We present a machine learning (ML) force-field framework for simulating the non-equilibrium dynamics of charge-density-wave (CDW) order driven by the Peierls instability. Since the Peierls distortion arises from the coupling between lattice displacements and itinerant electrons, evaluating the adiabatic forces during time evolution is computationally intensive, particularly for large systems. To overcome this bottleneck, we develop a generalized Behler-Parrinello neural-network architecture -- originally formulated for ab initio molecular dynamics -- to accurately and efficiently predict forces from local structural environments. Using the locality of electronic responses, the resulting ML force field achieves linear scaling efficiency while maintaining quantitative accuracy. Large-scale dynamical simulations using this framework uncover a two-stage coarsening behavior of CDW domains: an early-time regime characterized by a power-law growth $L \sim t^{\alpha}$ with an effective exponent $\alpha \approx 0.7$, followed by a crossover to the Allen-Cahn scaling $L \sim \sqrt{t}$ at late times. The enhanced early-time coarsening is attributed to anisotropic domain-wall motion arising from electron-mediated directional interactions. This work demonstrates the promise of ML-based force fields for multiscale dynamical modeling of condensed-matter lattice models.

A spin-polarized muon implanted into a fluoride forms a coupled F--$\mu$--F complex in which the muon spin and neighbouring fluorine nuclear spins become entangled. Here we apply radio-frequency (RF) excitation to this coupled system and use the three-dimensional distribution of emitted positrons to reconstruct the time-dependent evolution of the muon spin polarization. This three-dimensional readout, using single spin detection, is not possible in a single NMR experiment and demonstrates significant advantages that are achieved by using RF muon techniques. We demonstrate the application of this vector-readout method to the experimental observation of a muon spin echo signal that is controlled by the dipolar coupling to fluorine, as well as to a double resonance experiment, in which we use pulses tuned to separate frequencies to address both the muon and fluorine spins. This targeted approach, in which selective RF pulses can control the muon spin and other spins to which it is coupled, provides a novel route for probing systems of entangled spins.

The quantum geometric properties of typical diamond-type (C, Si, Ge) and zincblende-type (GaAs, InP, etc) semiconductors are investigated by means of the $sp^{3}s^{\ast}$ tight-binding model, which allows to calculate the quantum metric of the valence band states throughout the entire Brillouin zone. The global maximum of the metric is at the $\Gamma$ point, but other differential geometric properties like Ricci scalar, Ricci tensor, and Einstein tensor are found to vary significantly in the momentum space, indicating a highly distorted momentum space manifold. The momentum integration of the quantum metric further yields the gauge-invariant part of the spread of valence band Wannier function, whose value agrees well with that experimentally extracted from an optical sum rule of the dielectric function. Furthermore, the dependence of these geometric properties on the energy gap offers a way to quantify the quantum criticality of these common semiconductors.

Recent angle-dependent magnetoresistance measurements in underdoped cuprates have revealed compelling evidence for small hole pockets in the pseudogap regime, including observation of the Yamaji effect in HgBa$_2$CuO$_{4+\delta}$ (Chan et al., Nature Physics https://doi.org/10.1038/s41567-025-03032-2 (2025)). A key distinction between theories is their predicted Fermi volumes, measured as fractions of the square lattice Brillouin zone: $p/4$ per pocket for spin density wave (SDW) versus $p/8$ for fractionalized Fermi liquid (FL*), where $p$ is the hole doping. We calculate the $c$-axis magnetoresistance $\rho_{zz}(\theta, \phi)$ within the semiclassical Boltzmann formalism for both states, and using the ancilla layer model (ALM) for FL* in a single-band Hamiltonian. The results from the $\text{FL}^*$ phase show good consistency with current experimental data. Conversely, the results for the SDW phase are highly sensitive to the ordering momentum along the $z$-direction. An ordering vector of $Q = (\pi, \pi, \pi)$ yields predictions that starkly disagree with the experiment. The only possibility for agreement within the SDW scenario is to assume an ordering momentum of $Q = (\pi, \pi, 0)$. However, even in this specific case, the SDW scenario predicts a marginally smaller Yamaji angle at $\phi=0$ than the FL* theory, and a second Yamaji peak near in-plane angle $\phi = 45^\circ$, which was not observed in the experiment. In reality, the Néel ordering vector is likely uncorrelated between adjacent layers, so that there is no coherent interlayer transport of hole-pocket quasiparticles in the SDW scenario, and consequently no Yamaji effect. Our results support the FL* interpretation of Fermi arcs in the pseudogap phase, and establish Yamaji angle measurements as a discriminatory tool between theoretical models.

The Holstein-Primakoff boson representation of quantum spins and associated large-$S$ expansion have been the standard framework for describing the spin wave excitations in magnetically order phases of quantum spin systems. However, we will show that the omission of projection operators and normal-ordering in this representation can produce incorrect magnon hamiltonians for finite $S$. We will present the exact normal-ordered forms of the finite-$S$ projection operators and projected Holstein-Primakoff boson representations of spin and quadrupole operators, which can produce exact two-magnon interaction terms under ferromagnetic or fully polarized states. We will also discuss the difficulties of applying this projected representation to antiferromagnetic spin wave theory.

Going beyond isolated system dynamics, we examine how local and spatially correlated reservoirs influence the work extraction in quantum batteries. By employing a one-dimensional spin-1/2 model coupled to baths via dephasing and amplitude-damping noise, we demonstrate that correlations in reservoirs can significantly enhance battery's performance compared to local noise. In the dephasing scenario, we prove that correlated reservoirs produce a finite amount of extractable work, or ergotropy, during the transient regime when a two-cell battery is initialized in a product state while local noise yields vanishing ergotropy at all times, despite nonvanishing stored energy in both cases. Numerical simulations confirm that this advantage persists across larger system sizes and for both entangled and product initial states. We also find that the dynamics of quantum coherence closely mirror those of ergotropy, highlighting coherence as a key resource underlying the enhanced performance of quantum batteries. Further, we observe that the fraction of stored energy extracted from quantum batteries displays a sharper contrast between the correlated and local reservoirs. Moreover, for dephasing noise, this fraction remains independent of system size, whereas in the amplitude damping case, it exhibits a clear system-size dependence within the transient regime, highlighting distinct operational behaviors under different noise models. In addition, we reveal that when the battery dynamics is governed by an effective Hamiltonian with long-range interactions, it yields higher ergotropy compared to short-range interactions, emphasizing the advantages of reservoir engineering for efficient device design.

We present a rigorous derivation of the orbital magnetization formula for interacting electrons within the self-consistent Hartree-Fock approximation. Our results are expressed entirely in terms of the self-consistent wavefunctions and the Hartree-Fock energy spectrum at zero magnetic field. We test the formula on an interacting Rashba model, finding an agreement with calculations performed at small but non-zero external magnetic field. Our method allows us to also derive formulas for the orbital magnetic susceptibility.

Understanding the timescales associated with relaxation to equilibrium in closed quantum many-body systems is one of the central focuses in the study of their non-equilibrium dynamics. At late times, these relaxation processes exhibit universal behavior, emerging from the inherent randomness of chaotic Hamiltonians. In this work, we investigate a disordered spin-$1/2$ XX ladder - an experimentally realizable model known for its diffusive dynamics - to explore the connection between transport properties and spectral measures derived solely from the system's energy levels via these relaxation timescales. We begin by analyzing the spectral form factor, which yields the time when the system begins to follow the random matrix theory (RMT) statistics, known as the RMT time. We then determine the Thouless times - the average times for a local excitation to diffuse across the entire finite system - through the linear-response theory for both spin and energy transport. Our numerical results confirm that the RMT time scales quadratically with system size and upper bounds the Thouless times. Interestingly, we also find that, unlike other non-integrable models, spin diffusion proceeds faster than energy diffusion.

Topological phases are expected to carry enhanced computational power, stemming from the long-range entanglement that characterizes them. Here we investigate whether this advantage is reflected in quantum magic, quantified through stabilizer Rényi entropies (SREs). We analyze one-dimensional models with an exact duality between a symmetry-protected topological phase and a trivial one. Surprisingly, a finite (parameters dependent) asymmetry appears only when boundary conditions break the duality, and emerges as well in the transverse-field Ising chain, which lacks topological order. These results complement recent analysis in the literature and show that the total magic of a state is unable to detect topological phases, indicating either that a different property is required to capture their unique quantum contribution, or that not all forms of long-range entanglement constitute a genuine computational resource.

We investigate the phase diagram of moiré double bilayer transition metal dichalcogenides with ABBA stacking as a function of twist angle and applied pressure. At hole filling $\nu = 2$ per moiré unit cell, the noninteracting system hosts a Dirac semimetal with graphene-like low-energy bands in the moiré Brillouin zone. At small twist angles, the Fermi velocity is reduced and interactions dominate the low-temperature behavior. A strong-coupling analysis identifies insulating ferromagnetic and antiferromagnetic ground-state candidates, characterized by spin-density modulations set by the moiré scale. Using a realistic continuum model with long-range Coulomb interactions, we perform self-consistent Hartree-Fock calculations to study the competition between these states. Varying the twist angle or pressure drives a transition from a Dirac semimetal to an antiferromagnetic insulator, which breaks SU(2) spin rotation and two-fold lattice rotation symmetries. This semimetal-to-insulator transition is continuous and belongs to the (2+1)D relativistic Gross-Neveu-Heisenberg universality class with $N = 2$ four-component Dirac fermions. Finite heterostrain, relevant in realistic samples, induces a crossover from Gross-Neveu-Heisenberg universality at intermediate temperatures to conventional (2+1)D Heisenberg criticality at the lowest temperatures. Further decreasing the twist angle can cause a level crossing from the antiferromagnetic insulator into a ferromagnetic insulator with spin-split bands. Our results provide a comprehensive theoretical framework that complements and elucidates recent experiments in twisted double bilayer WSe$_2$.

Moiré lattices provide a highly tunable platform for exploring the interplay between electronic correlations and band topology. Introducing a second moiré pattern extends this paradigm: interference between the two moiré patterns produces a supermoiré modulation, opening a route to further tailor electronic properties. Twisted trilayer graphene generally exemplifies such a system: two distinct moiré patterns arise from the relative twists between adjacent graphene layers. Here, we report the observation of correlated phenomena across a wide range of twisted trilayer graphene devices whose twist angles lie along two continuous lines in the twist-angle parameter space. Depending on the degree of lattice relaxation, twisted trilayer graphene falls into two classes: moiré polycrystals, composed of periodic domains with locally commensurate moiré order, and moiré quasicrystals, characterized by smoothly varying local moiré configurations. In helically twisted moiré polycrystals, we observe an anomalous Hall effect, consistent with topological bands arising from domains with broken $xy$-inversion symmetry. In contrast, superconductivity appears generically in our moiré quasicrystals. A subset of these systems exhibits signatures of spatially modulated superconductivity, which we attribute to the supermoiré structure. Our findings uncover the organizing principles of the observed correlated phases in twisted trilayer graphene, highlight the critical roles of the supermoiré modulation and lattice relaxation, and suggest a broader framework in which magic conditions arise not as isolated points but as extended manifolds within the multi-dimensional twist-angle space of complex moiré materials.

Partial chemical substitution inevitably introduces disorder. In doped Hund's metals, such as the iron-based superconductors, effects like charge doping and chemical pressure are often considered dominant. Here, we investigate spin excitations in Ba(Fe$_{1-x}$Cr$_x$)$_2$As$_{2}$ (CrBFA) by high-resolution Resonant inelastic X-ray scattering (RIXS) for samples with $x = 0, 0.035,$ and $0.085$. In CrBFA, Cr acts as a hole dopant, but also introduces localized spins that compete with Fe-derived magnetic excitations. We found that the Fe-derived magnetic excitations are softened primarily by damping, becoming overdamped for $x = 0.085$. At this doping level, complementary angle-resolved photoemission spectroscopy measurements (ARPES) show the absence of electronic structure reconstruction effects such as the nematic band splitting. We propose a localized spin model that explicitly incorporates substitutional disorder and Cr local moments, successfully reproducing our key observations. These results reveal a case where disorder dominates over charge doping in the case of a correlated Hund's metal.

Altermagnetism, an unconventional magnetic phase characterized by zero net magnetism and a spin-split electronic band, has been studied exclusively in conventional crystalline materials. In this work, we extend the theoretical framework of altermagnetism to quasicrystals (QCs), which lack translational symmetry. We classify magnetic phases in 2D QCs with $n$-fold rotational symmetry without spin-orbit coupling, by using the irreducible representation (IRRP) of the $D_n$ point group. Based on symmetry analysis, we propose the conjecture that magnetic phases corresponding to 1D non-identity IRRPs are generally altermagnetic, with the exception of those possessing parity-time symmetry. To verify our conjecture, we take the Hubbard model as an example and develop a systematic approach to determine the magnetic pattern in the QC, which effectively avoids getting trapped at local energy minima. Consequently, our tests for the Hubbard model on various QCs with different symmetries are unexceptionally consistent with our proposal. Our work highlights the QC as a platform where the altermagnetism is common among magnetic phases.

We explore the quench dynamics of PT-symmetric non-Hermitian systems by utilizing the biorthogonal formalism. We analyze quench dynamics of observable quantities, the quantum geometric tensor, and various entanglement quantities, including the entanglement entropy, the SVD entropy, and the Tu-Tzeng-Chang entropy. Our results show that a sudden quench into a PT-broken phase generally leads to exponential growth in these quantities, driven by the biorthogonal density matrix's non-positivity. In contrast to generic interacting systems, we observe a surprising linear decay in the TTC entropy for non-interacting fermionic systems. This finding originates from the approximate spectral symmetry of the biorthogonal reduced density matrix, and we confirm our findings using the Yang-Lee and non-Hermitian XXZ models.

The rapid development of neural quantum states (NQS) has established it as a promising framework for studying quantum many-body systems. In this work, by leveraging the cutting-edge transformer-based architectures and developing highly efficient optimization algorithms, we achieve the state-of-the-art results for the doped two-dimensional (2D) Hubbard model, arguably the minimum model for high-Tc superconductivity. Interestingly, we find different attention heads in the NQS ansatz can directly encode correlations at different scales, making it capable of capturing long-range correlations and entanglements in strongly correlated systems. With these advances, we establish the half-filled stripe in the ground state of 2D Hubbard model with the next nearest neighboring hoppings, consistent with experimental observations in cuprates. Our work establishes NQS as a powerful tool for solving challenging many-fermions systems.

Holographic duality describes gravitational theories in terms of quantum many-body systems. In holography, quantum information theory provides a crucial tool that directly connects microscopic structures of these systems to the geometries of gravitational spacetimes. One manifestation is that the entanglement entropy in quantum many-body systems can be calculated from the area of an extremal surface in the corresponding gravitational spacetime. This implies that a gravitational spacetime can emerge from an enormous number of entangled qubits. In this Essay, I will discuss open problems in this area of research, considering recent developments and outlining future prospects towards a complete understanding of quantum gravity. The first step in this direction is to understand what kind of quantum circuits each holographic spacetime corresponds to, drawing on recent developments in quantum complexity theories and studying concrete examples of holography in string theory. Next, we should extend the concept of holography to general spacetimes, e.g., those spacetimes which appear in realistic cosmologies, by utilizing the connections between quantum information and holography. To address the fundamental question of how time emerges, I will propose the concepts of pseudo-entropy and time-like entanglement as a useful tool in our exploration.