Spin Model Research Articles

Tight Lipschitz hardness for optimizing mean field spin glasses

AbstractWe study the problem of algorithmically optimizing the Hamiltonian of a spherical or Ising mixed ‐spin glass. The maximum asymptotic value of is characterized by a variational principle known as the Parisi formula, proved first by Talagrand and in more generality by Panchenko. Recently developed approximate message passing (AMP) algorithms efficiently optimize up to a value given by an extended Parisi formula, which minimizes over a larger space of functional order parameters. These two objectives are equal for spin glasses exhibiting a no overlap gap property (OGP). However, can also occur, and no efficient algorithm producing an objective value exceeding is known. We prove that for mixed even ‐spin models, no algorithm satisfying an overlap concentration property can produce an objective larger than with non‐negligible probability. This property holds for all algorithms with suitably Lipschitz dependence on the disorder coefficients of . It encompasses natural formulations of gradient descent, AMP, and Langevin dynamics run for bounded time and in particular includes the algorithms achieving mentioned above. To prove this result, we substantially generalize the OGP framework introduced by Gamarnik and Sudan to arbitrary ultrametric forbidden structures of solutions.

Cluster truncated Wigner approximation for bond-disordered Heisenberg spin models

Cluster truncated Wigner approximation for bond-disordered Heisenberg spin models

Comparative Raman scattering study of crystal field excitations in Co-based quantum magnets

Comparative Raman scattering study of crystal field excitations in Co-based quantum magnets

Probing the weak limit of magnetocrystalline anisotropy through a spin‒flop transition in the van der Waals antiferromagnet CrPS4

The influence of magnetocrystalline anisotropy (MCA) on antiferromagnetism is elucidated through the characterization of the spin‒flop transition. However, due to a lack of suitable candidates for investigation, a detailed understanding of the preservation of the spin‒flop transition in the presence of low MCA energy remains elusive. In this study, we introduce CrPS4, which is a two-dimensional van der Waals antiferromagnet, as an ideal system to explore the exceedingly weak limit of the thermally-evolved MCA energy. By employing a uniaxially anisotropic spin model and fitting it to the experimental magnetic properties, we quantify the MCA energy and identify the discernible spin configurations in different magnetic phases. Notably, even at the limit of extremely weak MCA, with a mere 0.12% of the interlayer antiferromagnetic exchange interaction at T = 33 K, which is slightly below the Néel temperature (TN) of 38 K, the spin‒flop transition remains intact. We further establish a direct correlation between the visualized spin arrangements and the progressive reversal of magnetic torque induced by rotating magnetic fields. This analysis reveals the essential role of MCA in antiferromagnetism, thus extending our understanding to previously undetected limits and providing valuable insights for the development of spin-processing functionalities based on van der Waals magnets.

An integrated structural model of the DNA damage-responsive H3K4me3 binding WDR76:SPIN1 complex with the nucleosome

Serial capture affinity purification (SCAP) is a powerful method to isolate a specific protein complex. When combined with cross-linking mass spectrometry and computational approaches, one can build an integrated structural model of the isolated complex. Here, we applied SCAP to dissect a subpopulation of WDR76 in complex with SPIN1, a histone reader that recognizes trimethylated histone H3 lysine4 (H3K4me3). In contrast to a previous SCAP analysis of the SPIN1:SPINDOC complex, histones and the H3K4me3 mark were enriched with the WDR76:SPIN1 complex. Next, interaction network analysis of copurifying proteins and microscopy analysis revealed a potential role of the WDR76:SPIN1 complex in the DNA damage response. Since we detected 149 pairs of cross-links between WDR76, SPIN1, and histones, we then built an integrated structural model of the complex where SPIN1 recognized the H3K4me3 epigenetic mark while interacting with WDR76. Finally, we used the powerful Bayesian Integrative Modeling approach as implemented in the Integrative Modeling Platform to build a model of WDR76 and SPIN1 bound to the nucleosome.

Observation of anisotropy-independent magnetization dynamics in spatially disordered Heisenberg spin systems

An important step towards a comprehensive understanding of far-from-equilibrium dynamics of quantum many-body systems is the identification of unifying features that are independent of microscopic details of the system. We experimentally observe such robust features in the magnetization relaxation dynamics of disordered Heisenberg XX, XXZ, and Ising Hamiltonians. We realize these Heisenberg spin models with tunable anisotropy parameter and power-law interactions in an ensemble of Rydberg atoms by encoding the spin in suitable Rydberg state combinations. We consistently observe stretched-exponential relaxation of magnetization for all considered spin models, collapsing onto a single curve after appropriate rescaling of time. This robust short-time relaxation behavior is explained by a perturbative treatment that exploits the strong disorder in pairwise couplings, which leads to a description in terms of approximately independent pairs of spins. In numerical simulations of small systems, we show that these pairs of spins constitute approximate local integrals of motion, which remain at least partially conserved on a timescale exceeding the duration of the relaxation dynamics of the magnetization. Published by the American Physical Society 2024

Solid–liquid transition in a skyrmion matter

We report Monte-Carlo studies of the orientational order and melting of a 2D skyrmion lattice containing more than one million spins. Two models have been investigated, a microscopic model of lattice spins with Dzyaloshinskii–Moryia interaction that possesses skyrmions, and the model in which skyrmions are treated as point particles with repulsive interaction derived from a spin model. They produce similar results. The skyrmion lattice exhibits a sharp one-step transition between solid and liquid phases on temperature and the magnetic field. This solid–liquid transition is characterized by the kink in the magnetization. The field-temperature phase diagram is computed. We show that the application of the field gradient to a 2D system of skyrmions produces a solid–liquid interface that must be possible to observe in experiments.

Half Landau–Zener ramp to a quantum phase transition in a dissipative single spin model

We study the dynamics of a single spin coupled to a bosonic bath at zero temperature driven by a ramp of the bias field. A single spin coupled to a bosonic sub-Ohmic bath exhibits a quantum phase transition at a certain strength of spin-boson coupling. When the bias field is ramped from a large value to zero at this critical coupling strength, the system initialized at the ground state ends up with a finite magnetization due to the critical slowing down near the transition. On the basis of the pulse-impulse approximation, we derive a scaling law between the residual magnetization and the ramp speed. The obtained scaling relation is examined using a numerical simulation based on the tensor network. The data are in favor of the scaling law to hold. We discuss the demonstration of our theoretical results by means of quantum simulation using the quantum annealer.Graphical abstract

LiHoF4 as a spin-half non-standard quantum Ising system

LiHoF_{4}4 is a magnetic material known for its Ising-type anisotropy, making it a model system for studying quantum magnetism. However, the theoretical description of LiHoF_{4}4 using the quantum Ising model has shown discrepancies in its phase diagram, particularly in the regime dominated by thermal fluctuations. In this study, we investigate the role of off-diagonal dipolar terms in LiHoF_{4}4, previously neglected, in determining its properties. We analytically derive the low-energy effective Hamiltonian of LiHoF_{4}4, including the off-diagonal dipolar terms perturbatively, both in the absence and presence of a transverse field. Our results encompass the full phase diagram, confirming the significance of the off-diagonal dipolar terms in reducing the zero-field critical temperature and determining the critical temperature’s dependence on the transverse field. We also highlight the sensitivity of this mechanism to the crystal structure by comparing our calculations with the Fe_{8}8 system.

Unveiling non-classical correlations, quantum coherence, and steering measurement uncertainty in two-qubit $$XY-\Gamma$$ spin model

Unveiling non-classical correlations, quantum coherence, and steering measurement uncertainty in two-qubit $$XY-\Gamma$$ spin model

Mathematical analysis of spin transport in topological insulators to optimize memory devices performance using numerical simulations

Understanding spin transport in topological insulators (TIs) is crucial for the development of spin-based technologies, such as magnetic memory, sensors, and quantum bits. To optimize memory device performance, we developed a comprehensive mathematical model that describes the evolution of spin density, as a function of space and time, taking into account spin-momentum locking, spin-orbit coupling, spin dynamics, and diffusive transport processes (including phonon and impurity scattering). Using numerical simulations (finite element method and Backward Euler Method) implemented in Python, we analyzed the spin transport in TIs. Our study demonstrated a critical dependence of spin transport efficiency on device length, with a maximum efficiency of 75% at a length of 8 micrometers. Beyond a critical length of 10 micrometers, efficiency recovered, reaching 80% at 14 micrometers. We observed oscillatory behavior in spin polarization, with amplitude modulation indicating constructive and destructive interference patterns. The inclusion of spin-orbit coupling and Dirac terms in our model revealed a non-uniform spin polarization distribution, with a 30% increase in polarization near the center. Defects and boundaries significantly impacted spin transport, reducing polarization by 40% near the defect region. Through optimization, we achieved a 25% increase in spin transport efficiency and a 20% enhancement in memory device performance. Our results demonstrate the crucial role of optimizing device length, material quality, and interface engineering in achieving efficient spin transport and improved memory device performance, paving the way for the development of high-performance spin-based technologies.

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We explore the supercritical phase of the vertex-reinforced jump process (VRJP) and the H2|2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {H}^{2|2}$$\\end{document}-model on rooted regular trees. The VRJP is a random walk, which is more likely to jump to vertices on which it has previously spent a lot of time. The H2|2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {H}^{2|2}$$\\end{document}-model is a supersymmetric lattice spin model, originally introduced as a toy model for the Anderson transition. On infinite rooted regular trees, the VRJP undergoes a recurrence/transience transition controlled by an inverse temperature parameter β>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta > 0$$\\end{document}. Approaching the critical point from the transient regime, β↘βc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta \\searrow \\beta _{\ extrm{c}}$$\\end{document}, we show that the expected total time spent at the starting vertex diverges as ∼exp(c/β-βc)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim \\exp (c/\\sqrt{\\beta - \\beta _{\ extrm{c}}})$$\\end{document}. Moreover, on large finite trees we show that the VRJP exhibits an additional intermediate regime for parameter values βc<β<βcerg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta _{\ extrm{c}}< \\beta < \\beta _{\ extrm{c}}^{\ extrm{erg}}$$\\end{document}. In this regime, despite being transient in infinite volume, the VRJP on finite trees spends an unusually long time at the starting vertex with high probability. We provide analogous results for correlation functions of the H2|2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {H}^{2|2}$$\\end{document}-model. Our proofs rely on the application of branching random walk methods to a horospherical marginal of the H2|2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {H}^{2|2}$$\\end{document}-model.

Transforming from Kitaev to Disguised Ising Chain: Application to CoNb_{2}O_{6}.

For many years, CoNb_{2}O_{6} has served as an exemplar of the one-dimensional Ising model. However, recent experimental and theoretical analyses challenge its applicability to this material. Prior to that, a tailored spin model for 3d^{7} systems such as Co^{2+}, known as the JKΓ model, has emerged, featuring Heisenberg (J), Kitaev (K), and Gamma (Γ) interactions. While these interactions are permitted by the symmetry of the system, their role in CoNb_{2}O_{6} remains enigmatic. We present a microscopic theory based on spin-orbit entangled J_{eff}=1/2 states, aimed at elucidating the roles of Kitaev and Gamma interactions in shaping Ising anisotropy. Leveraging strong coupling theory, we identify a dominant ferromagnetic Kitaev interaction. Furthermore, by comparing dynamical structure factors obtained via exact diagonalization with those from inelastic neutron scattering experiments, we find an antiferromagnetic Γ interaction, which dictates the Ising axis and explains the mechanism behind moment pinning. Our theory provides a microscopic origin for Ising behavior in spin-orbit coupled one-dimensional chains and posits CoNb_{2}O_{6} as a rare Kitaev chain.

Molecular beam epitaxy growth and doping modulation of topological semimetal NiTe2

In this study, high-quality thin films of the topological semimetal phase NiTe2 were prepared using the molecular beam epitaxy technique, confirmed through x-ray diffraction with pronounced Laue oscillations. Electrical transport experiments reveal that thick films have properties similar to bulk materials. By employing co-deposition, we introduced either magnetic or non-magnetic elements during the growth of thinner films, significantly altering their electrical properties. Notably, the magnetic element Cr induces long-range ferromagnetic ordering, leading to the observation of a significant anomalous Hall effect in NiTe2 thin films. The Hall conductivity remains nearly constant well below the Curie temperature, indicating the correlation with the intrinsic topological nature of the band structure. Theoretical first principles band calculations support the generation of the Weyl semimetal state in the material through magnetic doping. These findings pave the way for exploring more magnetic Weyl semimetals and related low-dimensional quantum devices based on topological semimetals.

Higher Order Topological Defects in a Moiré Lattice

AbstractTopological defects are ubiquitous, they manifest in a wide variety of systems such as liquid crystals, magnets or superconductors. The recent quest for non‐abelian anyons in condensed matter physics stimulates the interest for topological defects since they can be hosted in vortices in quantum magnets or topological superconductors. In addition to these vortex defects, this study proposes to investigate edge dislocations in 2D magnets as new building blocks for topological physics since they can be described as vortices in the structural phase field. It demonstrates the existence of higher order topological dislocations within the higher order moiré pattern of the van der Waals 2D magnet CrCl3 deposited on Au(111). Surprisingly, these higher order dislocations arise from ordinary simple edge dislocations in the atomic lattice of CrCl3. This study provide a theoretical framework explaining the higher order dislocations as vortices with a winding Chern number of 2. It is expected that these original defects can stabilize some anyons either in a 2D quantum magnet or within a 2D superconductor coupled to it.

Quantum phase transition between spin liquid and spin nematics in spin-1 Kitaev honeycomb model

Besides the exactly solvable spin-1/2 Kitaev model, higher spin-S ones, not exactly solvable, are promising playgrounds for researches on the quantum spin liquid as well. One of the main interests in higher spin-S cases is the interplay between the Kitaev spin liquid (KSL) and spin nematics. We probe this interplay in a spin-1 model on the honeycomb lattice with competing bilinear-biquadratic and Kitaev interactions. Utilizing the 2D infinite projected entangled-pair state (iPEPS), we map out the phase diagram for the ferro-biquadratic interaction. In the phase diagram, we discover the direct phase transitions between the KSL phases and ferro-quadrupolar ordered spin nematic phase, which we call the FQ phase. It has been revealed that the ferro KSL exhibits robustness against perturbations from ferro-quadrupolar interactions. Also, the FQ phase is extended to the parameter region near the antiferro-Kitaev limit. Published by the American Physical Society 2024

Entropic uncertainty relations and quantum coherence in the two-dimensional XXZ spin model with Dzyaloshinskii–Moriya interaction

Quantum renormalization group (QRG) is a tractable method for studying the criticalities of one-dimensional (1D) and two-dimensional (2D) many-body systems. By employing the QRG method, we first derive the effective Hamiltonian and QRG equations of a 2D XXZ model with Dzyaloshinskii–Moriya (DM) interaction analytically. The linear-entropy-based uncertainty, the quantum discord (QD), and the multipartite quantum coherence based on the square root of the quantum Jensen–Shannon divergence of the 2D XXZ model are then studied as the indicators of quantum phase transitions (QPTs). The nonanalytic and scaling behaviors of the uncertainty, QD and quantum coherence are also analyzed through numerical calculations. Moreover, we investigate the effect of the easy-axis anisotropy parameter and DM interaction on the QPT. We find that the uncertainty, QD, and quantum coherence can all be utilized to detect QPTs. Our findings could shed new light on the observable of the QPT of the many-body system with the uncertainty and quantum coherence, and enrich the application of QRG method to Heisenberg spin models.

Inertial spin model of flocking with position-dependent forces.

We propose an extension to the inertial spin model (ISM) of flocking and swarming. The model has been introduced to explain certain dynamic features of swarming (second sound, a lower than expected dynamic critical exponent) while preserving the mechanism for onset of order provided by the Vicsek model. The inertial spin model (ISM) has only been formulated with an imitation ("ferromagnetic") interaction between velocities. Here we show how to add position-dependent forces in the model, which allows to consider effects such as cohesion, excluded volume, confinement, and perturbation with external position-dependent field, and thus study this model without periodic boundary conditions. We study numerically a single particle with an harmonic confining field and compare it to a Brownian harmonic oscillator and to a harmonically confined active Browinian particle, finding qualitatively different behavior in the three cases.

The star–square relation and the generalized star–triangle relation from 3d supersymmetric dualities I

We study duality transformations of the star–square relation and the generalized star–triangle relation for Ising-like lattice spin models. The lattice spin models are obtained via gauge/YBE correspondence which connects the supersymmetric gauge theories and lattice spin models of statistical mechanics. By the use of integral identities coming from the duality of three-dimensional supersymmetric gauge theories, we construct hyperbolic, lens hyperbolic, trigonometric, and rational solutions to the duality transformations. These duality transformations allow us to construct spin lattice models with four-spin (the star–square relation) and three-spin (the generalized star–triangle relation) interactions.

Adiabatic quantum imaginary time evolution

We introduce an adiabatic state preparation protocol which implements quantum imaginary time evolution under the Hamiltonian of the system. Unlike the original quantum imaginary time evolution algorithm, adiabatic quantum imaginary time evolution does not require quantum state tomography during its runtime and, unlike standard adiabatic state preparation, the final Hamiltonian is not the system Hamiltonian. Instead, the algorithm obtains the adiabatic Hamiltonian by integrating a classical differential equation that ensures that one follows the imaginary time evolution state trajectory. We introduce some heuristics that allow this protocol to be implemented on quantum architectures with limited resources. We explore the performance of this algorithm via classical simulations in a one-dimensional spin model and highlight essential features that determine its cost, performance, and implementability for longer times, and compare to the original quantum imaginary time evolution for ground-state preparation. More generally, our algorithm expands the range of states accessible to adiabatic state preparation methods beyond those that are expressed as ground states of simple explicit Hamiltonians. Published by the American Physical Society 2024