group and exact diagonalization methods. Two intriguing phases are found. In the gapless phase, although the exact symmetry group of the system is discrete, the low energy theory is described by an emergent SU(2)_{1} Wess-Zumino-Witten (WZW) model. On the other hand, the spin-spin correlation functions exhibit SU(2) breaking prefactors, even though the exponents and the logarithmic corrections are consistent with the SU(2)_{1} predictions. A modified non-Abelian bosonization formula is proposed to capture such exotic emergent "partial" SU(2) symmetry. In the ordered phase, there is numerical evidence for an O_{h}→D_{4} spontaneous symmetry breaking.

Tensor network renormalization group study of spin-1 random Heisenberg chains

We use a tensor network strong-disorder renormalization group (tSDRG) method to study spin-1 random Heisenberg antiferromagnetic chains. The ground state of the clean spin-1 Heisenberg chain with uniform nearest-neighbor couplings is a gapped phase known as the Haldane phase. Here we consider disordered chains with random couplings, in which the Haldane gap closes in the strong disorder regime. As the randomness strength is increased further and exceeds a certain threshold, the random chain undergoes a phase transition to a critical random-singlet phase. The strong-disorder renormalization group method formulated in terms of a tree tensor network provides an efficient tool for exploring ground-state properties of disordered quantum many-body systems. Using this method we detect the quantum critical point between the gapless Haldane phase and the random-singlet phase via the disorder-averaged string order parameter. We determine the critical exponents related to the average string order parameter, the average end-to-end correlation function and the average bulk spin-spin correlation function, both at the critical point and in the random-singlet phase. Furthermore, we study energy-length scaling properties through the distribution of energy gaps for a finite chain. Our results are in closer agreement with the theoretical predictions than what was found in previous numerical studies. As a benchmark, a comparison between tSDRG results for the average spin correlations of the spin-1/2 random Heisenberg chain with those obtained by using unbiased zero-temperature QMC method is also provided.

Universal spin dynamics in infinite-temperature one-dimensional quantum magnets

We address the nature of spin dynamics in various integrable and non-integrable, isotropic and anisotropic quantum spin-$S$ chains, beyond the paradigmatic $S=1/2$ Heisenberg model. In particular, we investigate the algebraic long-time decay $\propto t^{-1/z}$ of the spin-spin correlation function at infinite temperature, using state-of-the-art simulations based on tensor network methods. We identify three universal regimes for the spin transport, independent of the exact microscopic model: (i) superdiffusive with $z=3/2$, as in the Kardar-Parisi-Zhang universality class, when the model is integrable with extra symmetries such as spin isotropy that drive the Drude weight to zero, (ii) ballistic with $z=1$ when the model is integrable with a finite Drude weight, and (iii) diffusive with $z=2$ with easy-axis anisotropy or without integrability, at variance with previous observations.

Probing the Possibilities of Ergodicity in the 1D Spin-1/2 XY Chain with Quench Dynamics

Ergodicity sits at the heart of the connection between statistical mechanics and dynamics of a physical system. By fixing the initial state of the system into the ground state of the Hamiltonian at zero temperature and tuning a control parameter, we consider the occurrence of the ergodicity with quench dynamics in the one-dimensional (1D) spin-1/2 XY model in a transverse magnetic field. The ground-state phase diagram consists of two ferromagnetic and paramagnetic phases. It is known the magnetization in this spin system is non-ergodic. We set up two different experiments as we call them single and double quenches and test the dynamics of the magnetization along the Z-axis and the spin-spin correlation function along the X-axis which are the order parameters of the zero-temperature phases . Our exact results reveal that for single quenches at zero-temperature, the ergodicity depends on the initial state and the order parameter. In single quenches for a given order parameter, ergodicity will be observed with an ergodic-region for quenches from another phase, non-correspond to the phase of the order parameter, into itself. In addition, a quench from a ground-state phase point corresponding to the order parameter into or very close to the quantum critical point, hc = 1.0, discloses an ergodic behavior. Otherwise, for all other single quenches, the system behaves non-ergodic. Interestingly on the other setup, a double quench on a cyclic path, ergodicity is completely broken for starting from the phase corresponding to the order parameter. Otherwise, it depends on the first quenched point, and the quench time T when the model spent before a second quench in the way back which gives an ability to controlling the ergodicity in the system. Therefore, and contrary to expectations, in the mentioned model the ergodicity can be observed with probing quench dynamics at zero-temperature. Our results provide further insight into the zero-temperature dynamical behavior of quantum systems and their connections to the ergodicity phenomenon.

Persistence of power-law correlations in nonequilibrium steady states of gapped quantum spin chains

The existence of quasi-long range order is demonstrated in nonequilibrium steady states in isotropic $XY$ spin chains including of two types of additional terms that each generate a gap in the energy spectrum. The system is driven out of equilibrium by initializing a domain-wall magnetization profile through application of an external magnetic field and switching off the magnetic field at the same time the energy gap is activated. An energy gap is produced by either applying a staggered magnetic field in the $z$ direction or introducing a modulation to the $XY$ coupling. The magnetization, spin current, and spin-spin correlation functions are computed analytically in the thermodynamic limit at long times after the quench. For both types of systems, we find the persistence of power-law correlations despite the ground-state correlation functions exhibiting exponential decay.

Spin Hall magnetoresistance in a low-dimensional Heisenberg ferromagnet

We report the spin Hall magnetoresistance (SMR) in Pt deposited on a tensile-strained ${\mathrm{LaCoO}}_{3}$ (LCO) thin film, which is a ferromagnetic insulator with a Curie temperature ${T}_{\mathrm{c}}=85\phantom{\rule{0.28em}{0ex}}\mathrm{K}$. The SMR displays a strong magnetic-field dependence below ${T}_{\mathrm{c}}$, with the SMR amplitude continuing to increase (linearly) with increasing the field far beyond the saturation value of the ferromagnet. The SMR amplitude decreases gradually with raising the temperature across ${T}_{\mathrm{c}}$ and remains measurable even above ${T}_{\mathrm{c}}$. Moreover, no hysteresis is observed in the field dependence of the SMR. These unusual behaviors indicate that a low-dimensional magnetic system forms at the surface of LCO and that the LCO/Pt interface decouples magnetically from the rest of the LCO thin film. Transmission electron microscopy analysis of the heterostructure reveals that an ultrathin Co-rich layer forms at the LCO surface upon deposition of Pt, which is separated from the rest of the LCO film by a \ensuremath{\sim}1-nm La/O-rich layer, thus supporting the presence of a low-dimensional ferromagnetic system. To explain the magnetoresistance measurements, we revisit the derivation of the SMR corrections and relate the spin-mixing conductances to the spin-spin correlation functions and microscopic quantities describing the magnetism at the interface. Comparisons between theory and experiment confirm the existence of a low-dimensional Heisenberg ferromagnet at the interface. Our results pave the way for exploring complex magnetic textures of insulating films by simple transport measurements.

Heat capacity of anisotropic Heisenberg antiferromagnet within the spin Hartree-Fock approach in quasi-1D regime

We study the anisotropic quantum Heisenberg antiferromagnet for spin-1/2 that interpolates smoothly between the one-dimensional (1D) and the two-dimensional (2D) limits. Using the spin Hartree-Fock approach we construct a quantitative theory of heat capacity in the quasi-1D regime with a finite coupling between spin chains. This theory reproduces closely the exact result of Bethe Ansatz in the 1D limit and does not produces any spurious phase transitions for any anisotropy in the quasi-1D regime at finite temperatures in agreement with the Mermin-Wagner theorem. We study the static spin-spin correlation function in order to analyse the interplay of lattice geometry and anisotropy in these systems. We compare the square and triangular lattice. For the latter we find that there is a quantum transition point at an intermediate anisotropy of $\sim0.6$. This quantum phase transition establishes that the quasi-1D regime extends upto a particular point in this geometry. For the square lattice the change from the 1D to 2D occurs smoothly as a function of anisotropy, i.e. it is of the crossover type. Comparing the newly developed theory to the available experimental data on the heat capacity of $\rm{Cs}_2\rm{CuBr}_4$ and $\rm{Cs}_2\rm{CuCl}_4$ we extract the microscopic constants of the exchange interaction that previously could only be measured using inelastic neutron scattering in high magnetic fields.

Measurement-driven entanglement transition in hybrid quantum circuits

In this paper we continue to explore "hybrid" quantum circuit models in one-dimension with both unitary and measurement gates, focussing on the entanglement properties of wavefunction trajectories at long times, in the steady state. We simulate a large class of Clifford circuits, including models with or without randomness in the unitary gates, and with or without randomness in the locations of measurement gates, using stabilizer techniques to access the long time dynamics of systems up to 512 qubits. In all models we find a volume law entangled phase for low measurement rates, which exhibits a sub-dominant logarithmic behavior in the entanglement entropy, S_A = {\alpha} ln |A| + s|A|, with sub-system size |A|. With increasing measurement rate the volume law phase is unstable to a disentangled area law phase, passing through a single entanglement transition at a critical rate of measurement. At criticality we find a purely logarithmic entanglement entropy, S_A = {\alpha}(p_c) ln|A|, a power law decay and conformal symmetry of the mutual information, with exponential decay off criticality. Various spin-spin correlation functions also show slow decay at criticality. Critical exponents are consistent across all models, indicative of a single universality class. These results suggest the existence of an effective underlying statistical mechanical model for the entanglement transition. Beyond Clifford circuit models, numerical simulations of up to 20 qubits give consistent results.

Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point

We study the dynamics of a spin-\frac{1}{2}12 XXZ chain which is initially prepared in a domain-wall state. We compare the results of time-dependent Density Matrix Renormalization Group simulations with those of an effective description in terms of a classical anisotropic Landau-Lifshitz (LL) equation. Numerous quantities are analyzed: magnetization (xx, yy and zz components), energy density, energy current, but also some spin-spin correlation functions or entanglement entropy in the quantum chain. Without any adjustable parameter a quantitative agreement is observed between the quantum and the LL problems in the long time limit, when the models are close to the isotropic point. This is explained as a consequence of energy conservation. At the isotropic point the mapping between the LL equation and the nonlinear Schrödinger equation is used to construct a variational solution capturing several aspects of the problem.

Exactly Solvable Quantum Impurity Model with Inverse-Square Interactions.

We construct an exactly solvable quantum impurity model which consists of spin-1/2 conduction fermions and a spin-1/2 magnetic moment. The ground state is a Gutzwiller projected Fermi sea with nonorthonormal modes and its wave function in the site-occupation basis is a Jastrow-type homogeneous polynomial. The parent Hamiltonian has all-to-all inverse-square hopping terms between the conduction fermions and inverse-square spin-exchange terms between the conduction fermions and the magnetic moment. The low-lying energy levels, spin-spin correlation function, and von Neumann entanglement entropy of our model demonstrate that it exhibits the essential aspects of spin-1/2 Kondo physics. The machinery developed in this work can generate many other exactly solvable quantum impurity models.

Theory of Spin Hall Magnetoresistance from a Microscopic Perspective.

We present a theory of the spin Hall magnetoresistance of metals in contact with magnetic insulators. We express the spin mixing conductances, which govern the phenomenology of the effect, in terms of the microscopic parameters of the interface and the spin-spin correlation functions of the local moments on the surface of the magnetic insulator. The magnetic-field and temperature dependence of the spin mixing conductances leads to a rich behavior of the resistance due to an interplay between the Hanle effect and the spin mixing at the interface. We describe an unusual negative magnetoresistance originating from a nonlocal Hanle effect. Our theory provides a useful tool for understanding the experiments on heavy metals in contact with magnetic insulators of different kinds, and it enables the spin Hall magnetoresistance effect to be used as a technique to study magnetism at interfaces.

Degenerate orbital effect in a three-orbital periodic Anderson model

The competition between the Ruderman-Kittel-Kasuya-Yosida effect and Kondo effect is a central subject of periodic Anderson model. By using the density matrix embedding theory, we study a three orbital periodic Anderson model, in which the effects of degenerate conduction orbitals via the local magnetic moments, number of electrons, and spin-spin correlation functions, are investigated. From the phase diagram at half filling, we find there exists two different anti-ferromagnetic phases and one paramagnetic phase. To explore the difference of the two anti-ferromagnetic phases, the topology of Fermi surface and the connection with standard periodic Anderson model are considered. The spin-spin correlation functions yield insight into the competition between Ruderman-Kittel-Kasuya-Yosida interaction and Kondo interaction. We further find there is a "scaling transformation" connects different ratio of the hybridization strength.

Spatial anisotropy of the Kondo screening cloud in a type-II Weyl semimetal

We theoretically study the Kondo screening of a spin-1/2 magnetic impurity in the bulk of a type-II Weyl semimetal (WSM) by use of the variational wave function method. We consider a type-II WSM model with two Weyl nodes located on the $k_z$-axis, and the tilting of the Weyl cones are along the $k_x$ direction. Due to co-existing electron and hole pockets, the density of states at the Fermi energy becomes finite, leading to a significant enhancement of Kondo effect. Consequently, the magnetic impurity and the conduction electrons always form a bound state, this behavior is distinct from that in the type-I WSMs, where the bound state is only formed when the hybridization exceeds a critical value. Meanwhile, the spin-orbit coupling and unique geometry of the Fermi surface lead to strongly anisotropic Kondo screening cloud in coordinate space. The tilting terms break the rotational symmetry of the type-II WSM about the $k_z$-axis, but the system remains invariant under a combined transformation $\mathcal{T}R^{y}(\pi)$, where $\mathcal{T}$ is the time-reversal operation and $R^{y}(\pi)$ is the rotation about the $y$-axis by $\pi$. Largely modified diagonal and off-diagonal components of the spin-spin correlation function on three principal planes reflect this change in band symmetry. Most saliently, the tilting terms trigger the emergence of non-zero off-diagonal components of spin-spin correlation function on the $x$-$z$ principal plane.