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A discrete time crystal (DTC) is the paradigmatic example of a phase of matter that occurs exclusively in systems out of equilibrium. This phenomenon is characterized by the spontaneous symmetry breaking of discrete time-translation and provides a rich playground to study a fundamental question in statistical physics: what mechanism allows for driven quantum systems to exhibit emergent behavior that deviates from their counterparts with time-independent evolution? Unlike equilibrium phases, DTCs exhibit macroscopic manifestations of coherent quantum dynamics, challenging the conventional narrative that thermodynamic behavior universally erases quantum signatures. However, due to the difficulty of simulating these systems with either classical or quantum computers, previous studies have been limited to a set of models with Ising-like couplings -- and mostly only in one dimension -- thus precluding our understanding of the existence (or not) of DTCs in models with interactions that closely align with what occurs in nature. In this work, by combining the latest generation of IBM quantum processors with state-of-the-art tensor network methods, we are able to demonstrate the existence of a DTC in a two-dimensional system governed by anisotropic Heisenberg interactions. Our comprehensive analysis reveals a rich phase diagram encompassing spin-glass, ergodic, and time-crystalline phases, highlighting the tunability of these phases through multiple control parameters. Crucially, our results emphasize the interplay of initialization, interaction anisotropy, and driving protocols in stabilizing the DTC phase. By extending the study of Floquet matter beyond simplified models, we lay the groundwork for exploring how driven systems bridge the gap between quantum coherence and emergent non-equilibrium thermodynamics.

It is widely accepted that noisy quantum devices are limited to logarithmic depth circuits unless mid-circuit measurements and error correction are employed. However, this conclusion holds only for unital error channels, such as depolarizing noise. Building on the idea of the "quantum refrigerator" [Ben-Or, Gottesman and Hassidim (2013)], we improve upon previous results and show that geometrically local circuits in the presence of nonunital noise, in any dimension $d\geq 1$, can correct errors without mid-circuit measurements and extend computation to any depth, with only polylogarithmic overhead in the depth and the number of qubits. This implies that local quantum dynamics subjected to sufficiently weak nonunital noise is computationally universal and nearly as hard to simulate as noiseless dynamics. Additionally, we quantify the contraction property of local random circuits in the presence of nonunital noise., Comment: 33 pages, 3 figures

Superconductivity and Bloch band Berry curvature responses represent two distinct paradigms of quantum coherent phenomena. The former relies on the collective motion of a many-body state while the latter proceeds from the momentum-space winding of Bloch wavefunctions. Here we reveal a superconducting Berry curvature dipole (BCD) that arises as a collective many-body phenomena in noncentrosymmetric superconductors. Strikingly, we find the superconducting BCD is sensitive to the phase of the superconducting gap and depends on the noncentrosymmetric structure of its pairing. This unusual property enables a BCD proximity effect in hybrid quantum materials that induces nonreciprocity even in a target centrosymmetric metal. We find superconducting BCD naturally produces nonreciprocal electromagnetic responses that includes a giant second-order nonlinearity. This renders noncentrosymmetric superconductors an exciting platform for realizing pronounced nonlinearities and its BCD responses a novel diagnostic of the superconducting gap., Comment: 11 pages, 2 figures

We demonstrate that periodically driven Fermions coupled to simple bosonic baths have steady state occupations of Floquet Bloch bands that generically display non-analyticties at certain momenta which resemble the Fermi surfaces of equilibrium non-Fermi liquids. Remarkably these non-equilibrium Fermi surfaces remain sharp even when the bath is at finite temperature, leading to critical power-law decaying correlations at finite temperature, a phenomenon with no analogue in equilibrium. We also show that generically there is in-gap current rectification for clean metals lacking inversion symmetry, and explain why this occurs universally regardless of the details of collisions.

Tensor networks and quantum computation are two of the most powerful tools for the simulation of quantum many-body systems. Rather than viewing them as competing approaches, here we consider how these two methods can work in tandem. We introduce a novel algorithm that combines tensor networks and quantum computation to produce results that are more accurate than what could be achieved by either method used in isolation. Our algorithm is based on multiproduct formulas (MPF) - a technique that linearly combines Trotter product formulas to reduce algorithmic error. Our algorithm uses a quantum computer to calculate the expectation values and tensor networks to calculate the coefficients used in the linear combination. We present a detailed error analysis of the algorithm and demonstrate the full workflow on a one-dimensional quantum simulation problem on $50$ qubits using two IBM quantum computers: $ibm\_torino$ and $ibm\_kyiv$.

Kramers degeneracies play an essential role in the spectrum of electronic materials. Here we argue that beyond spectral properties, Kramers degeneracy plays a critical role in the nonlinear response of PT symmetric magnets. In particular, we uncover a class of second-order Kramers nonlinearities that only arise in the presence of Kramers degeneracy, vanishing in non-degenerate PT symmetric materials. Kramers nonlinearties depend on a circular dichroism between PT related Kramers states and enable to trace out the quantum geometry of the degenerate band structure. We find pronounced Kramers nonlinearitites in the nonlinear polarization responses of even layer antiferromagnetic MnBi$_2$Te$_4$ that enable to identify its antiferromagnetic order. This provides novel means for diagnosing Kramers pairs and addressing the internal Kramers degree of freedom., Comment: 9 pages, 2 figures

In this paper, we show that transferring knowledge from other domains of video understanding combined with large-scale learning can improve robustness of Video Object Segmentation (VOS) under complex circumstances. Namely, we focus on integrating scene global motion knowledge to improve large-scale semi-supervised Video Object Segmentation. Prior works on VOS mostly rely on direct comparison of semantic and contextual features to perform dense matching between current and past frames, passing over actual motion structure. On the other hand, Optical Flow Estimation task aims to approximate the scene motion field, exposing global motion patterns which are typically undiscoverable during all pairs similarity search. We present WarpFormer, an architecture for semi-supervised Video Object Segmentation that exploits existing knowledge in motion understanding to conduct smoother propagation and more accurate matching. Our framework employs a generic pretrained Optical Flow Estimation network whose prediction is used to warp both past frames and instance segmentation masks to the current frame domain. Consequently, warped segmentation masks are refined and fused together aiming to inpaint occluded regions and eliminate artifacts caused by flow field imperfects. Additionally, we employ novel large-scale MOSE 2023 dataset to train model on various complex scenarios. Our method demonstrates strong performance on DAVIS 2016/2017 validation (93.0% and 85.9%), DAVIS 2017 test-dev (80.6%) and YouTube-VOS 2019 validation (83.8%) that is competitive with alternative state-of-the-art methods while using much simpler memory mechanism and instance understanding logic.

The recent works on Video Object Segmentation achieved remarkable results by matching dense semantic and instance-level features between the current and previous frames for long-time propagation. Nevertheless, global feature matching ignores scene motion context, failing to satisfy temporal consistency. Even though some methods introduce local matching branch to achieve smooth propagation, they fail to model complex appearance changes due to the constraints of the local window. In this paper, we present DeVOS (Deformable VOS), an architecture for Video Object Segmentation that combines memory-based matching with motion-guided propagation resulting in stable long-term modeling and strong temporal consistency. For short-term local propagation, we propose a novel attention mechanism ADVA (Adaptive Deformable Video Attention), allowing the adaption of similarity search region to query-specific semantic features, which ensures robust tracking of complex shape and scale changes. DeVOS employs an optical flow to obtain scene motion features which are further injected to deformable attention as strong priors to learnable offsets. Our method achieves top-rank performance on DAVIS 2017 val and test-dev (88.1%, 83.0%), YouTube-VOS 2019 val (86.6%) while featuring consistent run-time speed and stable memory consumption

Supercurrent flow can induce a nonvanishing spin magnetization in noncentrosymmetric superconductors with spin-orbit interaction. Often known as the non-dissipative magnetoelectric effect, these are most commonly found at linear order in supercurrent flow. Here, we propose that a {\it nonlinear} superconducting magnetoelectric (NSM) effect can naturally manifest in magnet/superconductor heterostructures. In such platforms, NSM manifests as the spin polarization generated as a second-order response to a driving supercurrent. Strikingly, we find NSM survives centrosymmetry and is the leading order magnetic response in a variety of magnetic materials that include both collinear magnets [e.g., $d$-wave planar altermagnet thin film/superconductor (ALM/SC)] as well as noncollinear magnets (e.g., Kagome/SC systems). This renders NSM a powerful electric and non-dissipative means of controlling magnetization in magnet/superconductor heterostructures, a promising platform for superconducting spintronics., Comment: 6 pages, 3 figures, plus Supplementary

We present the pressure dependence of the electronic and dynamical properties of six different CoGe phases: orthorhombic Cmmm, hexagonal P6/mmm and P$\bar{6}$2m, monoclinic C2/m, cubic P2$_{1}$3, and orthorhombic Pnma. Using first-principles DFT calculations and the direct force-constants method, we study the dynamical stability of individual phases under external pressure. We show that the orthorombic Cmmm and hexagonal P6/mmm structures are unstable over a broad pressure range and most pronounced imaginary phonon soft mode in both cases leads to a stable hexagonal P$\bar{6}$2m structure of the lowest ground-state energy of all studied phases at ambient and low (below $\sim 3$ GPa) external pressure. Under these conditions, the cubic P2$_{1}$3 phase has the highest energy, however, together with monoclinic C2/m and orthorombic Pnma it is dynamically stable and all these three structures can potentially coexist as meta-stable phases. Above $\sim 3$ GPa, the cubic P2$_{1}$3 phase becomes the most energetically favorable. Fitting the Birch--Murnaghan equation of state we derive bulk modulus for all mentioned phases, which indicate relatively high resistance of CoGe to compression. Such conclusions are confirmed by band structure calculations. Additionally, we show that electronic bands of the hexagonal P$\bar{6}$2m phase reveal characteristic features of the kagome-like structure, while in the cubic P2$_{1}$3 phase spectrum, one can locate spin-1 and double Weyl fermions. In both cases, the external pressure induces the Lifshitz transition, related to the modification of the Fermi surface topology., Comment: 10 pages, 7 figures

Electron-correlation-driven phonon soft modes have been recently reported in the antiferromagnetic kagome FeGe compound and associated with the observed charge density wave (CDW). In this paper, we present a systematic investigation of the CDW origin in the context of the ab initio lattice dynamics study. Performing the group theory analysis of the mentioned soft mode, we found that the stable structure has the Immm symmetry and can be achieved by shifts of Ge atoms. Additionally, we show that the final structure realizes a distorted honeycomb Ge lattice as well as a non-flat kagome-like Fe net. For completeness, we present the electronic properties calculations. From the theoretical STM topography simulation, we indicate that the observed CDW occurs in the deformed honeycomb Ge sublattice., Comment: 9 pages, 5 figures

Although ransomware has received broad attention in media and research, this evolving threat vector still poses a systematic threat. Related literature has explored their detection using various approaches leveraging Machine and Deep Learning. While these approaches are effective in detecting malware, they do not answer how to use this intelligence to protect against threats, raising concerns about their applicability in a hostile environment. Solutions that focus on mitigation rarely explore how to prevent and not just alert or halt its execution, especially when considering Linux-based samples. This paper presents GuardFS, a file system-based approach to investigate the integration of detection and mitigation of ransomware. Using a bespoke overlay file system, data is extracted before files are accessed. Models trained on this data are used by three novel defense configurations that obfuscate, delay, or track access to the file system. The experiments on GuardFS test the configurations in a reactive setting. The results demonstrate that although data loss cannot be completely prevented, it can be significantly reduced. Usability and performance analysis demonstrate that the defense effectiveness of the configurations relates to their impact on resource consumption and usability.

A promising strategy to protect quantum information from noise-induced errors is to encode it into the low-energy states of a topological quantum memory device. However, readout errors from such memory under realistic settings is less understood. We study the problem of decoding quantum information encoded in the groundspaces of topological stabilizer Hamiltonians in the presence of generic perturbations, such as quenched disorder. We first prove that the standard stabilizer-based error correction and decoding schemes work adequately well in such perturbed quantum codes by showing that the decoding error diminishes exponentially in the distance of the underlying unperturbed code. We then prove that Quantum Neural Network (QNN) decoders provide an almost quadratic improvement on the readout error. Thus, we demonstrate provable advantage of using QNNs for decoding realistic quantum error-correcting codes, and our result enables the exploration of a wider range of non-stabilizer codes in the near-term laboratory settings., Comment: 25 pages, 5 figures

Quantum control plays an irreplaceable role in practical use of quantum computers. However, some challenges have to be overcome to find more suitable and diverse control parameters. We propose a promising and generalizable average-fidelity-based machine-learning-inspired method to optimize the control parameters, in which a neural network with periodic feature enhancement is used as an ansatz. In the implementation of a single-qubit gate by cat-state nonadiabatic geometric quantum computation via reverse engineering, compared with the control parameters in the simple form of a trigonometric function, our approach can yield significantly higher-fidelity ($>99.99\%$) phase gates, such as the $\pi / 8$ gate (T gate). Single-qubit gates are robust against systematic noise, additive white Gaussian noise and decoherence. We numerically demonstrate that the neural network possesses the ability to expand the model space. With the help of our optimization, we provide a feasible way to implement cascaded multi-qubit gates with high quality in a bosonic system. Therefore, the machine-learning-inspired method may be feasible in quantum optimal control of nonadiabatic geometric quantum computation., Comment: 12 pages, 8 figures

We find that an oscillon can possess a characteristic double oscillation structure even though it results in a decay of a sphaleron which does not have any positive energy vibrational mode. We show that dynamics of such an oscillon can still be captured by collective coordinates provided by the sphaleron. Namely, its unstable mode and its scaling deformation i.e., Derrick mode., Comment: 10 pages, 12 figures

We demonstrate the existence of a non-equilibrium "Floquet Fermi Liquid" state arising in partially filled Floquet Bloch bands weakly coupled to ideal fermionic baths, which possess a collection of "Floquet Fermi surfaces" enclosed inside each other, resembling matryoshka dolls. We elucidate several properties of these states, including their quantum oscillations under magnetic fields which feature slow beating patterns of their amplitude reflecting the different areas of the Floquet Fermi surfaces, consistent with those observed in microwave induced resistance oscillation experiments. We also investigate their specific heat and thermodynamic density of states and demonstrate how by controlling properties of the drive, such as its frequency, one can tune some of the Floquet Fermi surfaces towards non-equilibrium van-Hove singularities without changing the electron density., Comment: 17 pages, 3 figures

RhPb was initially recognized as one of a CoSn-like compounds with $P6/mmm$ symmetry, containing an ideal kagome lattice of $d$-block atoms. However, theoretical calculations predict the realization of the phonon soft mode which leads to the kagome lattice distortion and stabilization of the structure with $P\bar{6}2m$ symmetry [A. Ptok et al., Phys. Rev. B 104, 054305 (2021)]. Here, we present the single crystal x-ray diffraction results supporting this prediction. Furthermore, we discuss the main dynamical properties of RhPb with $P\bar{6}2m$ symmetry. The bulk phononic dispersion curves contain several flattened bands, Dirac nodal lines, and triple degenerate Dirac points. As a consequence, the phononic drumhead surface state is realized for the (100) surface, terminated by the zigzag-like edge of Pb honeycomb sublattice., Comment: 10 pages, 7 figures

Autonomous quantum memories are a way to passively protect quantum information using engineered dissipation that creates an "always-on'' decoder. We analyze Markovian autonomous decoders that can be implemented with a wide range of qubit and bosonic error-correcting codes, and derive several upper bounds and a lower bound on the logical error rate in terms of correction and noise rates. For many-body quantum codes, we show that, to achieve error suppression comparable to active error correction, autonomous decoders generally require correction rates that grow with code size. For codes with a threshold, we show that it is possible to achieve faster-than-polynomial decay of the logical error rate with code size by using superlogarithmic scaling of the correction rate. We illustrate our results with several examples. One example is an exactly solvable global dissipative toric code model that can achieve an effective logical error rate that decreases exponentially with the linear lattice size, provided that the recovery rate grows proportionally with the linear lattice size., Comment: 51 pages, 8 figures, 1 table

We construct a simple field theory in which a sphaleron, i.e., a saddle-point particle-like solution, forms a semi-BPS state with a background defect that is an impurity. This means that there is no static force between the sphaleron and the impurity. Therefore such a sphaleron-impurity system is very much like usual BPS multi-solitons, however, still possessing an unstable direction allowing for its decay. We study dynamics of the sphaleron in such a system., Comment: 13 pages, 12 figures, references added and improved discussion

The Gromov--Hausdorff distance measures the difference in shape between metric spaces and poses a notoriously difficult problem in combinatorial optimization. We introduce its quadratic relaxation over a convex polytope whose solutions provably deliver the Gromov--Hausdorff distance. The optimality guarantee is enabled by the fact that the search space of our approach is not constrained to a generalization of bijections, unlike in other relaxations such as the Gromov--Wasserstein distance. We suggest conditional gradient descent for solving the relaxation in cubic time per iteration, and demonstrate its performance on metric spaces of hundreds of points. In particular, we use it to obtain a new bound of the Gromov--Hausdorff distance between the unit circle and the unit hemisphere equipped with Euclidean metric. Our approach is implemented as a Python package dGH.

Interacting many-body quantum systems and their dynamics, while fundamental to modern science and technology, are formidable to simulate and understand. However, by discovering their symmetries, conservation laws, and integrability one can unravel their intricacies. Here, using up to 124 qubits of a fully programmable quantum computer, we uncover local conservation laws and integrability in one- and two-dimensional periodically-driven spin lattices in a regime previously inaccessible to such detailed analysis. We focus on the paradigmatic example of disorder-induced ergodicity breaking, where we first benchmark the system crossover into a localized regime through anomalies in the one-particle-density-matrix spectrum and other hallmark signatures. We then demonstrate that this regime stems from hidden local integrals of motion by faithfully reconstructing their quantum operators, thus providing a detailed portrait of the system's integrable dynamics. Our results demonstrate a versatile strategy for extracting hidden dynamical structure from noisy experiments on large-scale quantum computers., Comment: 8 pages, 4 figures (main text) + 19 pages, 17 figures (supplementary)

To establish a solid-state-based framework for the coexistence of quantum many-body scars and quantum criticality, we investigate the spin-1 Kitaev chain with uniaxial single-ion anisotropy (SIA). In the subspace with uniform $\mathbb{Z}_2$ gauge fields, this model can be exactly mapped to the spin-1/2 effective detuned PXP Hamiltonian, where the SIA plays a role of the static detuning term. The quench dynamics starting from the product states is symmetric between positive and negative values of the SIA, while a quantum phase transition from the Kitaev spin liquid to the dimer phase only occurs at the critical point with a negative $D_c$, implying the spontaneous breaking of the translational symmetry. We find that the coherent oscillations of quantum fidelity and certain local observables are sustained against small SIA perturbations in a quantum quench from special initial states. While the oscillation amplitudes of these observables decay with time as the SIA strength is increased, the system completely thermalizes upon approaching the critical point. In contrast, the initial polarized state, which shows an absence of revivals of quantum fidelity, will exhibit long revivals for $D

We analyze the perturbative Relativistic Moduli Space approach, where the amplitudes of the Derrick modes are promoted to collective coordinates. In particular, we analyse the possibility to calculate the critical velocity, i.e., the initial velocity of kinks at which single bounce scattering changes into a multi-bounce or annihilation collision, in the resulting Collective Coordinate Model (CCM). We find that for a growing number of modes the critical velocity of the CCM approaches the full field theory value. This is verified in the case of the $\phi^4$ model, where we reach a $99\%$ accuracy. We also see such a convergence for a wide range of models belonging to the family of the double sine-Gordon and Christ-Lee theories, especially in those cases where the kinks do not reveal a too well pronounced half-kink inner structure., Comment: 12 pages

We apply the collective coordinate model framework to describe collisions of a kink and an antikink with nonzero total momentum, i.e., when the solitons possess different velocities. The minimal moduli space with only two coordinates (the mutual distance and the position of the center of mass) is of a wormhole type, whose throat shrinks to a point for symmetric kinks. In this case, a singularity is formed. For non-zero momentum, it prohibits solutions where the solitons pass through each other. We show that this unphysical feature can be cured by enlarging the dimension of the moduli space, e.g., by the inclusion of internal modes.

Regular object detection methods output rectangle bounding boxes, which are unable to accurately describe the actual object shapes. Instance segmentation methods output pixel-level labels, which are computationally expensive for real-time applications. Therefore, a polygon representation is needed to achieve precise shape alignment, while retaining low computation cost. We develop a novel Deformable Polar Polygon Object Detection method (DPPD) to detect objects in polygon shapes. In particular, our network predicts, for each object, a sparse set of flexible vertices to construct the polygon, where each vertex is represented by a pair of angle and distance in the Polar coordinate system. To enable training, both ground truth and predicted polygons are densely resampled to have the same number of vertices with equal-spaced raypoints. The resampling operation is fully differentable, allowing gradient back-propagation. Sparse polygon predicton ensures high-speed runtime inference while dense resampling allows the network to learn object shapes with high precision. The polygon detection head is established on top of an anchor-free and NMS-free network architecture. DPPD has been demonstrated successfully in various object detection tasks for autonomous driving such as traffic-sign, crosswalk, vehicle and pedestrian objects.

The phenomenon of negative thermal expansion (NTE) deals with the increase of the lattice parameters and the volume of the unit cell when the material is thermally cooled. The NTE is typically associated with thermal phonons and anomalous spin-lattice coupling at low temperatures. However, the underlying mechanisms in the presence of strong electron correlations in multi-orbital systems are not yet fully established. Here, we investigate the role of Coulomb interaction in the presence of lattice distortions in setting out the NTE effect, by focusing on the physical case of layered Ca$_2$RuO$_4$ with $d^4$ configuration at each Ru ion site. We employ the Slater-Koster parametrization to describe the electron-lattice coupling through the dependence of the $d-p$ hybridization on the Ru-O-Ru bond angle. The evaluation of the minimum of the free energy at finite temperature by fully solving the multi-orbital many-body problem on finite size cluster allows us to identify the regime for which the system is prone to exhibit NTE effects. The analysis shows that the nature of the spin-orbital correlations is relevant to drive the reduction of the bond angle by cooling, and in turn the tendency toward a NTE. This is confirmed by the fact that a changeover of the electronic and orbital configuration from $d^4$ to $d^3$ by transition metal substitution is shown to favor the occurrence of NTE in Ca$_2$RuO$_4$. This finding is in agreement with the experimental observations of a NTE effect which is significantly dependent on the transition metal substitution in the Ca$_2$RuO$_4$ compound., Comment: 20 pages, 14 figures, published in Physical Review B

Recently, superconductivity was discovered in the infinite layer of hole-doped nickelates NdNiO$_{2}$. Contrary to this, superconductivity in LaNiO$_{2}$ is still under debate. This indicates the crucial role played by the $f$ electrons on the electronic structure and the pairing mechanism of infinite-layer nickelates. Here we discuss the role of the electron correlations on the $f$ electron states and their influence on the electronic structure. We show that the lattice parameters are in good agreement with the experimental values, independent of the chosen parameters within the DFT+$U$ approach. Increasing Coulomb interaction $U$ tends to shift the $f$ states away from the Fermi level. Surprisingly, independently of the position of $f$ states with respect to the Fermi energy, these states play an important role in the electronic band structure, which can be reflected in the modification of the NdNiO$_{2}$ effective models., Comment: 10 pages, 3 figures

We argue that the layer electric polarization of noncentrosymmetric layered heterostructures can be generically controlled by light yielding a layer photovoltaic effect (LPE). The LPE possesses a rich phenomenology and can arise from myriad distinct mechanisms displaying strong sensitivity to symmetry (e.g., point group and time-reversal) as well as the presence/absence of a Fermi surface. We systematically classify these and unveil how LPE manifests for a range of light polarizations and even for unpolarized light. These unusual layer photoresponses can be realized in a range of layered heterostructures such as bilayer graphene aligned on hexagonal Boron Nitride and manifest sizeable layer polarization susceptibilities in the terahertz frequency range that can be used as novel means of bulk photodetection., Comment: 8 pages, 2 figures

We consider a model of a Bloch band subjected to an oscillating electric field and coupled to a featureless fermionic heat bath, which can be solved exactly. We demonstrate rigorously that in the limit of vanishing coupling to this bath (so that it acts as an ideal thermodynamic bath) the occupation of the Floquet band is not a simple Fermi-Dirac distribution function of the Floquet energy, but instead it becomes a ``staircase'' version of this distribution. We show that this distribution generically leads to a finite rectified electric current within the optical gap of a metal even in the limit of vanishing carrier relaxation rates, providing a rigorous demonstration that such rectification is generically possible and clarifying previous statements in the optoelectronics literature. We show that this current remains non-zero even up to the leading perturbative second order in the amplitude of electric fields, and that it approaches the standard perturbative expression of the Jerk current obtained from a simpler Boltzmann description within a relaxation time approximation when the frequencies are small compared to the bandwidth., Comment: 18 pages, 4 figures

In recent years, nanostructures with hexagonal polytypes of gold have been synthesised, opening new possibilities in nanoscience and technology. As bulk gold crystallizes in the \textit{fcc} phase, surface effects can play an important role in stabilizing hexagonal gold nanostructures. Here we investigate several hetero-structures with Ge substrate, including the \textit{fcc} and \textit{hcp} phases of gold that have been observed experimentally. We determine and discuss their interfacial energies and optimized atomic arrangements, comparing the theory results with available experimental data. Our calculations for the Au-\textit{fcc}(011)/Ge(001) show how the presence of defects in the interface layer can help to stabilize the atomic pattern consistent with microscopic images. The Au-\textit{hcp}/Ge interface with the significant mismatch between two surfaces reveals large atomic displacements, which might indicate that the (111) germanium substrate is not responsible for the formation of the \textit{hcp} phase of gold. Finally, analyzing the electronic properties, we demonstrate that Au/Ge systems have metallic character but covalent-like bonding states between interfacial Ge and Au atoms are also present., Comment: 12 pages, 13 figures, submitted

We show that constrained $CP^1$ instantons, combined with the Relativistic Moduli Space approach, can accurately describe kink-antikink collisions in the $\phi^4$ model., Comment: 8 pages, 5 figures

We investigate the topological properties of the helical atomic chains occurring in elemental selenium and tellurium. We postulate a realistic model that includes spin-orbit interaction and show this to be topologically non-trivial, with a topological invariant protected by a crystalline symmetry. We describe the end-states, which are orbitally polarized, with an orbital density modulation strongly peaked at the edge. Furthermore, we propose a simplified model that decomposes into three orbital chains, allowing us to define a topological invariant protected by a crystalline symmetry. We contrast this result with recent observations made for the orbital Su-Schrieffer-Heeger model containing a $p$-orbital zigzag chain., Comment: 10 figures

Using the reflection positivity method we provide the rigorous proof of the existence of long range magnetic order for the XY model on the honeycomb lattice for large spins $S\ge 2$. This stays in contrast with the result obtained using the {\it same} method but on the square lattice -- which gives a stable long-range order for spins $S\ge 1$. We suggest that the difference between these two cases stems from the enhanced quantum spin fluctuations on the honeycomb lattice. Using linear spin-wave theory we show that the enhanced fluctuations are due to the overall much higher kinetic energy of the spin waves on the honeycomb lattice (with Dirac points) than on the square lattice (with good nesting properties)., Comment: 7 pages, 1 figure, accepted by Physical Review B

We demonstrate that the three-dimensional $e_g$ orbital Hubbard model can be generalized to arbitrary dimension $d$, and that the form of the result is determined uniquely by the requirements that (i) the two-fold degeneracy of the $e_g$ orbital be retained, and (ii) the cubic lattice be turned into a hypercubic lattice. While the local Coulomb interaction $U$ is invariant for each basis of orthogonal orbitals, the form of the kinetic energy depends on the orbital basis and takes the most symmetric form for the so-called complex-orbital basis. Characteristically, with respect to this basis, the model has two hopping channels, one that is orbital-flavor conserving, and a second one that is orbital-flavor non-conserving. We show that the noninteracting electronic structure consists of two nondegenerate bands of plane-wave real-orbital single-particle states for which the orbital depends on the wave vector. Due to the latter feature each band is unpolarized at any filling, and has a non-Gaussian density of states at $d=\infty$. The \textit{orbital liquid} state is obtained by filling these two bands up to the same Fermi energy. We investigate the $e_g$ orbital Hubbard model in the limit $d\to\infty$, treating the on-site Coulomb interaction $U$ within the Gutzwiller approximation, thus determining the correlation energy of the orbital liquid and the (disordered) para-orbital states. (...) We show that the orbital liquid is the ground state everywhere in the $(n,U)$ phase diagram except close to half-filling at sufficiently large $U$, where ferro-orbital order with real orbitals occupied is favored. The latter feature is shown to be specific for $d=\infty$, being of mathematical nature due to the exponential tails in the density of states., Comment: 24 pages, 12 figures; accepted for publication in Physical Review Research

An effective two-dimensional two-band model for infinite-layer nickelates consists of bands obtained from $d_{x^2-y^2}$ and $s$--like orbitals. We investigate whether it could be mapped onto a single-band Hubbard model and the filling of Hubbard bands. We find that both one-band physics and a Kondo-lattice regime emerge from the same two-orbital model, depending on the strength of electronic correlations and the filling of the itinerant $s$-band. Next we investigate one-particle excitations by changing the screening. First, for weak screening the strong correlations push electrons out of the $s$-band so that the undoped nickelate is similar to a cuprate. Second, for strong screening the $s$ and $d_{x^2-y^2}$ bands are both partly filled and weakly couple. Particularly in this latter regime mapping to a one-band model gives significant spectral weight transfer between the Hubbard subbands. Finally we point out that the superconducting phases may have either $d$-wave or $s$-wave symmetry., Comment: 6 pages, 5 figures, conference. arXiv admin note: substantial text overlap with arXiv:2208.03287

We find that for various solitonic processes the corresponding canonical moduli space can have a boundary which is accessible in a finite time evolution. We show that such a boundary is not a failure of the moduli space approach but has a physical meaning. In our example, it corresponds to the complete annihilation of a colliding kink and antikink after a finite time. We further find that, close to the boundary, the solutions have an approximate self-similar form., Comment: 8 pages, 8 figures

We show that thick spectral walls exist in antikink-kink collisions in the $\phi^6$ model. In this model, they are triggered by the so-called $delocalized$ $modes$ which do not exist in the single-soliton sector but emerge in antikink-kink ($\bar{K}K$) collisions. Therefore, spectral walls are a rather common phenomenon that should occur in many solitonic collisions involving non-symmetric kinks as, e.g., in the $\phi^8$ or higher power models., Comment: 6 pages, 4 figures

Antikink-kink ( $\bar{\rm K} $$ {\rm K}$) collisions in the $\phi^6$ model exhibit resonant scattering although the $\phi^6$ kinks do not support any bound states to which energy could be transferred. In Phys. Rev. Lett. 107 (2011) 091602 it was conjectured that, instead, energy is transferred to a collective bound mode of the full $\bar{\rm K} $$ {\rm K}$ configuration. Here we present further strong evidence for this conjecture. Further, we construct a collective coordinate model (CCM) for $\bar{\rm K} $$ {\rm K}$ scattering based on this collective bound mode trapped between the $\bar{\rm K} $$ {\rm K}$ pair which allows us to reproduce the full dynamics of $\bar{\rm K} $$ {\rm K}$ scattering with striking accuracy. We also study kink-antikink (${\rm K} $$ \bar{\rm K}$) scattering and its description by a CCM. In this case a significant role of radiation is discovered., Comment: 17 pages, 17 figures