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Exact bounds for dynamical critical exponents of transverse-field Ising chains with a correlated disorder

Highlights: • Analytic results in disordered quantum systems are obtained. • Correlated disorder changes the universality class of quantum phase transitions. • The lower and upper bounds of the dynamical critical exponent are obtained. This study investigates the dynamical critical exponent of disordered Ising chains under transverse fields to examine the effect of a correlated disorder on quantum phase transitions. The correlated disorder, where the on-site transverse field depends on the nearest-neighbor coupling strengths connecting the site, gives a qualitatively different result from the uncorrelated disorder. In the uncorrelated disorder cases where the transverse field is either homogeneous over sites or random independently of the nearest-neighbor coupling strengths, the dynamical critical exponent is infinite. In contrast, in the presence of the correlated disorder, we analytically show that the dynamical critical exponent is finite. We also show that the dynamical critical exponent depends on the tuning process of the transverse field strengths.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Unconventional supercurrent phase in Ising superconductor Josephson junction with atomically thin magnetic insulator

Abstract In two-dimensional (2D) NbSe 2 crystal, which lacks inversion symmetry, strong spin-orbit coupling aligns the spins of Cooper pairs to the orbital valleys, forming Ising Cooper pairs (ICPs). The unusual spin texture of ICPs can be further modulated by introducing magnetic exchange. Here, we report unconventional supercurrent phase in van der Waals heterostructure Josephson junctions (JJs) that couples NbSe 2 ICPs across an atomically thin magnetic insulator (MI) Cr 2 Ge 2 Te 6 . By constructing a superconducting quantum interference device (SQUID), we measure the phase of the transferred Cooper pairs in the MI JJ. We demonstrate a doubly degenerate nontrivial JJ phase ( ϕ ), formed by momentum-conserving tunneling of ICPs across magnetic domains in the barrier. The doubly degenerate ground states in MI JJs provide a two-level quantum system that can be utilized as a new dissipationless component for superconducting quantum devices. Our work boosts the study of various superconducting states with spin-orbit coupling, opening up an avenue to designing new superconducting phase-controlled quantum electronic devices.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Ising meson spectroscopy on a noisy digital quantum simulator

Abstract Quantum simulation has the potential to be an indispensable technique for the investigation of non-perturbative phenomena in strongly-interacting quantum field theories (QFTs). In the modern quantum era, with Noisy Intermediate Scale Quantum (NISQ) simulators widely available and larger-scale quantum machines on the horizon, it is natural to ask: what non-perturbative QFT problems can be solved with the existing quantum hardware? We show that existing noisy quantum machines can be used to analyze the energy spectrum of several strongly-interacting 1+1D QFTs, which exhibit non-perturbative effects like ‘quark confinement’ and ‘false vacuum decay’. We perform quench experiments on IBM’s quantum simulators to compute the energy spectrum of 1+1D quantum Ising model with a longitudinal field. Our results demonstrate that digital quantum simulation in the NISQ era has the potential to be a viable alternative to numerical techniques such as density matrix renormalization group or the truncated conformal space methods for analyzing QFTs.

Science & Technology - Other Topics↗

Liquid-like spin dynamics in a hybrid Heisenberg-Ising antiferromagnet

Two-dimensional (2D) materials and their heterostructures enable unconventional electronic properties and functionalities not accessible in their bulk counterparts. This approach is now being extended to magnetic materials to engineer their spin structures and magnetic fields produced by them. However, spin dynamics of 2D magnetic heterostructures remain largely unexplored. Here, we demonstrate that heterointerfacing Heisenberg square-lattice antiferromagnet (AF) Sr 2 IrO 4 with its bilayer variant Ising AF Sr 3 Ir 2 O 7 in a superlattice leads to liquid-like spin dynamics in the former, characterized by slow recovery of the AF order after its transient suppression by an optical pump, and complete absence of spin waves except in an immediate vicinity of the ordering wavevector. Instead, the spin excitation spectra are dominated by isotropic continua, which in previous works have been interpreted as fractional spin excitations, or spinons, that extends to unprecedentedly low energies. Thus, our results provide a pathway to frustrated magnetism in square lattices by heterointerfacing two distinct types of AFs.

RIXS↗

Electron-phonon coupling and spin fluctuations in the Ising superconductor NbSe2

Abstract Ising superconductivity, observed in NbSe 2 and similar materials, has generated tremendous interest. Recently, attention was called to the possible role that spin fluctuations (SF) play in this phenomenon, in addition to the dominant electron–phonon coupling (EPC); the possibility of a predominantly triplet state was discussed and led to a conjecture of viable singlet–triplet Leggett oscillations. However, these hypotheses have not been put to a quantitative test. In this paper, we report first principle calculations of the EPC and also estimate coupling with SF, including full momentum dependence. We find that: (1) EPC is strongly anisotropic, largely coming from the $$K-{K}^{{\prime} }$$ K − K ′ scattering, and therefore excludes triplet symmetry even as an excited state; (2) superconductivity is substantially weakened by SF, but anisotropy remains as above; and, (3) we do find the possibility of a Leggett mode, not in a singlet–triplet but in an s ++ – s ± channel.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Thermal evolution of spin excitations in honeycomb Ising antiferromagnetic FePSe 3

We use elastic and inelastic neutron scattering (INS) to study the antiferromagnetic (AF) phase transitions and spin excitations in the two-dimensional (2D) zig-zag antiferromagnet FePSe 3 . By determining the magnetic order parameter across the AF phase transition, we conclude that the AF phase transition in FePSe 3 is first-order in nature. In addition, our INS measurements reveal that the spin waves in the AF ordered state have a large easy-axis magnetic anisotropy gap, consistent with an Ising Hamiltonian, and possible biquadratic magnetic exchange interactions. On warming across T N , we find that dispersive spin excitations associated with three-fold rotational symmetric AF fluctuations change into FM spin fluctuations above T N . These results suggest that the first-order AF phase transition in FePSe 3 may arise from the competition between C 3 symmetric AF and C 1 symmetric FM spin fluctuations around T N , in place of a conventional second-order AF phase transition.

36 MATERIALS SCIENCE↗

Quantum approximate optimization of the long-range Ising model with a trapped-ion quantum simulator

Quantum computers and simulators may offer significant advantages over their classical counterparts, providing insights into quantum many-body systems and possibly improving performance for solving exponentially hard problems, such as optimization and satisfiability. Here, we report the implementation of a low-depth Quantum Approximate Optimization Algorithm (QAOA) using an analog quantum simulator. We estimate the ground-state energy of the Transverse Field Ising Model with long-range interactions with tunable range, and we optimize the corresponding combinatorial classical problem by sampling the QAOA output with high-fidelity, single-shot, individual qubit measurements. We execute the algorithm with both an exhaustive search and closed-loop optimization of the variational parameters, approximating the ground-state energy with up to 40 trapped-ion qubits. We benchmark the experiment with bootstrapping heuristic methods scaling polynomially with the system size. We observe, in agreement with numerics, that the QAOA performance does not degrade significantly as we scale up the system size and that the runtime is approximately independent from the number of qubits. We finally give a comprehensive analysis of the errors occurring in our system, a crucial step in the path forward toward the application of the QAOA to more general problem instances.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Magnetic ordering in the Ising antiferromagnetic pyrochlore Nd 2 ScNbO 7

The question of structural disorder and its effects on magnetism is relevant to a number of spin liquid candidate materials. Although commonly thought of as a route to spin glass behaviour, here we describe a system in which the structural disorder results in long-range antiferromagnetic order due to local symmetry breaking. Nd 2 ScNbO 7 is shown to have a dispersionless gapped excitation observed in other neodymium pyrochlores below T N = 0.37 K through polarized and inelastic neutron scattering. However the dispersing spin waves are not observed. This excited mode is shown to occur in only 14(2)% of the neodymium ions through spectroscopy and is consistent with total scattering measurements as well as the magnitude of the dynamic moment 0.26(2) μB . The remaining magnetic species order completely into the all-in all-out Ising antiferromagnetic structure. This can be seen as a result of local symmetry breaking due disordered Sc +3 and Nb +5 ions about the A-site. From this work, it has been established that B-site disorder restores the dipole-like behaviour of the Nd +3 ions compared to the Nd 2 ScNbO 7 parent series.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Tuning magnetism in Ising-type van der Waals magnet FePS 3 by lithium intercalation

Recently, layered transition metal thiophosphate MPX 3 (M = transition metals, X = S or Se) have gained significant attention because of their rich magnetic, optical, and electronic properties. Specifically, the diverse magnetic structures and the robustness of magnetism in the two-dimensional (2D) limit have made them prominent candidates to study 2D magnetism. Numerous efforts such as substitutions and interlayer intercalations have been adopted to tune the magnetic properties of these materials, which has greatly deepened the understanding of the underlying mechanisms that govern the properties. In this work, we focus on modifying the magnetism of Ising-type antiferromagnet FePS 3 using electrochemical lithium intercalation. Furthermore, our work demonstrate the effectiveness of electrochemical intercalation as a controllable tool to modulating magnetism, including tuning magnetic ordering temperature and inducing low temperature spin-glass state, offering an approach for implementing this material into applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Real-time scattering in Ising field theory using matrix product states

We study scattering in Ising field theory (IFT) using matrix product states and the time-dependent variational principle. IFT is a one-parameter family of strongly coupled nonintegrable quantum field theories in 1+1 dimensions, interpolating between massive free fermion theory and Zamolodchikov's integrable massive 𝐸 8 theory. Particles in IFT may scatter either elastically or inelastically. In the postcollision wave function, particle tracks from all final-state channels occur in superposition; processes of interest can be isolated by projecting the wave function onto definite particle sectors, or by evaluating energy density correlation functions. Using numerical simulations we determine the time delay of elastic scattering and the probability of inelastic particle production as a function of collision energy. We also study the mass and width of the lightest resonance near the 𝐸 8 point in detail. Close to both the free fermion and 𝐸 8 theories, our results for both elastic and inelastic scattering are in good agreement with expectations from form-factor perturbation theory. Using numerical computations to go beyond the regime accessible by perturbation theory, we find that the high-energy behavior of the two-to-two particle scattering probability in IFT is consistent with a conjecture of Zamolodchikov. Our results demonstrate the efficacy of tensor-network methods for simulating the real-time dynamics of strongly coupled quantum field theories in 1+1 dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Temporal entanglement transitions in the periodically driven Ising chain

Periodically driven quantum systems can host non-equilibrium phenomena without static analogs, including in their entanglement dynamics. Here, we discover (TET) in a Floquet spin chain, which correspond to a quantum phase transition in the spectrum of the entanglement Hamiltonian and are signaled by dynamical spontaneous symmetry breaking. We identify the symmetry principles underlying these transitions: they appear when the driven Hamiltonian preserves global symmetry (here, ℤ2), the initial state respects this symmetry, and the reduced density matrix carries weight in both subsystem-parity sectors, with TET occurring precisely when the sector weights become equal (given the previous two conditions are also satisfied). Intriguingly, we find these transitions across a broad range of driving frequencies (from adiabatic to high-frequency regime) and independently of drive details, where they manifest as periodic, sharp entanglement spectrum reorganizations marked by the Schmidt-gap closure, a vanishing entanglement echo, and symmetry-quantum-number flips, while remaining invisible to conventional local observables. At high frequencies, the entanglement Hamiltonian acquires an intrinsic timescale decoupled from the drive period, rendering the transitions genuine steady-state features. Finite-size scaling reveals universal critical behavior with correlation-length exponent 𝜈 = 1, matching equilibrium Ising universality despite its emergence from purely dynamical mechanisms decoupled from static criticality. Furthermore, our work establishes TET as novel features in Floquet quantum matter.

36 MATERIALS SCIENCE↗

Ising spin ladders of orthopyroxene CoGeO 3

Here, we present thermodynamic and spectroscopic measurements for an orthopyroxene CoGeO 3 with magnetic Co 2+ ions that form quasi-one-dimensional ladders. We show that noncollinear magnetic order below 𝑇 𝑁 = 32 K can be stabilized by a strong local easy-axis anisotropy of 𝑗 eff = 1/2 moments, which is induced by ligand octahedra distortions. Extraction of a magnetic Hamiltonian from inelastic neutron scattering measurements supports this interpretation and allows us to establish an effective magnetic model. The resulting exchange Hamiltonian justifies CoGeO 3 as a realization of an Ising spin ladder compound.

Maksimov, Pavel A. [Joint Inst. for Nuclear Resear↗

Spontaneously Broken Noninvertible Symmetries in Transverse-Field Ising Qudit Chains

Recent developments have revealed that symmetries need not form a group, but instead can be noninvertible. Here we use analytical arguments and numerical evidence to illuminate how spontaneous symmetry breaking of a noninvertible symmetry is similar yet distinct from ordinary, invertible, symmetry breaking. We consider one-dimensional chains of group-valued qudits, whose local Hilbert space is spanned by elements of a finite group 𝐺 (reducing to ordinary qubits when 𝐺=ℤ 2 ). We construct Ising-type transverse-field Hamiltonians with Rep⁡(𝐺) symmetry whose generators multiply according to the tensor product of irreducible representations (irreps) of the group 𝐺 . For non-Abelian 𝐺 , the symmetry is noninvertible. In the symmetry broken phase there is one ground state per irrep on a closed chain. The symmetry breaking can be detected by local order parameters but, unlike the invertible case, different ground states have distinct entanglement patterns. We show that for each irrep of dimension greater than one the corresponding ground state exhibits string order, entanglement spectrum degeneracies, and has gapless edge modes on an open chain—features usually associated with symmetry-protected topological order. Consequently, domain wall excitations behave as one-dimensional non-Abelian anyons with nontrivial internal Hilbert spaces and fusion rules. Our Letter identifies properties of noninvertible symmetry breaking that existing quantum hardware can probe.

1-dimensional spin chains↗

Three-dimensional Ising ferrimagnetism of Cr-Fe-Cr trimers in FeCr2Te4

We carried out a comprehensive study of magnetic critical behavior in single crystals of ternary chalcogenide Fe Cr 2 Te 4 that undergoes a ferrimagnetic transition below T c ~ 123 K. Detailed critical behavior analysis and scaled magnetic entropy change indicate a second-order ferrimagnetic transition. Critical exponents β = 0.30 ( 1 ) with T c = 122.4 ( 5 ) K , γ = 1.22 ( 1 ) with T c = 122.8 ( 1 ) K , and δ = 4.24 ( 2 ) at T c ~ 123 K suggest that the spins approach the three-dimensional Ising ( β = 0.325 , γ = 1.24 , and δ = 4.82 ) model coupled with attractive long-range interactions between spins that decay as J ( r ) ≈ r - 4.88 . Our results suggest that the ferrimagnetism in Fe Cr 2 Te 4 is due to itinerant ferromagnetism among the antiferromagnetically coupled Cr-Fe-Cr trimers.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Fulde-Ferrell-Larkin-Ovchinnikov pairing induced by a Weyl nodal line in an Ising superconductor with a high critical field

Superconductivity and electron topology are two quantum phenomena that have attracted much interest, but no causal relationship between them has been reported because superconductivity is a many-body effect due to electron-electron interaction, while electron topology is a single-particle manifestation of electron states. In this work, we demonstrate that electron topology can induce Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing in Ising Bardeen-Cooper-Schrieffer (IBCS) superconductors. Specifically, we predict that the nonmagnetic metals of the MA 2 Z 4 family, including α 1 -TaSi 2 P 4 , α 1 -TaSi 2 N 4 , α 2 -TaGe 2 P 4 , α 1 -NbSi 2 P 4 , and α 2 -NbGe 2 P 4 monolayers, are all IBCS superconductors with a transition temperature ranging from a few to tens of degrees Kelvin. The intrinsic IBCS pairing alone will enhance the in-plane critical field B c to ~20–60 times the Pauli limit B p , and the extrinsic FFLO pairing evoked by topological Weyl nodal lines under a magnetic field can further double the B c /B p ratio. Our findings not only enrich the fundamental relationship between superconductivity and electron topology, but they also yield an effective approach to enhance the robustness of superconductivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Magnetic ground state and perturbations of the distorted kagome Ising metal TmAgGe

Here, we present the magnetic orders and excitations of the distorted kagome intermetallic magnet TmAgGe. Using neutron single crystal diffraction we identify the propagation vectors k = ($\frac{1}{2}$ 0 0) and k = (0 0 0) and determine the magnetic structures of the zero-field and magnetic field-induced phases for H along the $\mathcal{a}$ and [–110] crystal directions. We determine the experimental magnetic field- temperature (H, T)-phase diagram and reproduce it by Monte Carlo simulations of an effective spin exchange Hamiltonian for one distorted kagome layer. Our model includes a strong axial single-ion anisotropy and significantly smaller exchange couplings, which span up to the third-nearest neighbors within the layer. Single crystal inelastic neutron scattering (INS) measurements reveal an almost flat, only weakly dispersive mode around 7 meV that we use alongside bulk magnetization data to deduce the crystal-electric field (CEF) scheme for the Tm 3+ ions. Random phase approximation (RPA) calculations based on the determined CEF wave functions of the two lowest quasidoublets enable an estimation of the interlayer coupling that is compatible with the experimental INS spectra. No evidence for low-energy spin waves associated to the magnetic order was found, which is consistent with the strongly Ising nature of the ground state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Magnetic structure and Ising-like antiferromagnetism in the bilayer triangular lattice compound NdZnPO

Here, the complex interplay of spin frustration and quantum fluctuations in low-dimensional quantum materials leads to a variety of intriguing phenomena. This research focuses on a detailed analysis of the magnetic behavior exhibited by NdZnPO, a bilayer spin-1/2 triangular lattice antiferromagnet. The investigation employs magnetization, specific heat, and powder neutron scattering measurements. At zero field, a long-range magnetic order is observed at T N = 1.64 K. Powder neutron diffraction experiments show the Ising-like magnetic moments along the c-axis, revealing a stripe like magnetic structure with magnetic propagation vector (1/2, 0, 1/2). Application of a magnetic field along the c-axis suppresses the antiferromagnetic order, leading to a fully polarized ferromagnetic state above B c = 4.5 T. This transition is accompanied by notable enhancements in the nuclear Schottky contribution. Moreover, the absence of spin frustration and expected field-induced plateau-like phases are remarkable observations. Detailed calculations of magnetic dipolar interactions revealed complex couplings reminiscent of a honeycomb lattice, suggesting the potential emergence of Kitaev-like physics within this system. This comprehensive study of the magnetic properties of NdZnPO highlights unresolved intricacies, underscoring the imperative for further exploration to unveil the underlying governing mechanisms.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

First-order preemptive Ising-nematic transition in K5Fe4Ag6Te10

Employing inelastic x-ray scattering and neutron scattering techniques, we observed nematic and magnetic phase transitions with distinct characters in K5Fe4Ag6Te10. Upon cooling, the nematic order undergoes a strongly first-order phase transition followed by a magnetic transition at TN≈34.7K that is consistent with a second-order transition. The temperature difference between these two phase transitions is ∼1.0(8) K. The observed phenomenon can be attributed to a distinctive first-order preemptive Ising-nematic transition, a characteristic unique to a quasi-two-dimensional scenario marked by strong out-of-plane spatial anisotropy due to weak coupling. Our studies establish K5Fe4Ag6Te10 as the first material in the family of iron pnictides and chalcogenides that possesses a nematic tricritical point preceding the magnetic one upon decreasing nematic coupling.

Giles-Donovan, N↗