We investigate the hole-doped Kitaev-Heisenberg (t-J-K) model on a two-leg ladder geometry using the density-matrix renormalization group (DMRG). We first consider the behavior of the antiferromagnetic Kitaev (AFK) spin-liquid phase as a function of hopping strength t and doping level. This reveals intriguing pairing tendencies only for t/K≲ 0.65, consistent with prior results on three-leg ladders, and firmly supports the emerging picture that the physics of doped Kitaev spin liquids strongly depends on the kinetic energy of the doped holes. Analysis of one- and two-hole doping uncovers close links between the spatial profiles of the plaquette operator and the charge density. We construct a doping-dependent phase diagram for antiferromagnetic Heisenberg interactions and intermediate hopping t=1. Upon doping, the rung-singlet region develops dominant superconducting correlations. Charge-density-wave correlations dominate at weak doping near the transition to the stripy phase. Spin-density wave-like behavior is found in the AFK and ferromagnetic Kitaev limits, and in the stripy phase.

We study interaction-driven edge reconstruction in a quantum spin Hall insulator described by the Bernevig-Hughes-Zhang model with Kanamori-Hubbard interactions using the real-space density matrix renormalization group method in both the grand-canonical and canonical ensembles. For a two-dimensional cylinder with a smooth edge, we identify discrete particle-number transitions that lead to a spin-polarized edge state stabilized by an emergent ferromagnetic exchange interaction. The reconstruction is orbital-selective, occurring predominantly in the s -orbital channel. Our results reveal a microscopic mechanism for emergent fluctuating moments at the edge that could compromise the topological protection of helical edge states by time-reversal symmetry.

Doped quantum magnets, especially spin liquids with fractionalized excitations, have long attracted attention as a promising path towards unconventional superconductivity. We investigate the hole-doped Kitaev-Heisenberg (t–J–K) model on a two-leg ladder geometry using the density-matrix renormalization group (DMRG). We consider the behavior of the antiferromagnetic Kitaev spin-liquid phase as a function of hopping strength t and doping level. This reveals intriguing pairing tendencies only for $$\frac{t}{K}\lesssim 0.65$$, consistent with prior results on three-leg ladders, and firmly supports the emerging picture that the physics of doped Kitaev spin liquids strongly depends on the kinetic energy of the doped holes. Analysis of one- and two-hole doping uncovers close links between spatial profiles of the plaquette operator and the charge density. We also construct a doping-dependent phase diagram for antiferromagnetic Heisenberg interactions and intermediate hopping t = 1. Upon doping, the rung-singlet region develops dominant superconducting correlations. Spin-density wave-like behavior is found in the Kitaev limits, and in the stripy phase. Quantum spin liquids-exotic phases of matter that defy ordering even at zero temperature-are believed to produce unconventional superconducting states upon doping. The authors reveal that pairing in the Kitaev-Heisenberg model strongly depends on the kinetic energy of doped holes, linking a pairing obstruction to deterioration of the spin liquid.

Quantum sensors offer exceptional sensitivity to nanoscale magnetic field fluctuations, where nonstationary effects-such as spin diffusion-and non-Markovian dynamics arising from coupling to few environmental degrees of freedom play critical roles. Because fully reconstructing the microscopic structure of realistic spin baths is often infeasible, a practical challenge is to identify the dynamical features that are actually encoded in the sensor's decoherence signal. Here we demonstrate how quantum sensors can operationally characterize the statistical nature of environmental noise, distinguishing between stationary and nonstationary behaviors, as well as Markovian and non-Markovian dynamics. Using nitrogen-vacancy centers in diamond as a platform, we develop a physical noise model that captures the essential dynamical features of realistic environments relevant to sensor observables-independently of the microscopic bath details-and provides analytical predictions for Ramsey decay across different regimes. These predictions are experimentally validated through controlled noise injection with tunable correlation properties. Our results showcase the capability of quantum sensors to isolate and identify key dynamical properties of complex environments, without requiring full microscopic bath reconstruction. This work clarifies the operational signatures of nonstationarity and non-Markovian behavior at the nanoscale and lays the foundation for strategies that mitigate decoherence while exploiting environmental dynamics for enhanced quantum sensing.

Quantum wake dynamics in quantum magnets have recently been inferred from the dynamical spin structure factor, which probes only a restricted class of local perturbations. Here, we show that resonant inelastic x-ray scattering (RIXS) selection rules act as an operator filter on fractionalized excitations, producing distinct quantum wakes in the spin-1/2 Heisenberg antiferromagnetic chain. Using explicit real-time evolution of single-spin and spin-conserving bond correlators, we find that the conventional spin response propagates up to the maximum spinon velocity, v_s=2 J, whereas the bond channels concentrate their spectral weight into a slower dominant wake with v≃ 0.92 J, while weaker components remain bounded by the full spinon light cone. The corresponding momentum- and frequency-resolved responses map onto experimentally accessible RIXS channels, demonstrating that different spectroscopic perturbations resolve complementary pathways of many-body propagation beyond the neutron-scattering spin structure factor. Their inelastic spectral weights further provide access to quantum Fisher information, while equal-time bond sum rules connect the same spectroscopic channels to the ground-state energy. Because the same correlators can be prepared and measured on quantum hardware, they also define direct, experimentally anchored benchmarks for quantum simulations, particularly in frustrated and higher-dimensional magnets where controlled classical real-time calculations become challenging.

Motivated by recent developments in the study of quasi-one-dimensional iron systems with Fe^2+, we comprehensively study the Fe^3+ chalcogenide chain system. Based on first-principles calculations, the Fe^3+ chain has a similar electronic structure as discussed before in the iron 2+ chain, due to similar FeX_4 (X = S or Se) tetrahedron chain geometry. Furthermore, a three-orbital electronic Hubbard model for this chain was constructed by using the density matrix renormalization group method. A robust antiferromagnetic coupling was unveiled in the chain direction. In addition, in the intermediate electronic correlation U/W region, we found an interesting orbital-selective Mott phase with the coexistence of localized and itinerant electrons (U is the on-site Hubbard repulsion, while W is the electronic bandwidth). Furthermore, we do not observe any obvious pairing tendency in the Fe^3+ chain in the electronic correlation U/W region, where superconducting pairing tendencies were reported before in iron ladders. This suggests that superconductivity is unlikely to emerge in the Fe^3+ systems. Our results establish with clarity the similarities and differences between Fe^2+and Fe^3+ iron chains, as well as iron ladders.

Advancing quantum sensing tools for investigating systems at atomic and nanoscales is crucial for the progress of quantum technologies. While numerous protocols employ quantum probes to extract information from stationary or weakly coupled environments, the challenges intensify at atomic- and nano-scales where the environment is inherently out-of-equilibrium or strongly coupled with the sensor. We here prove that the time-reversal symmetry in the quantum-sensor control dynamics is broken, when partial information is probed from an environment that is out-of-equilibrium with non stationary fluctuations or is described by quantum non-Gaussian, strongly coupled environmental correlations. We exploit this phenomenon as a quantum sensing paradigm with proof-of principle experimental quantum simulations using solid-state nuclear magnetic resonance (NMR). This introduces a signal contrast on a qubit-probe that quantifies how far the sensed environment is from equilibrium or its quantum non-Gaussian nature. Protocols are also presented to discern and filter a variety of environmental properties including stationary, non-stationary and non-Gaussian quantum noise fluctuations as a step toward sensing the ubiquitous environments of a quantum-sensor at atomic and nanoscales.

We propose a minimalist architecture for achieving various crystalline-symmetry-protected Majorana modes in an array of coupled quantum dots. Our framework is motivated by the recent experimental demonstrations of two-site and three-site artificial Kitaev chains in a similar setup. We find that introducing a π-phase domain wall in the Kitaev chain leads to a pair of mirror-protected Majorana zero modes located at or near the junction. Joining two π junctions into a closed loop, we can simulate two distinct classes of two-dimensional higher-order topological superconducting phases, both carrying symmetry-protected Majorana modes around the sample corners. As an extension of the π junction, we further consider a general vertex structure where n Kitaev chains meet, i.e., a Kitaev n vertex. We prove that such an n vertex, if respecting a dihedral symmetry group Dn, necessarily carries n vertex-bound Majorana modes protected by the Dn symmetry. Resilience of the junction and vertex Majorana bound states against disorder and correlation effects is also discussed. Our architecture paves the way for designing, constructing, and exploring a wide variety of artificial topological crystalline phases in quantum-dot experiments. Published by the American Physical Society 2025

Fractionalized excitations such as spinons and anyons have emerged as a central theme in condensed matter physics with broad implications for superconductivity, quantum statistics, and quantum computation. The nearly ideal one-dimensional S = 1/2 system β-VOSO4 without long-range order down to 85 mK provides a promising platform to experimentally explore such fractionalized excitations. Here, we employ Raman spectroscopy to probe magnetic excitations and the evolution of spin correlations in β-VOSO4. Spinon signatures are found along the chain direction, evidenced by a broad, gapless scattering continuum at low temperatures. The temperature dependence of the spinon spectral weight aligns considerably with numerical density matrix renormalization group calculations. By comparing the experimental spinon spectral weight with calculated results and evaluating the associated quantum Fisher information (QFI) therefrom, we observe a steep increase in QFI upon cooling, indicating rapidly growing correlation lengths. Our study showcases QFI as a probe of spin correlations in quantum magnets. Quantum entanglement plays a key role in contemporary condensed matter research, yet it remains highly elusive from an experimental standpoint. Here, the authors demonstrate that entangled quantum states are accessible through spinon excitations in a one-dimensional spin chain using Raman spectroscopy.

Quantum probes offer a powerful platform for exploring environmental dynamics, particularly through their sensitivity to decoherence processes. In this work, we investigate the emergence of critical behavior in the estimation of the environmental memory time τc, modeled as an Ornstein–Uhlenbeck process characterized by a Lorentzian spectral density. Using dynamically controlled qubit-based sensors—realized experimentally via solid-state Nuclear Magnetic Resonance (NMR) and supported by numerical simulations—we implement tailored filter functions to interrogate the environmental noise spectrum and extract τc from its spectral width. Our results reveal a sharp transition in estimation performance between short-memory (SM) and long-memory (LM) regimes, reflected in a non-monotonic estimation error that resembles a phase transition. This behavior is accompanied by an avoided-crossing-like structure in the estimated parameter space, indicative of two competing solutions near the critical point. These features underscore the interplay between control, decoherence, and inference in open quantum systems. Beyond their fundamental significance, these critical phenomena offer a practical diagnostic tool for identifying dynamical regimes and optimizing quantum sensing protocols. By exploiting this criticality, our findings pave the way for adaptive control strategies aimed at enhancing precision in quantum parameter estimation—particularly in complex or structured environments such as spin networks, diffusive media, and quantum materials.

Quantum computers hold the promise of solving certain problems that lie beyond the reach of conventional computers. However, establishing this capability, especially for impactful and meaningful problems, remains a central challenge. Here, we show that superconducting quantum annealing processors can rapidly generate samples in close agreement with solutions of the Schrödinger equation. We demonstrate area-law scaling of entanglement in the model quench dynamics of two-, three-, and infinite-dimensional spin glasses, supporting the observed stretched-exponential scaling of effort for matrix-product-state approaches. We show that several leading approximate methods based on tensor networks and neural networks cannot achieve the same accuracy as the quantum annealer within a reasonable time frame. Thus, quantum annealers can answer questions of practical importance that may remain out of reach for classical computation.

Non-Abelian anyons in quantum spin liquids (QSLs) provide a promising route to fault-tolerant topological quantum computation. In the exactly solvable Kitaev honeycomb model, such anyons of the QSL state can be bound to nonmagnetic spin vacancies and endowed with non-Abelian statistics by an infinitesimal magnetic field. Here, we investigate how this approach for stabilizing non-Abelian anyons extends to a finite magnetic field represented by a proper Zeeman term. Through large-scale density-matrix renormalization group simulations, we compute the vacancy-anyon binding energy as a function of magnetic field for both the ferromagnetic and antiferromagnetic Kitaev models. We find that anyon binding remains robust within the entire QSL phase for the ferromagnetic Kitaev model but breaks down already inside this phase for the antiferromagnetic Kitaev model. To compute a binding energy several orders of magnitude below the magnetic energy scale, we introduce both a refined definition and an extrapolation scheme based on carefully tailored perturbations.

Motivated by recent experimental progress in realizing Majorana zero modes (MZMs) using quantum dot systems, we investigate the diabatic errors associated with the movement of those MZMs. The movement is achieved by tuning time-dependent gate potentials applied to individual quantum dots, effectively creating a moving potential wall. To probe the optimized movement of MZMs, we calculate the experimentally accessible time-dependent fidelity and local density-of-states using many-body time-dependent numerical methods. Our analysis reveals that an optimal potential wall height is crucial to preserve the well-localized nature of the MZM during its movement. Moreover, we analyze diabatic errors in realistic quantum-dot systems, incorporating the effects of repulsive Coulomb interactions and disorder in both hopping and pairing terms. Additionally, we provide a comparative study of diabatic errors arising from the simultaneous versus sequential tuning of multiple gates during the MZMs movement. Finally, we estimate the timescale required for MZM transfer in a sixquantum-dot system, demonstrating that MZM movement is feasible and can be completed well within the qubit's operational lifetime in practical quantum-dot setups.

In a recent preprint [1] (arXiv:2503.05693), Tindall et al. presented impressive classical simulations of quantum dynamics using tensor networks. Their methods represent a significant improvement in the classical state of the art, and in some cases show lower errors than recent simulations of quantum dynamics using a quantum annealer [2] (King et al., Science, eado6285, 2025). However, of the simulations in Ref. [2], Ref. [1] did not attempt the most complex lattice geometry, nor reproduce the largest simulations in 3D lattices, nor simulate the longest simulation times, nor simulate the low-precision ensembles in which correlations grow the fastest, nor produce the full-state and fourth-order observables produced by Ref. [2]. Thus this work should not be misinterpreted as having overturned the claim of Ref. [2]: the demonstration of quantum simulations beyond the reach of classical methods. Rather, these classical advances narrow the parameter space in which beyond-classical computation has been demonstrated. In the near future these classical methods can be combined with quantum simulations to help sharpen the boundary between classical and quantum simulability.

Magnetic excitations in the spin chain candidate Sr2V3O9 have been investigated by inelastic neutron scattering on a single crystal sample. A spinon continuum with a bandwidth of similar to 22 meV is observed along the chain formed by alternating magnetic V4+ and nonmagnetic V5+ ions, which reveals the importance of the orbital degree of freedom in determining the chain axis as identified by prior electronic structure calculations. Incipient magnetic Bragg peaks due to weak ferromagnetic interchain couplings emerge when approaching the magnetic transition at TN similar to 5.3 K, while the excitations remain gapless within the instrumental resolution. Comparisons to the Bethe ansatz, density matrix renormalization group calculations, and effective field theories confirm Sr2V3O9 as a host of weakly coupled S = 1/2 chains dominated by antiferromagnetic intrachain interactions of similar to 7.1(1) meV.

Efficient quantum sensing technologies rely on precise control of quantum sensors, particularly two-level systems or qubits, to optimize estimation processes. We here exploit the Quantum Zeno Effect (QZE) as a tool for maximizing information obtainable by quantum sensors, with a specific focus on the level avoided crossing (LAC) phenomenon in qubit systems. While the estimation of the LAC energy splitting has been extensively studied, we emphasize the crucial role that the QZE can play in estimating the coupling strength. We introduce the concept of information amplification by the QZE for a LAC system under off-resonant conditions. The proposed approach has implications for AC magnetic field sensing and the caracterization of complex systems, including many-spin systems requiring the estimation of spin-spin couplings. Overall, our findings contribute to the advancement of quantum sensing by leveraging the QZE for improved control and information extraction.

Quasi-one-dimensional correlated electronic multiorbital systems with either ladder or chain geometries continue attracting considerable interest due to their complex electronic phases arising from the interplay of the hopping matrix, the crystal-field splitting, the electronic correlations (Hubbard repulsion U and Hund coupling JH), and strong quantum fluctuations. Recently, the intriguing cobalt zigzag chain system BaCoTe2O7, with electronic density n = 7, was prepared experimentally. Here, we systematically study the electronic and magnetic properties of this quasi-one-dimensional compound from the theoretical perspective. Based on first-principles density functional theory calculations, strongly anisotropic one-dimensional electronic Co 3d bands were found near the Fermi level. By evaluating the relevant hopping amplitudes, we provide the magnitude and origin of the nearest-neighbor (NN) and next-nearest-neighbor (NNN) hopping matrices in BaCoTe2O7. With this information, we constructed a three-orbital electronic Hubbard model for this zigzag chain system, and studied two cases: with only a NN hopping matrix, and with NN plus NNN hopping matrices. Introducing the Hubbard and Hund couplings and studying the model via the density matrix renormalization group method, we constructed the ground-state phase diagram. A robust staggered up arrow - down arrow - up arrow - down arrow antiferromagnetic (AFM) region was found when only the NN hopping matrix in the chain direction was employed. However, for the realistic case where the NNN hopping matrix is also included, the dominant state becomes instead a block AFM up arrow - up arrow - down arrow - down arrow order, in agreement with experiments. The system displays Mott insulator characteristics with three half-filled orbitals, when the block AFM order is stable. Our results for BaCoTe2O7 provide guidance to experimentalists and theorists working on this zigzag one-dimensional chain and related materials.

We study the impact of hole doping on the Kitaev-Heisenberg model on the honeycomb lattice. We investigate the pairing tendencies and correlation functions in the framework of a t - J - K model using density matrix renormalization group calculations on three-leg cylinders. In the case of the pure Kitaev model, which realizes a quantum spin-liquid phase at half-filling, we find that binding of two holes only occurs at low values of the hopping, where the holes are slow. We have theoretically verified that pair formation occurs in the limit of immobile holes, where the pure Kitaev model remains exactly solvable. When we instead fix the hopping at an intermediate, more realistic, value, and vary the Heisenberg and Kitaev interaction strengths, we find pairing tendencies only in the N & eacute;el phase. This is in contrast to prior mean-field calculations, highlighting the importance of accounting for the kinetic energy of dopants in generalized Kitaev models. Interestingly, we also find signatures of pair-density wave formation over the studied range of model parameters, namely, a periodic modulation of the charge density as well as the spin-spin and pair-pair correlations in real space. Moreover, we present a comparative study of the different correlations as a function of doping. We finally discuss the potential for experimentally observing the studied physics in quantum materials and heterostructures.

Motivated by the recently discovered high-Tc bilayer nickelate superconductor La3Ni2O7, we comprehensively research a bilayer 2 x 2 x 2 cluster for different electronic densities n by using the Lanczos method. We also employ the random-phase approximation to quantify the first magnetic instability with increasing Hubbard coupling strength, also varying n. Based on the spin structure factor S(q), we have obtained a rich magnetic phase diagram in the plane defined by n and U/W, at fixed Hund coupling, where U is the Hubbard strength and W the bandwidth. We have observed numerous states, such as A-AFM, Stripes, G-AFM, and C-AFM. At half-filling, n = 2 (two electrons per Ni site, corresponding to N = 16 electrons), the canonical superexchange interaction leads to a robust G-AFM state (pi, pi, pi) with antiferromagnetic couplings both in-plane and between layers. By increasing or decreasing electronic densities, ferromagnetic tendencies emerge from the "half-empty" and "half-full" mechanisms, leading to many other interesting magnetic tendencies. In addition, the spin-spin correlations become weaker both in the hole or electron doping regions compared with half-filling. At n = 1.5 (or N = 12), density corresponding to La3Ni2O7, we obtained the "Stripe 2" ground state (antiferromagnetic coupling in one in-plane direction, ferromagnetic coupling in the other, and antiferromagnetic coupling along the z axis) in the 2 x 2 x 2 cluster. In addition, we obtained a much stronger AFM coupling along the z axis than the magnetic coupling in the xy plane. The random-phase approximation calculations with varying n give very similar results as Lanczos, even though both techniques are based on quite different procedures. Additionally, a state with q/pi = (0.6, 0.6, 1) close to the E-phase wavevector is found in our RPA calculations by slightly reducing the filling to n = 1.25, possibly responsible for the E-phase SDW recently observed in experiments. Our predictions can be tested by chemically doping La3Ni2O7.

Out-of-time-order correlators (OTOCs) serve as a proxy for quantum information scrambling, which refers to the process where information stored locally disperses across the many-body degrees of freedom in a quantum system, rendering it inaccessible to local probes. Most experimental implementations of OTOCs to probe information scrambling rely on indirect measurements based on global observables, using techniques such as Loschmidt echoes andmultiple quantum coherences, via time-reversal evolutions. In this article, we establish a direct connection between OTOCs with global and local observables in the context of NMR experiments, where the observable is the total magnetization of the system. We conduct a numerical analysis to quantify the differences in the evolution of both magnitudes, evaluating the excitation dynamics in spin ring systems with 8 to 16 spins, using a many-body Hamiltonian and long-range interactions. Our analysis decomposes the global echo into a sum of local echoes and cross-contributions, leading to local and global OTOCs. The results indicate that, after an initial transient period, local OTOCs determine the global ones. We observe that the difference between the average of local OTOCs and the global one, as well as their fluctuations, becomes negligible as the system size increases. Thus, for large homogeneous systems, global and local OTOCs become equivalent. This behavior aligns with that observed in highly interacting or chaotic systems in several experiments.