Divergence of the entanglement range in low-dimensional quantum systems

Variational study of fermionic and bosonic systems with non-Gaussian states: Theory and applications

We characterize the dynamical state of many-body bosonic and fermionic many-body models with intersite Gaussian couplings, on-site non-Gaussian interactions, and local dissipation comprising incoherent particle loss, particle gain, and dephasing. We first establish that, for fermionic systems, if the dephasing noise is larger than the non-Gaussian interactions, irrespective of the Gaussian coupling strength, the system state is a convex combination of Gaussian states at all times. Furthermore, for bosonic systems, we show that if the particle loss and particle gain rates are larger than the Gaussian intersite couplings, the system remains in a separable state at all times. Building on this characterization, we establish that at noise rates above a threshold, there exists a classical algorithm that can efficiently sample from the system state of both the fermionic and bosonic models. Finally, we show that, unlike fermionic systems, bosonic systems can evolve into states that are not convex Gaussian even when the dissipation is much higher than the on-site non-Gaussianity. Similarly, unlike bosonic systems, fermionic systems can generate entanglement even with noise rates much larger than the intersite couplings.

Boundary conditions and amplitude ratios for finite-size corrections of a one-dimensional quantum spin model

We develop a general formalism for the magnetic oscillations (MO) in two dimensional (2D) systems. We consider general 2D Landau levels, which may depend on other variable or indices, besides the perpendicular magnetic field. In the ground state, we obtain expressions for the MO phase and amplitude. From this we use a Fourier expansion to write the MO, with the first term being a sawtooth oscillation. We also consider the effects of finite temperature, impurities or lattice imperfections, assuming a general broadening of the Landau levels. We develop two methods for describing these damping effects in the MO. One in terms of the occupancy of the Landau levels, the other in terms of reduction factors, which results in a generalization of the Lifshits-Kosevich (LK) formula. We show that the first approach is particularly useful at very low damping, when only the states close to the Fermi energy are excited. In contrast, the LK formula may be more convenient at higher damping, when only few terms are needed in its harmonic expansion. We compare different damping situations, showing how the MO are broadened in each case. The general formulation presented allows to relate the properties of the MO with those of the 2D systems.

We study non-Hermitian integrable fermion and boson systems from the perspectives of Grothendieck polynomials. The models considered in this article are the five-vertex model as a fermion system and the non-Hermitian phase model as a boson system. Both models are characterized by different solutions satisfying the same Yang–Baxter relation. From our previous works on the identification between the wavefunctions of the five-vertex model and Grothendieck polynomials, we introduce skew Grothendieck polynomials and derive the addition theorem among them. Using these relations, we derive the wavefunctions of the non-Hermitian phase model as a determinant form, which can also be expressed as Grothendieck polynomials. Namely, we establish a K-theoretic boson–fermion correspondence at the level of wavefunctions. As a by-product, the partition function of the statistical mechanical model of a three-dimensional (3D) melting crystal is exactly calculated by use of the scalar products of the wavefunctions of the phase model. The resultant expression can be regarded as a K-theoretic generalization of the MacMahon function describing the generating function of the plane partitions, which interpolates the generating functions of two-dimensional (2D) and (3D) Young diagrams.

This thesis primarily consists of two parts. In the first one, we benchmarked the performance of the functionals in density functional theory which have the asymptotically correct behavior. We compare the performance of the two different asymptotically corrected schemes, the long-range corrected (LC) hybrid scheme and the asymptotically corrected (AC) model potential scheme, in a wide range of applications. These schemes aim at producing the correct asymptotic behavior, which is known to be important to the Rydberg excitations and the frontier orbital energies of molecules. Based on our investigation, we found that the LC hybrid scheme outperforms the AC model potential scheme almost on all the properties studied, and we conclude that the LC hybrid scheme provides a promising direction for the future development of new exchange-correlation functionals. Besides, in the process of the benchmark, I established a molecular database ``IP131 full set', which consists of 131 experimental geometries of atoms and molecules, and their reference values of 131 experimental vertical ionization energies, 131 CCSD(T) calculated vertical electron affinities, 131 CCSD(T) calculated fundamental gaps and 113 CCSD(T) calculated atomization energies. The IP131 full set can be used in the benchmarks for other Ab Initio calculation methods, or in the parameter fitting in the development of density functionals in the future. In the second part, we adopted the Schrodinger equation numerical solutions to improve the applicability of the normal mode analysis in the case of TMA-H+-H2O, for the motivation that the theoretical simulated infrared spectrum of TMA-H+-H2O given by the normal mode analysis is far from the experiment results. Normal mode analysis is a convenient and widely adopted method that people usually use it to analyse the vibrational motions of multi-body mechanical systems, both classical and quantum. However, normal mode analysis is a approximate method and its assumptions, which make the analysis procedures simple and systematically solvable, also make the normal mode analysis not applicable to some vibrational motions in some mechanical systems. Our main modification method in this work is to regard the vibrational normal modes as some low dimensional quantum systems and adopt the Schrodinger equation numerical solutions in these quantum systems to replace the results from the normal mode analysis. By doing so, we can not only get a closer result to the experimental infrared spectrum, but also have a deeper understanding of the capability and applicability of normal mode analysis. Once in the future we encounter same problems when using the normal mode analysis in different systems, we may again adopt the procedures developed here to make it better.

Correlation effects in low dimensional quantum systems

The characteristics of pairwise entanglement and local polarization (LP) are discussed by studying the ground state (states) of the Heisenberg XX model. The results show that: the ground state (states) is (are) composed of the micro states with the minimal polarization (0 for even qubit and 1/2 for odd qubit); LP and the probability of the micro state have an intimate relation, i.e. the stronger the LP, the smaller the probability, and the same LP corresponds to the same probability; the pairwise entanglement of the ground state is the biggest in all eigenvectors. It is found that the pairwise entanglement is decreased by the state degeneracy and the system size. The concurrence approaches a fixed value of about 0.3412 (for odd-qubit chain) or 0.3491 (for even-qubit chain) if the qubit number is large enough.

We study the Riemannian metric and the Euler characteristic number of the Bloch band in a one-dimensional spin model with multisite spins exchange interactions. The Euler number of the Bloch band originates from the Gauss-Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone. We study this approach analytically in a transverse field XY spin chain with three-site spin coupled interactions. We define a class of cyclic quantum distance on the Bloch band and on the ground state, respectively, as a local characterization for quantum phase transitions. Specifically, we give a general formula for the Euler number by means of the Berry curvature in the case of two-band models, which reveals its essential relation to the first Chern number of the band insulators. Finally, we show that the ferromagnetic-paramagnetic phase transition in zero temperature can be distinguished by the Euler number of the Bloch band.

We continue a series of numerical experiments on many-body systems with random two-body interactions, by examining correlations in ratios in excitation energies of yrast $J=0,2,4,6,8$ states. Previous studies, limited only to $J=0,2,4$ states, had shown strong correlations in boson systems but not fermion systems. By including $J\ensuremath{\geqslant}6$ states and considering different scatter plots, strong correlations between ratios of yrast excitation energies appear in both boson and fermion systems. Such correlations agree with real nuclear data and include the well-known limits of seniority, vibrations, and rotations.

In the present investigation, linear and nonlinear electrostatic drift waves in the presence of trapped electrons with quantizing magnetic field and finite electron temperature effects in dense plasmas have been studied. The linear dispersion relation of the ion drift wave has been derived and it has been found that the Landau quantization and finite temperature effects significantly alter the linear propagation characteristics of the wave under consideration. Employing the Sagdeev potential approach, the formation of finite amplitude drift solitary structures has been investigated in the presence of a quantizing magnetic field for both fully and partially degenerate plasmas. Both compressive and rarefactive drift solitary structures have been obtained for different values of quantizing magnetic field and finite electron temperature effects. The theoretical results obtained have been analyzed numerically for the parameters typically found in white dwarfs.

The dynamics of the pairwise entanglement in a qubit lattice in the presence of static imperfections exhibits different regimes. We show that there is a transition from a perturbative region, where the entanglement is stable against imperfections, to the ergodic regime, in which a pair of qubits becomes entangled with the rest of the lattice and the pairwise entanglement drops to zero. The transition is almost independent of the size of the quantum computer. We consider both the case of an initial maximally entangled and separable state. In this last case there is a broad crossover region in which the computer imperfections can be used to create a significant amount of pairwise entanglement.

Optimal control theory is a powerful mathematical tool, which has known a rapid development since the 1950s, mainly for engineering applications. More recently, it has become a widely used method to improve process performance in quantum technologies by means of highly efficient control of quantum dynamics. This tutorial aims at providing an introduction to key concepts of optimal control theory that is accessible to physicists and engineers working in quantum control or in related fields. The different mathematical results are introduced intuitively, before being rigorously stated. This tutorial describes modern aspects of optimal control theory, with a particular focus on the Pontryagin maximum principle, which is the main tool for determining open-loop control laws without experimental feedback. The different steps to solve an optimal control problem are discussed, before moving on to more advanced topics such as the existence of optimal solutions or the definition of the different types of extremals, namely normal, abnormal, and singular. The tutorial covers various quantum control issues and describes their mathematical formulation suitable for optimal control. The connection between the Pontryagin maximum principle and gradient-based optimization algorithms used for high-dimensional quantum systems is described. The optimal solution of different low-dimensional quantum systems is presented in detail, illustrating how the mathematical tools are applied in a practical way.

Brief Introduction of Physics Researches in Chinese Academy of Sciences

Rayleigh instability is investigated in a Hall thruster under the effect of finite temperature and density gradient of the plasma species. The instability occurs only when the frequency of the oscillations ω falls within a frequency band described by k{y}u₀+1/k_{y}∂²u_{0}/∂x²+Ω/k_{y}n_{0}∂n₀/∂x≪ω<sqrt[Y{i}T{i}k{y}²/M+ω{p}{i}²(Ω²+Y{e}T{e}k{y}²/m)/(ω{p}{e}²+Ω²+Y{e}T{e}k{y}²/m], where u₀ is the drift velocity of the electrons, Ω is their gyration frequency under the effect of the magnetic field, k{y} is the wave propagation constant, n₀ is the plasma density together with ∂n₀/∂x as the density gradient, and T{i}(T{e}), M(m), Y{i}(Y{e}), and ω{p}{i}(ω{p}{e}) are the temperature, mass, specific heat ratio, and plasma frequency of the ions (electrons), respectively. A relevant Rayleigh equation is derived and solved numerically using the fourth-order Runge-Kutta method for investigating the perturbed potential under the effect of electron drift velocity, channel length, magnetic field, ion temperature, and electron temperature. The instability grows faster because of the magnetic field, ion temperature, and drift velocity of the electrons but its growth rate is reduced because of the electron temperature, channel length, and also its far distances from the anode.