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An emergent numerical approach to solve quantum impurity problems is to encode the impurity path integral as a matrix product state. For time-dependent problems, the cost of this approach generally scales with the evolution time. Here we consider a common non-equilibrium scenario where an impurity, initially in equilibrium with a thermal bath, is driven out of equilibrium by a time-dependent force term. Despite that there is no time-translational invariance in the problem, we show that we could still make full use of the infinite matrix product state technique, resulting in a method whose cost is essentially independent of the evolution time. We demonstrate the effectiveness of this method in the integrable case against exact diagonalization, and against existing calculations on the L-shaped Kadanoff-Baym contour in the general case. Our method could be a very competitive method for studying long-time non-equilibrium quantum dynamics, and be potentially used as an efficient impurity solver in the non-equilibrium dynamical mean field theory., Comment: 10 pages, 8 figures

Developing numerical exact solvers for open quantum systems is a challenging task due to the non-perturbative and non-Markovian nature when coupling to structured environments. The Feynman-Vernon influence functional approach is a powerful analytical tool to study the dynamics of open quantum systems. Numerical treatments of the influence functional including the quasi-adiabatic propagator technique and the tensor-network-based time-evolving matrix product operator method, have proven to be efficient in studying open quantum systems with bosonic environments. However, the numerical implementation of the fermionic path integral suffers from the Grassmann algebra involved. In this work, we present a detailed introduction of the Grassmann time-evolving matrix product operator method for fermionic open quantum systems. In particular, we introduce the concepts of Grassmann tensor, signed matrix product operator, and Grassmann matrix product state to handle the Grassmann path integral. Using the single-orbital Anderson impurity model as an example, we review the numerical benchmarks for structured fermionic environments for real-time nonequilibrium dynamics, real-time and imaginary-time equilibration dynamics, and its application as an impurity solver. These benchmarks show that our method is a robust and promising numerical approach to study strong coupling physics and non-Markovian dynamics. It can also serve as an alternative impurity solver to study strongly-correlated quantum matter with dynamical mean-field theory., Comment: 17 pages, 10 figures

3D deblurring reconstruction techniques have recently seen significant advancements with the development of Neural Radiance Fields (NeRF) and 3D Gaussian Splatting (3DGS). Although these techniques can recover relatively clear 3D reconstructions from blurry image inputs, they still face limitations in handling severe blurring and complex camera motion. To address these issues, we propose Event-assisted 3D Deblur Reconstruction with Gaussian Splatting (EaDeblur-GS), which integrates event camera data to enhance the robustness of 3DGS against motion blur. By employing an Adaptive Deviation Estimator (ADE) network to estimate Gaussian center deviations and using novel loss functions, EaDeblur-GS achieves sharp 3D reconstructions in real-time, demonstrating performance comparable to state-of-the-art methods.

The path integral formalism is the building block of many powerful numerical methods for quantum impurity problems. However, existing fermionic path integral based numerical calculations have only been performed in either the imaginary-time or the real-time axis, while the most generic scenario formulated on the L-shaped Kadanoff-Baym contour is left unexplored. In this work, we extended the recently developed Grassmann time-evolving matrix product operator (GTEMPO) method to solve quantum impurity problems directly on the Kadanoff-Baym contour. The resulting method is numerically exact, with only two sources of numerical errors, e.g., the time discretization error and the matrix product state bond truncation error. The accuracy of this method is numerically demonstrated against exact solutions in the noninteracting case, and against existing calculations on the real- and imaginary-time axes for the single-orbital Anderson impurity model. We also show that the numerical errors of the method can be well suppressed as we refine the hyperparameters. Our method is a perfect benchmarking baseline for its alternatives which often employ less-controlled approximations, and can also be used as a real-time impurity solver in dynamical mean field theory., Comment: 13 pages, 8 figures

The Grassmann time-evolving matrix product operator (GTEMPO) method has proven to be an accurate and efficient numerical method for the real-time dynamics of quantum impurity problems. Whereas its application for imaginary-time calculations is much less competitive compared to well-established methods such as the continuous-time quantum Monte Carlo (CTQMC). In this work, we unleash the full power of GTEMPO for zero-temperature imaginary-time calculations: the multi-time impurity state is time-translationally invariant with infinite boundary condition, therefore it can be represented as an infinite Grassmann matrix product state (GMPS) with nontrivial unit cell in a single time step, instead of an open boundary GMPS spanning the whole imaginary-time axis. We devise a very efficient infinite GTEMPO algorithm targeted at zero-temperature equilibrium quantum impurity problems, which is known to be a hard regime for quantum Monte Carlo methods. To demonstrate the performance of our method, we benchmark it against exact solutions in the noninteracting limit, and against CTQMC calculations in the Anderson impurity models with up to two orbitals, where we show that the required bond dimension of the infinite GMPS is much smaller than its finite-temperature counterpart., Comment: 9 pages, 7 figures

We present an infinite Grassmann time-evolving matrix product operator method for quantum impurity problems, which directly works in the steady state. The method embraces the well-established infinite matrix product state algorithms with the recently developed GTEMPO method, and benefits from both sides: it obtains real-time Green's functions without sampling noises and bath discretization error, it is applicable for any temperature without the sign problem, its computational cost is independent of the transient dynamics and does not scale with the number of baths. We benchmark the method on the finite-temperature equilibrium Green's function in the noninteracting limit against exact solutions and in the single-orbital Anderson impurity model against GTEMPO calculations. We also study the zero-temperature non-equilibrium steady state of an impurity coupled to two baths with a voltage bias, obtaining consistent particle currents with existing calculations. The method is ideal for studying steady-state quantum transport, and can be readily used as an efficient real-time impurity solver in the dynamical mean field theory and its non-equilibrium extension., Comment: 11 pages, 7 figures

The time-evolving matrix product operator (TEMPO) method has become a very competitive numerical method for studying the real-time dynamics of quantum impurity problems. For small impurities, the most challenging calculation in TEMPO is to construct the matrix product state representation of the Feynman-Vernon influence functional. In this work we propose an efficient method for this task, which exploits the time-translationally invariant property of the influence functional. The required number of matrix product state multiplication in our method is almost independent of the total evolution time, as compared to the method originally used in TEMPO which requires a linearly scaling number of multiplications. The accuracy and efficiency of this method are demonstrated for the Toulouse model and the single impurity Anderson model., Comment: 9 pages, 4 figures

An emergent and promising tensor-network-based impurity solver is to represent the path integral as a matrix product state, where the bath is analytically integrated out using Feynman-Vernon influence functional. Here we present an approach to calculate the equilibrium impurity spectral function based on the recently proposed Grassmann time-evolving matrix product operators method. The central idea is to perform a quench from a separable impurity-bath initial state as in the non-equilibrium scenario. The retarded Green's function $G(t+t_0, t'+t_0)$ is then calculated after an equilibration time $t_0$ such that the impurity and bath are approximately in thermal equilibrium. There are two major advantages of this method. First, since we focus on real-time dynamics, we do not need to perform the numerically ill-posed analytic continuation in the continuous-time quantum Monte Carlo case that relies on imaginary-time evolution. Second, the entanglement growth of the matrix product states in real-time calculations is observed to be much slower than that in imaginary-time calculations, leading to a significant improvement in numerical efficiency. The accuracy of this method is demonstrated in the single-orbital Anderson impurity model and benchmarked against the continuous-time quantum Monte Carlo method., Comment: 9 pages, 6 figures

Tensor-network-based methods are promising candidates to solve quantum impurity problems. They are free of sampling noises and the sign problem compared to state-of-the-art continuous-time quantum Monte Carlo methods. Recent progress made in tensor-network-based impurity solvers is to use the Feynman-Vernon influence functional to integrate out the bath analytically, retaining only the impurity dynamics and representing it compactly as a matrix product state. The recently proposed Grassmann time-evolving matrix product operator (GTEMPO) method is one of the representative methods in this direction. In this work, we systematically study the performance of GTEMPO in solving equilibrium quantum impurity problems at a finite temperature with a semicircular spectrum density of the bath. Our results show that its computational cost would generally increase as the temperature goes down and scale exponentially with the number of orbitals. In particular, the single-orbital Anderson impurity model can be efficiently solved with this method, for two orbitals we estimate that one could possibly reach inverse temperature $\beta\approx 20$ if high-performance computing techniques are utilized, while beyond that only very high-temperature regimes can be reached in the current formalism. Our work paves the way to apply GTEMPO as an imaginary-time impurity solver., Comment: 12 pages, 10 figures

The time-evolving matrix product operators (TEMPO) method, which makes full use of the Feynman-Vernon influence functional, is the state-of-the-art tensor network method for bosonic impurity problems. However, for fermionic impurity problems the Grassmann path integral prohibits application of this method. We develop Grassmann time-evolving matrix product operators, a full fermionic analog of TEMPO, that can directly manipulates Grassmann path integrals with similar numerical cost as the bosonic counterpart. We further propose a zipup algorithm to compute expectation values on the fly without explicitly building a single large augmented density tensor, which boosts our efficiency on top of the vanilla TEMPO. Our method has a favorable complexity scaling over existing tensor network methods, and we demonstrate its performance on the non-equilibrium dynamics of the single impurity Anderson models. Our method solves the long standing problem of turning Grassmann path integrals into efficient numerical algorithms, which could significantly change the application landscape of tensor network based impurity solvers, and could also be applied for broader problems in open quantum physics and condensed matter physics., Comment: 4 pages, 3 figures

In this article, using the numerically exact time-evolving matrix product operators method, we study the fidelity out-of-time-order correlator (FOTOC) in the unbiased spin-boson model at zero temperature. It is found that after the initial exponential growth of FOTOC, the information of the system dynamics will adulterate into the FOTOC. This makes the FOTOC an advanced epitome of the system dynamics, i.e., the FOTOC shows similar behavior to that of system dynamics within a shorter time interval. Eventually the progress of the FOTOC is ahead of the system dynamics, which can provide a prediction of the system dynamics., Comment: 5pages, 4 figures

Stochastic resonance is a phenomenon where the response signal to external driving is enhanced by environment noise. In quantum regime, the effect of environment is often intrinsically non-Markovian. Due to the combination of such non-Markovian quantum noise and external driving force, it is difficult to evaluate the correlation function and hence the power spectrum. Nevertheless, a recently developed algorithm, which is called time-evolving matrix product operators (TEMPO), and its extensions provide an efficient and numerically exact approach for this task. Using TEMPO we investigate non-Markovian effects in quantum stochastic resonance in a two level system. The periodic signal and the time-averaged asymptotic correlation function, along with the power spectrum, are calculated. From the power spectrum the signal-to-noise ratio is evaluated. It is shown that both signal strength and signal-to-noise ratio are enhanced by non-Markovian effects, which indicates the importance of non-Markovian effects in quantum stochastic resonance. In addition, we show that the non-Markovian effects can shift the peak position of the background noise power spectrum., Comment: 8 pages, 8 figures

We generalize time-evolving matrix product operators method to nonequilibrium quantum transport problems. The nonequilibrium current is obtained via numerical differentiation of the generating functional which is represented as a tensor network. The approach is numerically exact and the non-Markovian effects are fully taken into account. In the transport process, a part of the heat that flows out from a bath flows into the system and other baths, and the rest is stored in the system-bath coupling part. We take the spin-boson model as a demonstration to show the details of this heat flowing and the establishment of a steady current between two baths., Comment: 9 pages, 9 figures

We study Landau-Zener transitions in a fermionic dissipative environment where a two-level (up and down states) system is coupled to two metallic leads kept with different chemical potentials at zero temperature. The dynamics of the system is simulated by an iterative numerically exact influence functional path integral method. In the pure Landau-Zener problem, two kinds of transition (from up to down state and from down to up state) probability are symmetric. However, this symmetry is destroyed by coupling the system to the bath. In addition, in both kinds of transitions, there exists a nonmonotonic dependence of the transition probability on the sweep velocity; meanwhile nonmonotonic dependence of the transition probability on the system-bath coupling strength is only shown in one of them. As in the spin-boson model, these phenomena can be explained by a simple phenomenological model., Comment: 10 pages, 9 figures

The ground state electronic structure and magnetic behaviors of curium dioxide (CmO$_{2}$) are controversial. In general, the formal valence of Cm ions in CmO$_{2}$ should be tetravalent. It implies a $5f^{6.0}$ electronic configuration and a non-magnetic ground state. However, it is in sharp contrast with the large magnetic moment measured by painstaking experiments. In order to clarify this contradiction, we tried to study the ground state electronic structure of CmO$_{2}$ by means of a combination of density functional theory and dynamical mean-field theory. We find that CmO$_{2}$ is a wide-gap charge transfer insulator with strong 5$f$ valence state fluctuation. It belongs to a mixed-valence compound indeed. The predominant electronic configurations for Cm ions are $5f^{6.0}$ and $5f^{7.0}$. The resulting magnetic moment agrees quite well with the experimental value. Therefore, the magnetic puzzle in CmO$_{2}$ can be appropriately explained by the mixed-valence scenario., Comment: 9 pages, 6 figures

A combination of the density functional theory and the single-site dynamical mean-field theory is employed to study the electronic structures of various allotropes of elemental curium (Cm-I, Cm-II, and Cm-III). We find that the 5$f$ valence electrons in the high-symmetry Cm-I and Cm-II phases remain localized, while they turn into itinerancy in the low-symmetry monoclinic Cm-III phase. In addition, conspicuous quasiparticle multiplets are identified in the 5$f$ electronic density of states of the Cm-III phase. We believe that it is the many-body transition between $5f^{7}$ and $5f^{8}$ configurations that gives rise to these quasiparticle multiplets. Therefore, the Cm-III phase is probably a new realization of the so-called Racah metal., Comment: 7 pages, 4 figures

We study a generic spin-fermion model, where a two-level system (spin) is coupled to two metallic leads with different chemical potentials, in the presence of monochromatic driving fields. The real-time dynamics of the system is simulated beyond the Markovian limit by an iterative numerically exact influence functional path integral method. Our results show that although both system-bath coupling and chemical potential difference contribute to dissipation, their effects are distinct. In particular, under certain drivings the asymptotic Floquet states of the system exhibit robustness against a range of system-bath coupling strength: the asymptotic behaviors of the system are insensitive to different system-bath coupling strength, while they are highly tunable by the chemical potential difference of baths. Further simulations show that such robustness may be essentially a result of the interplay between driving, bath electronic structure and system-bath coupling. Therefore the robustness could break down depending on the characteristics of the interplay. In addition, under fast linearly polarized driving the quantum stochastic resonance is demonstrated that stronger system-bath coupling (stronger dissipation) enhances rather than suppresses the amplitude of coherent oscillations of the system., Comment: 13 pages, 14 figures

At low temperatures, EuTiO$_3$ system has very large resistivities and exhibits colossal magnetoresistance. Based on a first principle calculation and the dynamical mean-field theory for small polaron we have calculated the transport properties of EuTiO$_3$. It is found that due to electron-phonon interaction the conduction band may form a tiny subband which is close to the Fermi level. The tiny subband is responsible for the large resistivity. Besides, EuTiO$_3$ is a weak antiferromagnetic material and its magnetization would slightly shift the subband via exchange interaction between conduction electrons and magnetic atoms. Since the subband is close to the Fermi level, a slight shift of its position gives colossal magnetoresistance., Comment: 6 pages, 5 figures

We have investigated the magnetocaloric effect in single and polycrystalline samples of quantum paraelectric EuTiO3 by magnetization and heat capacity measurements. Single crystalline EuTiO3 shows antiferromagnetic ordering due to Eu2+ magnetic moments below TN = 5.6 K. This compound shows a giant magnetocaloric effect around its Neel temperature. The isothermal magnetic entropy change is 49 Jkg-1K-1, the adiabatic temperature change is 21 K and the refrigeration capacity is 500 JKg-1 for a field change of 7 T at TN. The single crystal and polycrystalline samples show similar values of the magnetic entropy change and adiabatic temperature changes. The large magnetocaloric effect is due to suppression of the spin entropy associated with localized 4f moment of Eu2+ ions. The giant magnetocaloric effect together with negligible hysteresis, suggest that EuTiO3 could be a potential material for magnetic refrigeration below 20 K., Comment: 12 pages, 4 figures

We report the magnetic entropy change (Delta Sm) in magnetoelectric Eu1-xBaxTiO3 for x = 0.1- 0.9. We find - delta Sm = 11 (40) J/kg.K in x = 0.1 for a field change of 1 (5) Tesla respectively, which is the largest value among all Eu-based oxides. Delta Sm arises from the field-induced suppression of the spin entropy of Eu2+:4f7 localized moments. While -delta Sm decreases with increasing x, -DeltaSm = 6.58 J/kg.K observed in the high spin diluted composition x = 0.9 is larger than that in many manganites. Our results indicate that these magnetoelectrics are potential candidates for cryogenic magnetic refrigeration., Comment: 13 pages, 6 figures

We investigate electronic band structure and transport properties in bilayer graphene superlattices of Thue-Morse sequence. It is interesting to find that the zero-$\bar{k}$ gap center is sensitive to interlayer coupling $t'$, and the centers of all gaps shift versus $t'$ at a linear way. Extra Dirac points may emerge at $k_{y}\ne$0, and when the extra Dirac points are generated in pairs, the electronic conductance obeys a diffusive law, and the Fano factor tends to be 1/3 as the order of Thue-Morse sequence increases. Our results provide a flexible and effective way to control the transport properties in graphene., Comment: 5 pages, 6 figures. Accepted for publication in Applied Physics Letters

In a pristine monolayer graphene subjected to a constant electric field along the layer, the Bloch oscillation of an electron is studied in a simple and efficient way. By using the electronic dispersion relation, the formula of a semi-classical velocity is derived analytically, and then many aspects of Bloch oscillation, such as its frequency, amplitude, as well as the direction of the oscillation, are investigated. It is interesting to find that the electric field affects the component of motion, which is non-collinear with electric field, and leads the particle to be accelerated or oscillated in another component., Comment: Published version