Weak Transverse Field Research Articles

Evidence of Spin Density Waves in La_{3}Ni_{2}O_{7-δ}.

The recently discovered superconductivity with critical temperature T_{c} up to 80K in the double-layer Nickelate La_{3}Ni_{2}O_{7-δ} under pressure has drawn great attention. Here, we report the positive muon spin relaxation (μ^{+}SR) study of polycrystalline La_{3}Ni_{2}O_{6.92} under ambient pressure. Zero-field μ^{+}SR experiments reveal the existence of magnetic order in La_{3}Ni_{2}O_{6.92} with T_{N}=154 K. The weak transverse field μ^{+}SR measurements reveal the bulk nature of magnetism. In addition, a small quantity of oxygen deficiencies can greatly broaden the internal magnetic field distribution sensed by muons.

Impact of Mn-Pn intermixing on magnetic properties of an intrinsic magnetic topological insulator: the µSR perspective

We investigated the magnetic properties of polycrystalline samples of the intrinsic magnetic topological insulators MnPn2Te4, with pnictogen Pn = Sb, Bi, by bulk magnetization and µSR. DC susceptibility detects the onset of magnetic ordering at TN = 27 K and 24 K and a field dependence of the macroscopic magnetization compatible with ferri- (or ferro-) and atiferro- magnetic ordering, respectively. Weak transverse field (wTF) Muon Spin Rotation (µSR) confirms the homogeneous bulk nature of magnetic ordering at the same two distinct transition temperatures. Zero Field (ZF) µSR shows that the Sb based material displays a broader distribution of internal field at the muon, in accordance with a larger deviation from the stoichiomectric composition and a higher degree of positional disorder (Mn at the Pn(6c) site), which however does not affect significantly the sharpness of the thermodynamic transition, as detected by the muon magnetic volume fraction and the observability of a critical divergence in the longitudinal and transverse muon relaxation rates.

Universality of Replica-Symmetry Breaking in the Transverse Field Sherrington–Kirkpatrick Model

The existence theorem for replica-symmetry breaking (RSB) in the transverse field Sherrington-Kirkpatrick (SK) model is extended to the model with a general random exchange interactions. The relation between the expectation value of the exchange interaction energy and the Duhamel correlation function of spin operators can be obtained by an approximate integration by parts for general random interactions. In addition to the Falk-Bruch inequality, these explicit evaluations enable us to prove that the variance of overlap between two replica spin operators does not vanish under sufficiently weak transverse field in sufficiently low temperature. The absence of the ferromagnetic long range order is also shown to distinguish RSB from the $\mathbb Z_2$-symmetry breaking.

Emergence of Hilbert Space Fragmentation in Ising Models with a Weak Transverse Field.

The transverse-field Ising model is one of the fundamental models in quantum many-body systems, yet a full understanding of its dynamics remains elusive in higher than one dimension. Here, we show for the first time the breakdown of ergodicity in d-dimensional Ising models with a weak transverse field in a prethermal regime. We demonstrate that novel Hilbert-space fragmentation occurs in the effective nonintegrable model with d≥2 as a consequence of only one emergent global conservation law of the domain wall number. Our results indicate nontrivial initial-state dependence for nonequilibrium dynamics of the Ising models with a weak transverse field.

Force-free magnetic flux ropes: String confinement of super-strong magnetic fields and flare energy release

ABSTRACT A new class of force-free solutions for a horizontal magnetic filament with a circular cross-section is found, in which the magnetic field strength on the axis significantly (up to 2–3 orders of magnitude and more) exceeds the strength of the longitudinal external field that keeps the rope from lateral expansion. A weak transverse field leads to a small deviation from the force-free field structure and results in a density deficit and an increase in temperature on the rope axis. The possibility of a flare release of magnetic energy is shown when critical values ​​of the longitudinal electric current density in the filament are reached at which ‘anomalous resistance’ occurs, caused by the development of the current ion-sound plasma instability. It turns out to be much larger than the usual Coulomb resistance. The following values are determined: the scale of the current dissipation region, the electric field strength in it, which significantly exceeds the Dreicer value, and the possible energy of accelerated charged particles (up to hundreds of MeV). The critical density of the longitudinal current at which the plasma turbulence is excited does not depend on the presence of a super-strong field on the flux-rope axis, so that the current density depends only on the electron concentration, temperature, and anomalous conductivity. However, super-strong magnetic fields can manifest themselves in the fact that, in their presence, the excitation of plasma instabilities can occur at sufficiently high electron concentrations. This effect may explain the large number of accelerated particles sometimes observed in solar flares.

Quantum dynamics of topological strings in a frustrated Ising antiferromagnet

AbstractWe investigate the quantum dynamics of the antiferromagnetic transverse field Ising model on the triangular lattice through large-scale quantum Monte Carlo simulations and stochastic analytic continuation. This model effectively describes a series of triangular rare-earth compounds, for example, TmMgGaO4. At weak transverse field, we capture the excitations related to topological quantum strings, which exhibit continuum features described by XY chain along the strings and those in accord with ‘Luttinger string liquid’ in the perpendicular direction. The continuum features can be well understood from the perspective of topological strings. Furthermore, we identify the contribution of strings from the excitation spectrum. Our study provides characteristic features for the experimental search for string-related excitations and proposes a theoretical method to pinpoint topological excitations in the experimental spectra.

Fragmentation and Emergent Integrable Transport in the Weakly Tilted Ising Chain.

We investigate emergent quantum dynamics of the tilted Ising chain in the regime of a weak transverse field. Within the leading order perturbation theory, the Hilbert space is fragmented into exponentially many decoupled sectors. We find that the sector made of isolated magnons is integrable with dynamics being governed by a constrained version of the XXZ spin Hamiltonian. As a consequence, when initiated in this sector, the Ising chain exhibits ballistic transport on unexpectedly long timescales. We quantitatively describe its rich phenomenology employing exact integrable techniques such as generalized hydrodynamics. Finally, we initiate studies of integrability-breaking magnon clusters whose leading-order transport is activated by scattering with surrounding isolated magnons.

Low-temperature domain-wall freezing and nonequilibrium dynamics in the transverse-field Ising model material CoNb2O6

${\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}$ is a rare realization of the transverse-field Ising model, making it a useful tool for studying both equilibrium and nonequilibrium many-body quantum physics. Despite a large body of work dedicated to characterizing this material, details of the ordered states in the presence of relatively weak transverse fields have not been discussed in detail. Here, we present a detailed study of ${\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}$ via ac susceptibility measurements in order to further characterize its low-temperature behavior in the presence of a transverse field. Specifically, we call attention to an unconventional freezing transition in zero field below ${T}_{F}=1.2$ K, occurring within the well-known commensurate antiferromagnetic (CAFM) state that onsets at ${T}_{N2}=1.9$ K. We performed a series of transverse-field quenches into this frozen state, which resulted in a slowly relaxing susceptibility, ${\ensuremath{\chi}}^{\ensuremath{'}}(t)$, that followed a logarithmic decay within the time range measured. We discuss the frozen state in the context of the freezing of previously discussed ``free'' chains arising from domain walls between the four degenerate sublattices of the CAFM state. We also attempted to observe Kibble-Zurek scaling by quenching the transverse field into the frozen state at different rates. This produced a null result; the behavior can be fully explained by coarsening of domains over the time scale of the quenches. The absence of a clear Kibble-Zurek scaling is itself surprising, given the proposed ubiquity of the phenomenon for general second-order phase transitions.

Quantum simulation of lattice gauge theories on superconducting circuits: Quantum phase transition and quench dynamics

Recently, quantum simulation of low-dimensional lattice gauge theories (LGTs) has attracted many interests, which may improve our understanding of strongly correlated quantum many-body systems. Here, we propose an implementation to approximate ℤ2 LGT on superconducting quantum circuits, where the effective theory is a mixture of a LGT and a gauge-broken term. By using matrix product state based methods, both the ground state properties and quench dynamics are systematically investigated. With an increase of the transverse (electric) field, the system displays a quantum phase transition from a disordered phase to a translational symmetry breaking phase. In the ordered phase, an approximate Gauss law of the ℤ2 LGT emerges in the ground state. Moreover, to shed light on the experiments, we also study the quench dynamics, where there is a dynamical signature of the spontaneous translational symmetry breaking. The spreading of the single particle of matter degree is diffusive under the weak transverse field, while it is ballistic with small velocity for the strong field. Furthermore, due to the emergent Gauss law under the strong transverse field, the matter degree can also exhibit confinement dynamics which leads to a strong suppression of the nearest-neighbor hopping. Our results pave the way for simulating the LGT on superconducting circuits, including the quantum phase transition and quench dynamics.

Probing eigenstate thermalization in quantum simulators via fluctuation-dissipation relations

The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems. So far, however, experimental studies have focused on the relaxation dynamics of observables as described by the diagonal part of ETH, whose verification requires substantial numerical input. This leaves many of the general assumptions of ETH untested. Here, we propose a theory-independent route to probe the full ETH in quantum simulators by observing the emergence of fluctuation-dissipation relations, which directly probe the off-diagonal part of ETH. We discuss and propose protocols to independently measure fluctuations and dissipations as well as higher-order time ordered correlation functions. We first show how the emergence of fluctuation dissipation relations from a nonequilibrium initial state can be observed for the 2D Bose-Hubbard model in superconducting qubits or quantum gas microscopes. Then we focus on the long-range transverse field Ising model (LTFI), which can be realized with trapped ions. The LTFI exhibits rich thermalization phenomena: For strong transverse fields, we observe prethermalization to an effective magnetization-conserving Hamiltonian in the fluctuation dissipation relations. For weak transverse fields, confined excitations lead to non-thermal features resulting in a violation of the fluctuation-dissipation relations up to long times. Moreover, in an integrable region of the LTFI, thermalization to a generalized Gibbs ensemble occurs and the fluctuation-dissipation relations enable an experimental diagonalization of the Hamiltonian. Our work presents a theory-independent way to characterize thermalization in quantum simulators and paves the way to quantum simulate condensed matter pump-probe experiments.

Quantum many-body scars in transverse field Ising ladders and beyond

We identify quantum many-body scars in the transverse field quantum Ising model on a ladder. We make explicit how the corresponding (mid spectrum, low entanglement) many-body eigenstates can be approximated by injecting quasi-particle excitations into an exact, zero-energy eigenstate, which is of valence bond solid type. Next, we present a systematic construction of product states characterized, in the limit of a weak transverse field, by a sharply peaked local density of states. We describe how the construction of these "peak states" generalizes to arbitrary dimension and show that on the ladder their number scales with system size as the square of the golden ratio.

Tuning the two-step melting of magnetic order in a dipolar kagome spin ice by quantum fluctuations

Complex magnetic orders in frustrated magnets may exhibit rich melting processes when the magnet is heated toward the paramagnetic phase. We show that one may tune such melting processes by quantum fluctuations. We consider a kagome lattice dipolar Ising model subject to transverse field and focus on the thermal transitions out of its magnetic ground state, which features a $\sqrt{3}\times\sqrt{3}$ magnetic unit cell. Our quantum Monte Carlo (QMC) simulations suggest that, at weak transverse field, the $\sqrt{3}\times\sqrt{3}$ phase melts by way of an intermediate magnetic charge ordered phase where the lattice translation symmetry is restored while the time reversal symmetry remains broken. By contrast, at stronger transverse field, QMC simulations suggest the $\sqrt{3}\times\sqrt{3}$ phase melts through a floating Kosterlitz-Thouless phase. The two distinct melting processes are separated by either a multicritical point or a short line of first order phase transition.

Spontaneous generation of spin current from the vacuum by strong electric fields

AbstractWe discuss spontaneous spin current generation from the vacuum by strong electric fields as a result of interplay between the Schwinger mechanism and a spin–orbit coupling. By considering a homogeneous slow strong electric field superimposed by a fast weak transverse electric field, we explicitly evaluate the vacuum expectation value of a spin current (the Bargmann–Wigner spin current) by numerically solving the Dirac equation. We show that a non-vanishing spin current polarized in the direction perpendicular to the electric fields flows mostly in the longitudinal direction. We also find that a relativistic effect due to helicity conservation affects the direction/polarization of a spin current.

Wave Vector Difference of Magnetic Bragg Reflections and Low Energy Magnetic Excitations in Charge-stripe Ordered La2NiO4.11

We report on the magnetism of charge-stripe ordered La2NiO4.11±0.01 by neutron scattering and μSR. On going towards zero energy transfer there is an observed wave vector offset in the centring of the magnetic excitations and magnetic Bragg reflections, meaning the excitations cannot be described as Goldstone modes of the magnetic order. Weak transverse field μSR measurements determine the magnetically order volume fraction is 87% from the two stripe twins, and the temperature evolution of the magnetic excitations is consistent with the low energy excitations coming from the magnetically ordered volume of the material. We will discuss how these results contrast with the proposed origin of a similar wave vector offset recently observed in a La-based cuprate, and possible origins of this effect in La2NiO4.11.

Mapping the weak plasmonic transverse field by a dielectric-nanoparticle-on-film structure with ultra-high precision.

Highly confined electromagnetic fields play a significant role in modern nano-optics, among which surface plasmon polaritons (SPPs) are outstanding because of their subwavelength and enhancement nature. While many state-of-the-art methods have been proposed to uncover the field distribution of SPPs, it still faces challenge to map the weak transverse field component (the field tangential to the interface) of SPPs with high contrast and precision. We propose a direct imaging technique, which employs a dielectric-nanoparticle-on-metal-film (DNP-MF) structure as a near-field probe, to overcome this difficulty. The angular distribution of the scattering radiation from the structure is strongly polarization dependent. By extracting the scattering signals that are mainly induced by the horizontal polarization, the imaging of the weak plasmonic transverse field with high precision can be achieved. The mappings of SPPs distributions excited by various vector beams were performed in experiment, which accord excellent with theory. This technique provides a new approach for near-field imaging with high contrast and reliability, which is expected to be valuable for studying the vectorial features of SPPs such as transverse spin, spin-orbit interactions, etc.

Specific heat and nonlinear susceptibility in spin glasses with random fields

We study magnetic properties of spin glass (SG) systems under a random field (RF), based on the suggestion that RFs can be induced by a weak transverse field in the compound ${\mathrm{LiHo}}_{x}{\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{F}}_{4}$. We consider a cluster spin model that allows long-range disordered interactions among clusters and short-range interactions inside the clusters, besides a local RF for each spin following a Gaussian distribution with standard deviation $\mathrm{\ensuremath{\Delta}}$. We adopt the one-step replica symmetry breaking approach to get an exactly solvable single-cluster problem. We discuss the behavior of order parameters, specific heat ${C}_{m}$, nonlinear susceptibility ${\ensuremath{\chi}}_{3}$, and phase diagrams for different disorder configurations. In the absence of RF, the ${\ensuremath{\chi}}_{3}$ exhibits a divergence at ${T}_{f}$, while the ${C}_{m}$ shows a broad maximum at a temperature ${T}^{**}$ around $30%$ above ${T}_{f}$, as expected for conventional SG systems. The presence of RF changes this scenario. The ${C}_{m}$ still shows the maximum at ${T}^{**}$ that is weakly dependent on $\mathrm{\ensuremath{\Delta}}$. However, the ${T}_{f}$ is displaced to lower temperatures, enhancing considerably the ratio ${T}^{**}/{T}_{f}$. Furthermore, the divergence in ${\ensuremath{\chi}}_{3}$ is replaced by a rounded maximum at a temperature ${T}^{*}$, which becomes increasingly higher than ${T}_{f}$ as $\mathrm{\ensuremath{\Delta}}$ is enhanced. As a consequence, the paramagnetic phase is unfolded in three regions: (i) a conventional paramagnetism ($T>{T}^{**}$); (ii) a region with formation of short-range order with frozen spins (${T}^{*}<T<{T}^{**}$); (iii) a region with slow growth of free-energy barriers slowing down the spin dynamics before the SG transition (${T}_{f}<T<{T}^{*}$) suggesting an intermediate Griffiths phase before the SG state. Our results reproduce qualitatively some findings of ${\mathrm{LiHo}}_{x}{\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{F}}_{4}$ as the rounded maximum of ${\ensuremath{\chi}}_{3}$ behavior triggered by RF and the deviation of the conventional relationship between the ${T}_{f}$ and ${T}^{**}$.

Multiphoton-resonance-induced fluorescence of a strongly driven two-level system under frequency modulation

We study the fluorescence spectrum of a strongly driven two-level system (TLS) with modulated transition frequency, which is a bichromatically driven TLS and has multiple resonance frequencies. We are aiming to provide a reliable description of the fluorescence in a regime that is difficult to tackle with perturbation theory and the rotating-wave approximation (RWA), and illustrate the spectral features of the fluorescence under off- and multiphoton-resonance conditions. To go beyond the RWA, we use a semianalytical counter-rotating-hybridized rotating-wave method that combines a unitary transformation and Floquet theory to calculate the two-mode Floquet states and quasienergies for the bichromatically driven TLS. We then solve the master equation accounting for the spontaneous decay in the bases of the two-mode Floquet states, and derive a physically transparent fluorescence spectrum. In comparison with the numerically exact spectrum from the generalized Floquet-Liouville approach, the present spectrum is found to be applicable in a wide range of the parameters where the RWA and the secular approximation may break down. We find that the counter-rotating (CR) terms of the transverse field omitted in the RWA have non-negligible contributions to the spectrum under certain conditions. Particularly, at the multiphoton resonance the width of which is comparable with the Bloch-Siegert shift, the RWA and non-RWA spectra markedly differ from each other because of the CR-induced shift. We also analyze the symmetry of the spectrum in terms of the transition matrix elements between the two-mode Floquet states. We show that the strict symmetry of the spectrum cannot be expected without the RWA but the almost symmetric spectrum can be obtained at the single-photon resonance that takes the Bloch-Siegert shift into account if the driving is moderately strong and at the multiphoton resonance with a sufficiently weak transverse field.

Vector Magnetic Field Synoptic Charts from the Helioseismic and Magnetic Imager (HMI)

Vector magnetic field synoptic charts from the Helioseismic and Magnetic Imager (HMI) are now available for each Carrington Rotation (CR) starting from CR 2097 in May 2010. Synoptic charts are produced using 720-second cadence full-disk vector magnetograms remapped to Carrington coordinates. The vector field is derived from the Stokes parameters (\(I, Q, U, V\)) using a Milne–Eddington-based inversion model. The \(180^{\circ}\) azimuth ambiguity is resolved using the minimum energy algorithm for pixels in active regions and for strong-field pixels (the field is greater than about 150 G) in quiet-Sun regions. Three other methods are used for the rest of the pixels: the potential-field method, the radial acute-angle method, and the random method. The vector field synoptic charts computed using these three disambiguation methods are evaluated. The noise in the three components of the vector magnetic field is generally much higher in the potential-field method charts. The component noise levels are significantly different in the radial-acute charts. However, the noise levels in the random-method charts are lower and comparable. The assumptions used in the potential-field and radial-acute methods to disambiguate the weak transverse field introduce bias that propagates differently into the three vector-field components, leading to unreasonable pattern and artifacts, whereas the random method appears not to introduce any systematic bias. The current sheet on the source surface, computed using the potential-field source-surface model applied to random-method charts, agrees with the best solution (the result computed from the synoptic charts with the minimum energy algorithm applied to each and every pixel in the vector magnetograms) much better than the other two. Differences in the synoptic charts determined with the best method and the random method are much smaller than those from the best method and the other two. This comparison indicates that the random method is better for vector field synoptic maps computed from near-central meridian data. The vector field synoptic charts provided by the Joint Science Operations Center (JSOC) are therefore produced with the random method.

Isogyres - Manifestation of Spin-orbit interaction in uniaxial crystal: A closed-fringe Fourier analysis of conoscopic interference.

Discovered in 1813, the conoscopic interference pattern observed due to light propagating through a crystal, kept between crossed polarizers, shows isochromates and isogyres, respectively containing information about the dynamic and geometric phase acquired by the beam. We propose and demonstrate a closed-fringe Fourier analysis method to disentangle the isogyres from the isochromates, leading us to the azimuthally varying geometric phase and its manifestation as isogyres. This azimuthally varying geometric phase is shown to be the underlying mechanism for the spin-to-orbital angular momentum conversion observed in a diverging optical field propagating through a z-cut uniaxial crystal. We extend the formalism to study the optical activity mediated uniaxial-to-biaxial transformation due to a weak transverse electric field applied across the crystal. Closely associated with the phase and polarization singularities of the optical field, the formalism enables us to understand crystal optics in a new way, paving the way to anticipate several emerging phenomena.

Internal magnetic field in the zigzag-chain family (Na,Ca)Cr2O4

In order to elucidate the magnetic nature for a novel one-dimensional zigzag chain compound, NaCr2O4, we have measured μ+SR spectra using a powder sample in the temperature range between 2 and 200 K. Weak transverse field (wTF-) μ+SR measurements indicated that the whole volume of the sample enters into an antiferromagnetic (AF) phase below TN = 125 K. The zero field (ZF-) μ+SR spectrum obtained below TN exhibits a clear oscillation with a single muon-spin precession frequency (fμ). This suggests that static AF order is formed below TN and that all the implanted muons sense the same internal magnetic field. The temperature dependence of fμ was found to be very similar to that for the intensity of the magnetic Bragg peak in neutron diffraction (ND) measurements. On the other hand, the ZF-μ+SR spectrum for the isostructural compound, β-CaCr2O4, showed a rapidly damped oscillation below TN = 21 K, supporting the formation of incommensurate AF order, as proposed by ND.