Correlated Spin Systems Research Articles

The direct role of nuclear motion in spin-orbit coupling in strongly correlated spin systems.

The interaction between the magnetic moment of an electron and the magnetic field generated by a moving charge is one component of the spin-orbit interaction. The nuclei in a molecule or solid are charged, are generally in vibrational motion, and so contribute to this interaction, but the direct coupling between nuclear momentum and electron spin is normally ignored in discussions of spin-forbidden phenomena such as transitions between states of different spin, even when the nuclei are recognized as playing a fundamental role (spin-vibronic coupling). Here, we investigate the spin-orbit interaction in a Heisenberg model interacting with vibrating point charges representing nearby bridging ligands. To reach the model, we apply second order perturbation theory to the Hubbard model with the spin-orbit interaction. In contrast to the other components of the spin-orbit interaction, the part that directly couples the momentum of the charge and electron spin appears at first order as an effective magnetic field at each site. We find that the inclusion of this nuclear-motion induced spin-orbit coupling can increase the rate of otherwise spin-forbidden transitions between different spin states of the Heisenberg model by many orders of magnitude. This overlooked interaction may, therefore, play a significant role in spin-forbidden phenomena such as spin relaxation in coupled spin-qubits.

Linear Combinations of Cluster Mean-Field States Applied to Spin Systems.

We present an innovative cluster-based method employing linear combinations of diverse cluster mean-field states and apply it to describe the ground state of strongly correlated spin systems. In cluster mean-field theory, the ground state wave function is expressed as a factorized tensor product of optimized cluster states. While our prior work concentrated on a single cMF tiling, this study removes that constraint by combining different tilings of cMF states. Selection criteria, including translational symmetry and spatial proximity, guide this process. We present benchmark calculations for the one- and two-dimensional J1 - J2 and XXZ Heisenberg models. Our findings highlight two key aspects. First, the method offers a semiquantitative description of the 0.4 ≲ J2/J1 ≲ 0.6 regime of the J1 - J2 model─a particularly challenging regime for existing methods. Second, our results demonstrate the capability of our method to provide qualitative descriptions for all the models and regimes considered, establishing it as a valuable reference. However, the inclusion of additional (weak) correlations is necessary for quantitative agreement, and we explore methods to incorporate these extra correlations.

Pressure-tuned quantum criticality in the large-D antiferromagnet DTN

Strongly correlated spin systems can be driven to quantum critical points via various routes. In particular, gapped quantum antiferromagnets can undergo phase transitions into a magnetically ordered state with applied pressure or magnetic field, acting as tuning parameters. These transitions are characterized by z = 1 or z = 2 dynamical critical exponents, determined by the linear and quadratic low-energy dispersion of spin excitations, respectively. Employing high-frequency susceptibility and ultrasound techniques, we demonstrate that the tetragonal easy-plane quantum antiferromagnet NiCl2 ⋅ 4SC(NH2)2 (aka DTN) undergoes a spin-gap closure transition at about 4.2 kbar, resulting in a pressure-induced magnetic ordering. The studies are complemented by high-pressure-electron spin-resonance measurements confirming the proposed scenario. Powder neutron diffraction measurements revealed that no lattice distortion occurs at this pressure and the high spin symmetry is preserved, establishing DTN as a perfect platform to investigate z = 1 quantum critical phenomena. The experimental observations are supported by DMRG calculations, allowing us to quantitatively describe the pressure-driven evolution of critical fields and spin-Hamiltonian parameters in DTN.

Symmetry-projected cluster mean-field theory applied to spin systems.

We introduce Sz spin-projection based on cluster mean-field theory and apply it to the ground state of strongly correlated spin systems. In cluster mean-fields, the ground state wavefunction is written as a factorized tensor product of optimized cluster states. In previous work, we have focused on unrestricted cluster mean-field, where each cluster is Sz symmetry adapted. We here remove this restriction by introducing a generalized cluster mean-field (GcMF) theory, where each cluster is allowed to access all Sz sectors, breaking Sz symmetry. In addition, a projection scheme is used to restore global Sz, which gives rise to the Sz spin-projected generalized cluster mean-field (SzGcMF). Both of these extensions contribute to accounting for inter-cluster correlations. We benchmark these methods on the 1D, quasi-2D, and 2D J1 - J2 and XXZ Heisenberg models. Our results indicate that the new methods (GcMF and SzGcMF) provide a qualitative and semi-quantitative description of the Heisenberg lattices in the regimes considered, suggesting them as useful references for further inter-cluster correlations, which are discussed in this work.

Observation of terahertz-induced dynamical spin canting in orthoferrite magnon by magnetorefractive probing

Intense terahertz pulses offer unique pathway to resonantly drive the correlated spin systems up to the nonlinear regime. However, detection of such nonlinear spin dynamics often suffers from the small signal amplitude that can be easily hindered by the linear background components. In order to efficiently extract the nonlinear signals, here we demonstrate that magnetooptical effect can be utilized. We excite spin precession in orthoferrite YFeO3 by the magnetic field of intense terahertz pulse and probe its dynamics by transient transmissivity change in the near infrared. The observed waveforms contain quasi-ferromagnetic-mode magnon oscillation and its second harmonics with a comparably strong amplitude. The result can be explained by dielectric function derived from magnetorefractive Hamiltonian. We reveal that the strong second harmonic signal microscopically originates from the dynamics of the quasi-ferromagnetic mode magnon at nonlinear regime, wherein spin canting angle periodically oscillates.

Coupled Cluster and Perturbation Theories Based on a Cluster Mean-Field Reference Applied to Strongly Correlated Spin Systems.

We introduce perturbation and coupled-cluster theories based on a cluster mean-field reference for describing the ground state of strongly correlated spin systems. In cluster mean-field, the ground state wave function is written as a simple tensor product of optimized cluster states. The cluster language and the mean-field nature of the ansatz allow for a straightforward improvement which uses perturbation theory and coupled-cluster to account for intercluster correlations. We present benchmark calculations on the 1D chain and 2D square J1-J2 Heisenberg model, using cluster mean-field, perturbation theory, and coupled-cluster. We also present an extrapolation scheme that allows us to compute thermodynamic limit energies accurately. Our results indicate that, with sufficiently large clusters, the correlated methods (cPT2, cPT4, and cCCSD) can provide a relatively accurate description of the Heisenberg model in the regimes considered, which suggests that the methods presented can be used for other strongly correlated systems. Some ways to improve upon the methods presented in this work are discussed.

Quantum Monte Carlo study of topological phases on a spin analogue of Benalcazar–Bernevig–Hughes model

We study the higher-order topological spin phases based on a spin analogue of Benalcazar–Bernevig–Hughes model in two dimensions using large-scale quantum Monte Carlo simulations. A continuous Néel-valence bond solid quantum phase transition is revealed by tuning the ratio between dimerized spin couplings, namely, the weak and strong exchange couplings. Through the finite-size scaling analysis, we identify the phase critical points, and consequently, map out the full phase diagrams in related parameter spaces. Particularly, we find that the valence bond solid phase can be a higher-order topological spin phase, which has a gap for spin excitations in the bulk while demonstrates characteristic gapless spin modes at corners of open lattices. We further discuss the connection between the higher-order topological spin phases and the electronic correlated higher-order phases, and find both of them possess gapless spin corner modes that are protected by higher-order topology. Our result exemplifies higher-order physics in the correlated spin systems and will contribute to further understandings of the many-body higher-order topological phenomena.

Magnetic Domain Control of ErFeO3 by Intense Terahertz Free Electron Laser Pulses

The control of magnetic domain in correlated spin systems by optical pulses has been gaining importance in spintronics and related fields. In particular, ultrafast control of magnetic domain is one of the top areas of interest. Herein we demonstrate the magnetic domain control in ErFeO3 single crystal, a weak ferromagnet, induced by high-intensity terahertz (THz) pulse excitation from a free-electron laser. THz pulses with a central frequency of 4 THz and pulse energy in the order of 10 mJ were used. The microscopic images of the magnetic domain inversion induced by the THz irradiation were recorded by the Faraday-rotation method using a He–Ne probe laser. The experimental results of the THz pulse irradiation at room temperature and at low temperature around the spin reorientation phase transition are presented. We show that the THz pulse excitation can expand the minor magnetic domain toward the direction of the THz beam spot. The magnetic domain inversion is caused by the combination of depinning of the magnetic domain due to local heating and the entropic force owing to the thermal gradient induced by THz irradiation.

Holographic quantum algorithms for simulating correlated spin systems

We present a suite of ``holographic'' quantum algorithms for efficient ground-state preparation and dynamical evolution of correlated spin systems, which require far fewer qubits than the number of spins being simulated. The algorithms exploit the equivalence between matrix-product states (MPS) and quantum channels, along with partial measurement and qubit reuse, in order to simulate a $D$-dimensional spin system using only a $(D\ensuremath{-}1)$-dimensional subset of qubits along with an ancillary qubit register whose size scales logarithmically in the amount of entanglement present in the simulated state. Ground states can either be directly prepared from a known MPS representation or obtained via a holographic variational quantum eigensolver (holoVQE). Dynamics of MPS under local Hamiltonians for time $t$ can also be simulated with an additional (multiplicative) $\mathrm{poly}(t)$ overhead in qubit resources. These techniques open the door to efficient quantum simulation of MPS with exponentially large bond dimension, including ground states of two- and three-dimensional systems, or thermalizing dynamics with rapid entanglement growth. As a demonstration of the potential resource savings, we implement a holoVQE simulation of the antiferromagnetic Heisenberg chain on a trapped-ion quantum computer, achieving within $10(3)%$ of the exact ground-state energy of an infinite chain using only a pair of qubits.

Dynamics of strongly correlated spin systems with reduced dimensionality and/or frustration

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Visualizing quantum phases and identifying quantum phase transitions by nonlinear dimensional reduction

Identifying quantum phases and phase transitions is key to understand complex phenomena in statistical physics. In this work, we propose an unconventional strategy to access quantum phases and phase transitions by visualization based on the distribution of ground states in Hilbert space. By mapping the quantum states in Hilbert space onto a two-dimensional feature space using an unsupervised machine learning method, distinct phases can be directly specified and quantum phase transitions can be well identified. Our proposal is benchmarked on gapped, critical, and topological phases in several strongly correlated spin systems. As this proposal directly learns quantum phases and phase transitions from the distributions of the quantum states, it does not require priori knowledge of order parameters of physical systems, which thus indicates a perceptual route to identify quantum phases and phase transitions particularly in complex systems by visualization through learning.

Tuning Magnetic Properties of a Carbon Nanotube-Lanthanide Hybrid Molecular Complex through Controlled Functionalization.

Molecular magnets attached to carbon nanotubes (CNT) are being studied as potential candidates for developing spintronic and quantum technologies. However, the functionalization routes used to develop these hybrid systems can drastically affect their respective physiochemical properties. Due to the complexity of this systems, little work has been directed at establishing the correlation between the degree of functionalization and the magnetic character. Here, we demonstrate the chemical functionalization degree associated with molecular magnet loading can be utilized for controlled tuning the magnetic properties of a CNT-lanthanide hybrid complex. CNT functionalization degree was evaluated by interpreting minor Raman phonon modes in relation to the controlled reaction conditions. These findings were exploited in attaching a rare-earth-based molecular magnet (Gd-DTPA) to the CNTs. Inductively coupled plasma mass spectrometry, time-of-flight secondary ion mass spectrometry and super conducting quantum interference device (SQUID) measurements were used to elucidate the variation of magnetic character across the samples. This controlled Gd-DTPA loading on the CNT surface has led to a significant change in the nanotube intrinsic diamagnetism, showing antiferromagnetic coupling with increase in the Weiss temperature with respect to increased loading. This indicates that synthesis of a highly correlated spin system for developing novel spintronic technologies can be realized through a carbon-based hybrid material.

Phase identification in many-body systems by virtual configuration binarization.

Artificial intelligence provides an unprecedented perspective for studying phases of matter in condensed-matter systems. Image segmentation is a basic technique of computer vision that belongs to a branch of artificial intelligence. Inspired by the image segmentation techniques, in this work, we propose a scheme named virtual configuration binarization (VCB) to unveil quantum phases and quantum phase transitions in many-body systems. By encoding the information of renormalized quantum states into a color image and binarize the color image through the VCB, the renormalized quantum states can be visualized, from which quantum phase transitions can be revealed and the corresponding critical points can be identified. Our scheme is benchmarked on several strongly correlated spin systems, which does not depend on the priori knowledge of order parameters of quantum phases. This demonstrates the potential to disclose the underlying structure of quantum phases by the techniques of computer vision.

Signature of correlated quantum tunneling and thermal dephasing in quantum-classical coupled Ho2Ti2O7 and Dy2Ti2O7 spin ices

Herein, a crucial external variable of spin dynamics responsible for classical and quantum behavior of strongly spin correlated frustrated magnetic systems has been revealed. An experimental procedure has been demonstrated, by which the dephasing of quantum mechanically correlated spins are prevented from thermalization in Ho2Ti2O7 and Dy2Ti2O7. Due to the coupling of Ho/Dy spin with thermal bath, thermalization of doubly degenerate Ising spin takes place independently. The role of external stimuli on quantum information associated with correlations in these systems has also been studied. It has been found that in the thermalized state, macroscopic properties are stationary and universal with respect to widely differing initial conditions, whereas in the non-thermalized state, macroscopic properties depend on widely differing initial conditions and vary with temporal evolution. Temperature dependent variation in Δχ′ as Intensity I(T) and decay rate R(T) of quantum information at a given temperature shows that, in these strongly correlated spin systems, strengthening of spin correlations ease the propagation of quantum information whereas spin constraints by underlying magnetic interactions prohibit the propagation of quantum information. These findings also reveal how quantum-classical correspondence plays a crucial role in the macroscopic properties of quantum materials.

Block product density matrix embedding theory for strongly correlated spin systems

Density matrix embedding theory (DMET) is a relatively new technique for the calculation of strongly correlated systems. Recently, block product DMET (BPDMET) was introduced for the study of spin systems such as the antiferromagnetic $J_1 - J_2$ model on the square lattice. In this paper, we extend the variational Ansatz of BPDMET using spin-state optimization, yielding improved results. We apply the same techniques to the Kitaev-Heisenberg model on the honeycomb lattice, comparing the results when using several types of clusters. Energy profiles and correlation functions are investigated. A diagonalization in the tangent space of the variational approach yields information on the excited states and the corresponding spectral functions.

Fractional topological states in quantum spin chains with periodical modulation

We report the findings of fractional topological states in one-dimensional periodically modulated quantum spin chains with up to third neighbor interactions. By exact numerical studies, we demonstrate the existence of topologically nontrivial degenerate ground states at some specific magnetizations, which can be characterized by the nonzero-integer total Chern numbers of the degenerate ground states and the emergence of nontrivial edge states under open boundary conditions. We find that the low-energy excitations obey bosonic $\nu=1/2$ fractional statistics for the spin-$1/2$ system and $\nu=1$ non-Abelian statistics for the spin-$1$ system, respectively. The discovered fractional quantum states provide another route to the theoretical exploration of fractional quantum states in correlated spin systems.

Magnetic resonance study of co-modified (Co,N)-TiO2 nanocomposites

Abstract Three nCo,N-TiO2 nanocomposites (where cobalt concentration index n = 1, 5 and 10 wt %) were prepared and investigated by magnetic resonance spectroscopy at room temperature. Ferromagnetic resonance (FMR) lines of magnetic cobalt agglomerated nanoparticle were dominant in all registered spectra. The relaxation processes and magnetic anisotropy of the investigated spin system essentially depended on the concentration of cobalt ions. It is suggested that the samples contained two magnetic types of sublattices forming a strongly correlated spin system. It is suggested that the existence of strongly correlated magnetic system has an essential influence of the photocatalytic properties of the studied nanocomposites.

Rabi oscillations of pinned solitons in spin chains: A route to quantum computation and communication

We provide evidence for the coherence and Rabi oscillations of spin solitons pinned by the local breaking of translational symmetry in isotropic Heisenberg chains (simple antiferromagnetic N\'eel or spin Peierls). We show that these correlated spin systems that are made of hundreds of coupled spins bear an overall spin $S=1/2$ and can be manipulated as a single spin. This is clearly contrary to known spin qubits which are paramagnetic centers, highly diluted to prevent decoherence. These results offer an alternative approach for spin qubits, paving the way for the implementation of a different type of quantum computer.

Cavity-assisted energy relaxation for quantum many-body simulations

We propose an energy relaxation mechanism whereby strongly correlated spin systems decay into their ground states. The relaxation is driven by cavity quantum electrodynamics interaction and the decay of cavity photons. It is shown that by applying broadband driving fields, strongly correlated systems can be cooled regardless of the specific details of their energy level profiles. The scheme would also have significant implications in other contexts, such as adiabatic quantum computation and steady-state entanglement in dissipative systems.

Low-Rank Tensor Methods with Subspace Correction for Symmetric Eigenvalue Problems

We consider the solution of large-scale symmetric eigenvalue problems for which it is known that the eigenvectors admit a low-rank tensor approximation. Such problems arise, for example, from the discretization of high-dimensional elliptic PDE eigenvalue problems or in strongly correlated spin systems. Our methods are built on imposing low-rank (block) tensor train (TT) structure on the trace minimization characterization of the eigenvalues. The common approach of alternating optimization is combined with an enrichment of the TT cores by (preconditioned) gradients, as recently proposed by Dolgov and Savostyanov for linear systems. This can equivalently be viewed as a subspace correction technique. Several numerical experiments demonstrate the performance gains from using this technique.