Papers

In this chapter we review results on the lattice Schwinger model. In par-ticular, we show how the effect of the anomaly is reproduced on the lattice. We connect these results to recent developments in the field of quantum simulation of interacting field theories. Schemes for the quantum simulation of (approximations of) Schwinger models are discussed.

Generalized Rosenfeld-Tarazona scaling predicts the power-law dependence of the excess heat capacity of simple liquids on temperature. The two-phase model treats a liquid as a superposition of gas- and solid-like components whose relative abundance is quantified by a liquid rigidity parameter. We demonstrate here that the generalized Rosenfeld-Tarazona scaling emerges naturally in the two-phase model from the scale invariance of the liquid rigidity parameter.

Quantum droplets (QDs) in weakly interacting ultracold quantum gases are typically characterized by mean-field theories incorporating Lee-Huang-Yang (LHY) quantum fluctuations under simplified zero-range interaction assumptions. However, bridging these models to broader physical regimes like superfluid helium requires precise understanding of short-range interatomic interactions. Here, we investigate how finite-range interactions–next-order corrections to zero-range potentials–significantly alter QDs mechanics. Using a consistent effective theory, we derive an analytical equation of state (EOS) for three-dimensional bosonic mixtures under finite-range interactions at zero temperature. Leveraging the Hubbard-Stratonovich transformation, we demonstrate that interspecies attraction facilitates bosonic pairing across components characterized by the non-perturbative parameter of $\Delta$, leading to nonuniversal LHY terms that encode short-range interaction details while recovering previous universal QDs EOS in the zero-range limit. Extending superfluid hydrodynamic equations for two-component systems, we predict fractional frequency shifts in breathing modes induced by these nonuniversal terms. Experimental observation of these shifts would reveal critical insights into QDs dynamics and interatomic potential characteristics.

It is known that cuprate artificial high Tc superlattices (AHTS) with period d, composed of quantum wells confining interface space charge in stoichiometric Mott insulator layers (S), with thickness L, at the interface with overdoped normal metallic cuprate layers (N) show a superconducting dome by tuning the geometric L over d ratio of the SNSN superlattice with the top predicted by quantum material design engineering quantum size effects. Here we report high-field magneto transport measurements up to 41 Tesla of AHTS across the entire superconducting dome. The results show the universal upward-concave behavior of the temperature dependent upper critical magnetic field in low Tc samples at rising edge and drop edge of the dome providing strong evidence consistent with two-band superconductivity for two-band superconductivity in agreement with multigap theory used for quantum design of the SNSN superlattices. The measured superconducting coherence length demonstrates that atomic-scale engineering controls not only the critical temperature but also the intrinsic pair size at Fano-Feshbach resonances physics paving the way toward next generation quantum devices and shedding light on unconventional superconductivity.

Here, we present two complementary approaches that advance quadratic unconstrained binary optimization (QUBO) toward practical use in data-driven materials design and other real-valued black-box optimization tasks. First, we introduce a simple yet powerful preprocessing scheme that, when applied to a machine-learned QUBO model, entirely removes system-level equality constraints by construction. This makes cumbersome soft-penalty terms obsolete, simplifies QUBO formulation, and substantially accelerates solution search. Second, we develop a multi-objective optimization strategy inspired by Tchebycheff scalarization that is compatible with non-convex objective landscapes and outperforms existing QUBO-based Pareto front methods. We demonstrate the effectiveness of both approaches using a simplified model of a multi-phase aluminum alloy design problem, highlighting significant gains in efficiency and solution quality. Together, these methods broaden the applicability of QUBO-based optimization and provide practical tools for data-driven materials discovery and beyond.

Classical nonlinear theories are highly successful in describing far-from-equilibrium dynamics of magnets, encompassing phenomena such as parametric resonance, ultrafast switching, and even chaos. However, at ultrashort length and time scales, where quantum correlations become significant, these models inevitably break down. While numerous methods exist to simulate quantum many-body spin systems, they are often limited to near-equilibrium conditions, capture only short-time dynamics, or obscure the intuitive connection between nonlinear behavior and its geometric origin in the su(2) spin algebra. To advance nonlinear magnetism into the quantum regime, we develop a theory in which semiclassical spin correlations, rather than individual spins, serve as the fundamental dynamical variables. Defined on the bonds of a bipartite lattice, these correlations are inherently nonlocal, with dynamics following through a semiclassical mapping that preserves the original spin algebra. The resulting semiclassical theory captures nonlinear dynamics that are entirely nonclassical and naturally accommodates phenomenological damping at the level of correlations, which is typically challenging to include in quantum methods. As an application, we focus on Heisenberg antiferromagnets, which feature significant quantum effects. We predict nonlinear scaling of the mean frequency of quantum oscillations in the Néel state with the spin quantum number S. These have no classical analog and exhibit features reminiscent of nonlinear parametric resonance, fully confirmed by exact diagonalization. The predicted dynamical features are embedded in the geometric structure of the semiclassical phase space of spin correlations, making their physical origin much more transparent than in full quantum methods. With this, semiclassical spin-correlation dynamics provide a foundation for exploring nonlinear quantum magnetism.

Over the past decade, a combinatorial framework for discrete, finite, and irreversibly aggregating systems has emerged. This work reviews its progress, practical applications, and limitations. We outline the approach's assumptions and foundations, based on direct enumeration of system states, contrasting with classical Smoluchowski and Marcus-Lushnikov methods. Using the constant kernel as an example, we derive combinatorial expressions for the average number of clusters of a given size and their standard deviation, and present the complete probability distribution for cluster counts. The method is then extended to several kernels (additive, product, linear-chain, condensation) by explicitly enumerating ways to form clusters of a given size. For general kernels, approximate solutions are obtained via recursive expressions, enabling predictions without explicit solutions. Applications to aerosol growth and planetesimal formation are demonstrated, with comparisons to numerical results. We summarize issues of validity and precision and propose open problems. The appendix includes partial Bell polynomials, generating functions, Lagrange inversion, potential applications, and links between combinatorial and scaling solutions of the Smoluchowski equation.

For the BCS theory of superconductivity, the electron-phonon interaction is transformed to an attractive electron-electron interaction in the vicinity of the Fermi energy only. At the same time, its formal derivation using a unitary transformation reveals that the electrons attract one another whenever their energies do not differ more than the phonon energy $\omega_\mathrm{D}$, independent of closeness to the Fermi energy. Consequently, the order parameter becomes finite even away from the Fermi level. Yet, for small interactions, its magnitude is usually small and can be safely ignored, justifying the BCS approximation. Intriguingly, we find that an accumulation of density-of-states at an energy $\varepsilon_\mathrm{peak}$ in proximity to the Fermi energy induces a significant order parameter magnitude around $\varepsilon_\mathrm{peak}$, which exceeds the one at $E_\mathrm{F}$ for moderate coupling strengths. This strong enhancement is heralded by the softening of an additional collective mode, which resembles a second phase transition. We predict measurable signatures in the thermodynamic and spectroscopic response of this unexpected phenomenon, guiding future experimental searches for it.

We report the first observations of a pressure-induced Lifshitz transition coupled with a quantum phase transition in electron-doped cuprate superconductor Pr0.87LaCe0.13CuO4 (PLCCO), by combining high-pressure electrical resistance, Hall coefficient and synchrotron X-ray diffraction (XRD) measurements at low temperatures. Our low-temperature Hall coefficient measurements reveal that the Hall coefficient decreases continuously and reaches zero at about 10 GPa (critical pressure of Pc1). Upon further compression beyond Pc1, Hall coefficient unexpectedly changes its sign from negative to positive, signaling a reconstruction of the Fermi surface from electron-dominated to hole-dominated topology. Concurrently, the superconducting transition temperature (Tc) exhibits a monotonic suppression, vanishing completely at 17.6 GPa (critical pressure of Pc2), where the system enters a non-superconducting metallic state. Our low temperature XRD measurements unequivocally demonstrate the absence of any structural phase transition across Pc1 and Pc2. Therefore, the sign change in RH at Pc1 is associated with a Lifshitz transition, which is never found in the compressed bulk electron- or hole-doped cuprate superconductors. Moreover, the quantum phase transition observed at Pc2 contrasts sharply with known high-pressure behavior of hole-doped cuprates, uncovering a fundamental difference on how pressure tunes the ground states of electron- versus hole-doped systems. These findings provide crucial insights into the different pressure responses on the interplay among Fermi surface topology, electronic correlations, and superconductivity between these two kinds of cuprate superconductors.

We propose a lattice formulation of the Arf-Brown-Kervaire (ABK) invariant which takes values in $\mathbb{Z}_8$. Compared to the standard $\mathbb{Z}$-valued index, the ABK invariant is more involved in that it arises in Majorana fermion partition functions with reflection symmetry on two-dimensional non-orientable manifolds, and its definition contains an infinite sum over Dirac eigenvalues that requires proper regularization. We employ the massive Wilson Dirac operator, with and without domain-walls, on standard two-dimensional square lattices, and use its Pfaffian for the definition. Twisted boundary conditions and cross-caps, which reverse the orientation, are introduced to realize nontrivial topologies equipped with nontrivial $\mathrm{Pin}^{-}$ structures of Majorana fermions. We verify numerically (and partly analytically) that our formulation on a torus, Klein bottle, real projective plane (as well as its triple connected sum), and two types of Möbius strip reproduces the known values in continuum theory.

In this Letter, we predict a structural phase transition unique to chiral crystals with screw symmetry. In chiral crystals, the phonon frequency renormalized by the electron-phonon coupling depends on the handedness of circular polarization. Consequently, the soft mode encoding phonon angular momentum induces spin-selective Peierls gaps in the electronic band, entailing a helical spin density wave and chiral lattice distortion. We also elucidate the chiral signatures and functional implications of collective modes. Our findings offer crucial insights into the emergence of chirality and highlight novel functional aspects of chiral materials and their design strategy.

We show that nonequilibrium dynamics can play a constructive role in unsupervised machine learning by inducing the spontaneous emergence of latent-state cycles. We introduce a model in which visible and hidden variables interact through two independently parametrized transition matrices, defining a Markov chain whose steady state is intrinsically out of equilibrium. Likelihood maximization drives this system toward nonequilibrium steady states with finite entropy production, reduced self-transition probabilities, and persistent probability currents in the latent space. These cycles are not imposed by the architecture but arise from training, and models that develop them reproduce the empirical distribution of data classes more faithfully, with a clear correlation between agreement with the data and entropy production. Compared with equilibrium approaches such as restricted Boltzmann machines, our model breaks the detailed balance between the forward and backward conditional transitions and relies on a log-likelihood gradient that depends explicitly on the last two steps of the Markov chain. Hence, this exploration of the interface between nonequilibrium statistical physics and modern machine learning suggests that introducing irreversibility into latent-variable models can improve the fidelity of the generated data distribution.

We investigate the dynamics of nonlinear optical Thouless pumps in the presence of disorder, using optical waveguide arrays. It was previously known that the displacement of solitons in Thouless pumps is quantized and may exhibit integer and fractional transport over the course of the pump cycle. Here, we demonstrate that, in disordered nonlinear pumps, quantization may be maintained despite the presence of disorder, even though it would not be in the linear domain. Moreover, nonlinearity allows pumps to be executed more quickly (i.e., less adiabatically). This may serve as a design principle for integrated non-reciprocal devices based on temporal modulation.

We consider a wire consisting of a conducting ferromagnetic layer and an insulating antiferromagnetic layer that are coupled. The ferromagnet hosts a domain wall, which is dynamically driven by a charge current. We show that for a specific time-dependent current, the domain wall moves according to a Rindler trajectory. This motion excites spin waves in the antiferromagnetic insulator, and their emission spectrum is characterised by an effective temperature analogous to the Unruh temperature, $T_U = \hbar a/2\pi c k_B$, with a the acceleration of the domain wall, c the maximum antiferromagnetic spin wave velocity, and kB the Boltzmann constant. This thermal signature is a direct consequence of the Unruh effect and could be experimentally observed. Our results establish magnetism as a promising platform for probing relativistic quantum field phenomena. Moreover, since the Unruh effect is inherently linked to entanglement, our proposal provides a route for entangling magnetic domain walls via relativistic effects.

Although the Kadanoff-Baym equations are typically solved using time-stepping methods, iterative global-in-time solvers offer potential algorithmic advantages, particularly when combined with compressed representations of two-time objects. We examine the computational complexity and stability of several global-in-time iterative methods, including multiple variants of fixed point iteration, Jacobian-free methods, and a Newton-Krylov method using automatic differentiation. We consider the ramped and periodically-driven Falicov-Kimball and Hubbard models within time-dependent dynamical mean-field theory. Although we observe that several iterative methods yield stable convergence at large propagation times, a standard forward fixed point iteration does not. We find that the number of iterations required to converge to a given accuracy with a fixed time step size scales roughly linearly with the number of time steps. This scaling is associated with the formation of a propagating front in the residual error, whose velocity is method-dependent. We identify key challenges which must be addressed in order to make global solvers competitive with time-stepping methods.

In this paper we examine how porosity fluctuations affect the hydrodynamic permeability of a porous matrix or membrane. We introduce a fluctuating Darcy model, which couples the Navier-Stokes equation to the space- and time-dependent porosity fluctuations via a Darcy friction term. Using a perturbative approach, a Dyson equation for hydrodynamic fluctuations is derived and solved to express the permeability in terms of the matrix fluctuation spectrum. Surprisingly, the model reveals strong modifications of the fluid permeability in fluctuating matrices compared to static ones. Applications to various matrix excitation models - breathing matrix, phonons, active forcing - highlight the significant influence of matrix fluctuations on fluid transport, offering insights for optimizing membrane design for separation applications.

Defect engineering can improve the linked charge, spin, and lattice behavior of thermoelectric topological insulators. Using density functional theory with spin orbit coupling, we study structural, electronic, optical, thermoelectric, piezoelectric, and charge density features of pristine and Cu doped Bi2Te3. Cu substitution slightly expands the lattice and lowers the total energy minimum, which stabilizes the structure. The density of states shows that Cu d and Te p hybridization creates sharp states near the Fermi level, raising the carrier concentration and supporting higher Seebeck coefficient and power factor. Transport calculations show an increase in the Seebeck coefficient from about 180 microvolts per kelvin in pristine Bi2Te3 to about 220 microvolts per kelvin at 300 K while keeping the electrical conductivity nearly unchanged. Optical spectra reveal strong low energy absorption and very large static dielectric constants (greater than 600), indicating tunable light matter coupling. The piezoelectric coefficient e33 rises from 0.19 C/m2 in pristine Bi2Te3 to 0.38 C/m2 at 5 percent Cu and 0.51 C/m2 at 10 percent Cu, reflecting symmetry breaking and strain driven polarization. Charge density difference maps show anisotropic redistribution, with Cu donating about 0.8 electrons mainly to Te sites, which enhances p type behavior and phonon scattering. Overall, Cu doping reshapes Bi2Te3 into a multifunctional material with coupled thermoelectric, piezoelectric, and optical responses suitable for hybrid energy harvesting, infrared detection, and spin based devices.

We experimentally investigate the angle dependence of magnetization $M(\alpha)$ for single crystals of CrSb. CrSb belongs to a new class of altermagnetic materials, the small net magnetization is accompanied by alternating spin splitting in the k-space. In addition, CrSb reveals also topological features with Weyl surface states originating from bulk band topology. We observe, that $M(\alpha)$ oscillates around zero value, so magnetization is positive for $M(\alpha)$ maxima and it is negative for $M(\alpha)$ minima. The magnetization reversal curves $M(H)$ are non-linear with low-field hysteresis, but with almost linear high-field branches. The slope of the linear branches well correlates with $M(\alpha)$ oscillations, so it is positive for $M(\alpha)$ maxima and negative for $M(\alpha)$ minima. We demonstrate, that the interplay between the positive and the negative $M(H)$ slopes originates from several magnetic phases in CrSb. In particular, current-carrying topological surface states are responsible for the diamagnetic-like $M(H)$ negative slope, which dominates for the directions of full spin compensation in the bulk CrSb altermagnetic spectrum. Due to the spin-momentum locking, topological surface states are spin-polarized, which is responsible for the low-field hysteresis. Thus, we experimentally demonstrate both the altermagnetic bulk and the topological surface magnetizations for the altermagnetic candidate CrSb.

A series of Mn-doped CaKFe4As4 samples, CaK(Fe1-xMnx)4As4 with x values of 0, 0.005, 0.01, 0.02, 0.03, 0.04, and 0.05, are synthesized using two distinct routes: conventional synthesis process at ambient pressure (CSP), and high gas-pressure and high-temperature synthesis (HP-HTS) method. Comprehensive characterizations are performed on these samples to investigate their superconducting properties. This study examines the effects of Mn substitution at Fe sites in the FeAs layer on the superconducting properties of the CaKFe4As4 (1144) material. The HP-HTS process improves the microstructure and phase purity of the parent sample (x = 0), resulting in an enhanced superconducting transition temperature (Tc). In contrast, Mn doping via the CSP method in CaKFe4As4 reduces the sample quality and superconducting performance. Notably, the high-pressure synthesis method leads to an increase in the Tc by 3 to 7 K, particularly at low Mn concentrations. While the critical current density (Jc) of the parent sample (x = 0) shows a significant enhancement under the applied magnetic fields, Jc decreases for Mn-doped CaKFe4As4 bulks. These results demonstrate that high-pressure synthesis is an effective approach to improve the superconducting properties of Mn-doped 1144 compounds.

When multiple degrees of freedom share similar energy scales in quantum materials, intertwined electronic orders, which exhibit broken symmetries, are often strongly coupled. Recent studies on kagome superconductors such as CsV$_3$Sb$_5$ report rotational and time-reversal symmetry breaking linked to a charge density wave. Here, we observe a momentum-selective response of the electronic structure of CsV$_3$Sb$_5$ to an external magnetic field. By performing angle-resolved photoemission spectroscopy in a tuneable magnetic field, we demonstrate that the response of the electronic structure is compatible with piezomagnetism along with strong orbital selectivity. Our results show that the origin of the time-reversal symmetry breaking is associated with the vanadium Van Hove singularities at the onset of the charge density wave order. We also demonstrate the presence of fluctuations beyond the charge ordering temperature. Our results reveal that magnetic fields can be used as tuning knobs for disentangling intertwined orders in the momentum space for quantum materials.

Recent numerical and theoretical studies on the two-dimensional $J$-$Q_3$ model suggests that the deconfined quantum critical point is actually a $SO(5)$-symmetry-enhanced first-order phase transition that is spontaneously broken to $O(4)$. However, this conclusion has mainly relied on finite-size scaling of the entanglement entropy, lacking direct evidence from physical observables.} Here, we investigate the dynamical spectra of spin and bond operators at the deconfined critical point of the $J$-$Q_3$ model using large-scale quantum Monte Carlo simulations, and contrasting them with the well-established $\mathrm{O(3)}$ Wilson-Fisher criticality in the $J_1$-$J_2$ Heisenberg model. Although both models exhibit two gapless magnon modes in the Néel phase, their critical behaviors diverge strikingly. At the $J_1$-$J_2$ critical point, the Higgs mode becomes gapless, yielding three gapless modes that reflect the full restoration of the $\mathrm{O(3)}$ symmetry. {In the $J$-$Q_3$ model, we instead observe four gapless transverse modes at the either side of the transition. This spectral feature, together with the entanglement entropy results, provides direct evidence for the weakly first-order scenario that the deconfined quantum critical point exhibits an emergent $\mathrm{SO(5)}$ symmetry that spontaneously breaks to $\mathrm{O(4)}$.

We investigate the spatial and temporal scales of dynamical quantum phase transitions in the one-dimensional Bose-Hubbard model in the strong interaction limit. Using Jordan-Wigner transformation, we obtain the time-dependent wavefunction and therefore the subsystem Loschmidt echo, and systematically investigate how its properties vary with subsystem size. It is found that when the subsystem is sufficiently large, it exhibits logarithmic divergence identical to that of the full system Loschmidt echo, yielding a critical exponent of zero. We also obtain the required subsystem size and temporal resolution for detecting dynamical quantum phase transitions using the subsystem Loschmidt echo. It is expected that the present results provide a reliable foundation for further experimental investigations.

A model including random alloy disorder is used to account for the outstanding optical properties of InGaN quantum wells. The model provides excellent agreement to experimental observations on various structures. This study clarifies the prevalent role played by disorder in optical features such as the luminescence lineshape, the Stokes shift, and the radiative rate. Finally, the relationship between disorder and the peculiar properties of long-wavelength InGaN emitters is investigated.

Two-dimensional (2D) materials exhibit a wide range of electronic properties that make them promising candidates for next-generation nanoelectronic devices. Accurate prediction of their quantum transport behavior is therefore of both fundamental and technological importance. While density functional theory (DFT) combined with the non-equilibrium Green$'$s function (NEGF) formalism provides reliable insights, its high computational cost limits applications to large-scale or high-throughput studies. Here we present DeePTB-NEGF, a framework that combines a deep learning-based tight-binding Hamiltonians derived learned directly from first-principles calculations (DeePTB) with efficient quantum transport simulations implemented in the DPNEGF package. To validate the method, we apply it to three prototypical 2D materials: graphene, hexagonal boron nitride (h-BN), and MoS$_2$. The resulting band structures and transmission spectra show excellent agreement with conventional DFT-NEGF results, while achieving orders-of-magnitude improvement in efficiency. These results highlight the capability of DeePTB-NEGF to enable accurate and efficient quantum transport simulations, thereby opening avenues for large-scale exploration and device design in 2D materials.

In this work, we have developed a model for irradiation-assisted grain growth in nanocrystalline UO$_2$ using the MARMOT code. We include the impact of irradiation on UO$_2$ grain growth by coupling a phase field grain growth model with a heat conduction simulation that features a random heat source representing thermal spikes. Our model parameters have been calibrated against experimental measurements at 300 K. The calibrated model predicts grain growth in an irradiated UO$_2$ thin film that compares well with experimental data at 50 K. These results suggest that thermal spikes are the major cause of the irradiation-assisted grain growth observed in the UO$_2$ experiments. They also indicate that irradiation-assisted grain growth is only significant with average grain sizes less than 35 nm, and thus can be neglected when considering fuel performance of typical UO$_2$ fuel pellets.

This work reports the electrical characteristics comparison study between Cr2O3 and NiOx based heterojunction diodes (HJD) on halide vapor phase epitaxy (HVPE) grown e̱ta}-Ga2O3 epitaxial layers. Both as-fabricated Cr2O3 and NiOx HJDs exhibited forward current density in a range of 130-150 A/cm^2 at 5 V with rectifying ratios >10^10 and a reverse leakage current density at 10^-8 A/cm^2 at -5 V. The differential specific on-resistance of Cr2O3 and NiOx HJDs was 12.01 m{\Omega}*cm^2 and 12.05 m{\Omega}*cm^2, respectively. Breakdown voltages of Cr2O3 HJDs ranged from 1.4-1.9 kV and 1.5-2.3 kV for NiOx HJDs. Theoretical band alignment between Cr2O3 and e̱ta}-Ga2O3 was calculated from first principles. The ambient exposed NiOx/HVPE e̱ta}-Ga2O3 HJDs forward current density degraded after 10 days while that of Cr2O3/HVPE e̱ta}-Ga2O3 HJDs remained nearly unchanged after the same amount of time. It was later confirmed that the ambient exposed sputtered NiOx sheet resistance (Rsh) degradation gave rise to the reduction of the forward current density of the NiOx based HJDs, and water (H2O) was qualitatively determined to be the agent attributed to the forward conduction degradation by measuring the Rsh of NiOx-on-sapphire reference wafer after exposing it to different environments. The Cr2O3/HVPE e̱ta}-Ga2O3 HJD also exhibited enhanced thermal stability compared to the NiOx/e̱ta}-Ga2O3 heterostructures at elevated temperatures. Interfacial nickel gallate (Ga2NiO4) phase formation expected from phase diagrams can explain the reduced thermal stability of NiOx/e̱ta}-Ga2O3 HJDs. This study indicates that Cr2O3 is a stable p-type oxide for the realization of robust multi-kV e̱ta}-Ga2O3 HJDs.

A range of twist angles between adjacent surfaces/volumes are intrinsic to natural graphite or artificially design in multi-layer graphene. In addition, stacking faults can be created by the application of mechanic, electric or magnetic fields. Charge and spin transport then occur in relation to the existing twist-angle pattern. In two dimensions, a saddle point in the electronic band structure leads to divergence in the density of states, known as van Hove singularities (vHs). The energy difference between vHs for the conduction and valence bands was found to increase with the twist angle between neighboring graphite domains with respect to the c axis (perpendicular to the graphite planes). In this work, we estimate for the superconducting (SC)-like nano-size multi-layer granular domain in hydrogenated graphitic fibers [1]. We show that this value for and the values found by others for few-layer graphene might actually form the Fibonacci mathematical sequence. Moreover, SC hydrogenated graphite can harbour higher-order topology as reflected in at least quadratic energy gap flattening. Charge transport and magnetization measurements on hydrogenated graphitic fibers have been done using a Quantum Design Physical Properties Measurement System.

We investigate how symmetry-associated topological properties, originally defined for ground states, can be consistently extended to dynamically isolated subspaces of quantum many-body systems. Focusing on quantum many-body scars (QMBS), we show that a scar subspace is invariant under the relevant symmetries, and it can support well-defined topological properties inherited from an underlying symmetry-protected topological (SPT) ground state, even though individual scar states need not themselves be symmetric. We refer to such structures as SPT-like scar subspaces, emphasizing that the topological properties are defined at the level of the symmetry-invariant subspace rather than on a state-by-state basis. As a concrete example, we analyze the spin-$1$ Affleck–Kennedy–Lieb–Tasaki (AKLT) model, where a restricted spectrum-generating algebra (rSGA) generates a tower of QMBS on top of a nontrivial SPT ground state admitting a matrix product state (MPS) representation. We demonstrate that the resulting symmetry-invariant scar subspace inherits well-defined topological characteristics, encoded in bond-space symmetry representations, expectation values of symmetry-twist operators, and long-range string order in the dilute regime. We further show that these features persist in a broader class of models, including deformations and higher-spin generalizations that preserve the relevant symmetries and admit nontrivial SPT ground states with MPS representations. Our results provide a general framework in which symmetry-associated topological properties, while inherited from the ground state, are consistently realized at the level of symmetry-invariant nonthermal subspaces. This perspective clarifies how topological structures can be meaningfully defined beyond individual eigenstates.

We study a quasiperiodic Aubry Andre lattice arranged along a spiral curve. In this setup, the changing angle of the spiral naturally stretches and compresses the distances between neighboring sites, which in turn modulates the hopping amplitudes. The onsite potential itself remains the familiar AA form, but this geometry induced variation in the hopping dramatically changes how the system behaves both in its energy spectrum and in how its states localize.Using inverse participation ratios together with a full multifractal analysis, we find that curvature makes the system localize much more easily, even at relatively small quasiperiodic strengths. It also produces clear windows where the eigenstates become strongly multifractal. This shows that quasiperiodicity and geometry do not act independently rather, they reinforce one another in shaping the wavefunctions. Overall, we observe a smooth evolution of the states from extended, to multifractal, and finally to strongly localized. Our results pave the way for creating tunable quasiperiodic and geometry-driven localization effects in photonic waveguide arrays, ultracold atoms, mechanical metamaterials, and nanoscale platforms.

Development of machine learned interatomic potentials (MLIP) is critical for performing reliable simulations of materials at length and time scales that are comparable to those in the laboratory. We present here a MLIP suitable for simulations of the temperature dependent structure and dynamics of single layer hexagonal boron nitride (h-BN) with defects and grain boundaries, developed using a strictly local equivariant deep neural network as formulated in the Allegro code. The training dataset consisted of about 30,000 images of h-BN with and without point defects generated with ab-initio molecular dynamics simulations, based on density functional theory (DFT), at 500, 1000, and 1500K. The developed MLIP predicts potential energies and forces with a mean absolute error (MAE) of 4 meV/atom and 60 meV/Angstrom , respectively. It also reproduces phonon dispersion curves and density of vibrational states of pristine bulk h-BN that are comparable with that obtained from density functional theory-based calculations. Molecular dynamics simulations of the motion of the 4|8 grain boundary unit in h-BN shows the first step to have an activation barrier ~2.2 eV, indicating immobility of the grain boundary. Moving the grain boundary units past the first shows much lower activation barriers of ~0.42eV, suggesting a facile motion of the grain boundary once the first movement is stimulated. These simulations yield a scaled mobility of 1.739*10^(-11) m^3/Js for a temperature of 1500K which, given the inherent differences in the set-ups, is not too far from the experimental value of 1.36*10^(-9) m^3/Js. The ability to predict grain boundary mobility within reasonable agreement with experiment demonstrates the robustness of the MLIP and its suitability for reliable simulations of defect structures and dynamics in single layer h-BN.