Perturbation theory of von Neumann entropy

In quantum information theory, von Neumann entropy plays an important role; it is related to quantum channel capacities. Only for a few states can one obtain their entropies. In a continuous variable system, numeric evaluation of entropy is not easy due to infinite dimensions. We develop the perturbation theory for systematically calculating von Neumann entropy of a non-degenerate system as well as a degenerate system.     

Quantum phase transition and entanglement in Li atom system

By use of the exact diagonalization method, the quantum phase transition and entanglement in a 6-Li atom system are studied. It is found that entanglement appears before the quantum phase transition and disappears after it in this exactly solvable quantum system. The present results show that the von Neumann entropy, as a measure of entanglement, may reveal the quantum phase transition in this model.     

Quantum coherence and ground-state phase transition in a four-chain Bose–Hubbard model

We study the quantum coherence and ground-state phase transition of a four-chain Bose–Hubbard model with the long-range interaction. In a special four-chain Bose–Hubbard model,i.e., each chain only has one optical potential, four types of the ground-state phases are discovered. The effects of the disorder, the on-site interaction and the long-range interaction on the quantum coherence are studied. For the system without the long-range interaction, the quantum coherence changes from one periodic oscillation to two periodic oscillations as the onsite interaction increases. By considering the long-range interaction, the quantum coherence goes back to one periodic oscillation again. The on-site interaction itself suppresses the quantum coherence, both the on-site interaction and long-range interaction together enhance the quantum coherence with the weak disorder. If the disorder strength is increased beyond a critical value,they start to suppress the quantum coherence. In a regular four-chain Bose–Hubbard model, i.e.,each chain has many optical potentials, the ground-state phase transitions are obtained by using the cluster Gutzwiller mean-field method. Exotic ground-state phases are found, i.e., superfluid phase, integer Mott insulator phase, supersolid phase and loophole insulator phase. The combination of the loophole insulator phase and the supersolid phase expands the lobes with the half-integer filling per site for the small ratio β = t_■/t_⊥.     

Replacing energy by von Neumann entropy in quantum phase transitions

We propose that quantum phase transitions are generally accompanied by non-analyticities of the von Neumann (entanglement) entropy. In particular, the entropy is non-analytic at the Anderson transition, where it exhibits unusual fractal scaling. We also examine two dissipative quantum systems of considerable interest to the study of decoherence and find that non-analyticities occur if and only if the system undergoes a quantum phase transition.     

一种基于von Neumann熵的双路径纠缠量子微波信号生成质量评估方法

针对目前没有合适的方法从产生方来表征纠缠量子微波信号的质量好坏, 提出了一种基于von Neumann熵的双路径纠缠量子微波信号生成质量评估方法. 利用双模压缩真空态描述了纠缠量子微波的信号格式, 给出了光子数与压缩参量之间的函数关系, 以熵评估纠缠态信号所占比例, 分析了熵与压缩参量和光子数之间的关系. 仿真结果表明, 纠缠量子微波信号中的光子数是由压缩参量决定的, 它们之间呈指数平方的规律性变化; 熵随着压缩参量的增大而减小, 但是减小的趋势越来越平缓, 近似呈负指数关系, 熵的极限值约为65%. 研究结果表明, 通过选择合适的压缩参量可以提高纠缠微波信号生成质量以满足实际需要, 因此, 本研究对于生成双路径纠缠量子微波电路参数选择、提高系统可用性提供了方法和依据.     

Calculation of von Neumann entropy for hydrogen and positronium negative ions

In the present work, we carry out calculations of von Neumann entropies and linear entropies for the hydrogen negative ion and the positronium negative ion. We concentrate on the spatial (electron–electron orbital) entanglement in these ions by using highly correlated Hylleraas functions to represent their ground states, and to take care of correlation effects. We apply the Schmidt decomposition method on the partial-wave expanded two-electron wave functions, and from which the one-particle reduced density matrix can be obtained, leading to the quantifications of linear entropy and von Neumann entropy in the H⁻ and Ps⁻ ions.     

Free probability and the von Neumann algebrasof free groups

This short note summarizes the circumstances of the birth of free probability theory andsome of the recent achievements.     

Quantum information entropy for one-dimensional system undergoing quantum phase transition

Calculations of the quantum information entropy have been extended to a non-analytically solvable situation. Specifically, we have investigated the information entropy for a one-dimensional system with a schematic "Landau" potential in a numerical way. Particularly, it is found that the phase transitional behavior of the system can be well expressed by the evolution of quantum information entropy. The calculated results also indicate that the position entropy S_x and the momentum entropy S_p at the critical point of phase transition may vary with the mass parameter M but their sum remains as a constant independent of M for a given excited state. In addition, the entropy uncertainty relation is proven to be robust during the whole process of the phase transition.     

A prototype of quantum von Neumann architecture

A modern computer system, based on the von Neumann architecture, is a complicated system with several interactive modular parts. It requires a thorough understanding of the physics of information storage, processing, protection, readout, etc. Quantum computing, as the most generic usage of quantum information, follows a hybrid architecture so far, namely, quantum algorithms are stored and controlled classically, and mainly the executions of them are quantum, leading to the so-called quantum processing units. Such a quantum–classical hybrid is constrained by its classical ingredients, and cannot reveal the computational power of a fully quantum computer system as conceived from the beginning of the field. Recently, the nature of quantum information has been further recognized, such as the no-programming and no-control theorems, and the unifying understandings of quantum algorithms and computing models. As a result, in this work, we propose a model of a universal quantum computer system, the quantum version of the von Neumann architecture. It uses ebits (i.e. Bell states) as elements of the quantum memory unit, and qubits as elements of the quantum control unit and processing unit. As a digital quantum system, its global configurations can be viewed as tensor-network states. Its universality is proved by the capability to execute quantum algorithms based on a program composition scheme via a universal quantum gate teleportation. It is also protected by the uncertainty principle, the fundamental law of quantum information, making it quantum-secure and distinct from the classical case. In particular, we introduce a few variants of quantum circuits, including the tailed, nested, and topological ones, to characterize the roles of quantum memory and control, which could also be of independent interest in other contexts. In all, our primary study demonstrates the manifold power of quantum information and paves the way for the creation of quantum computer systems in the near future.     

横场中具有周期性各向异性的一维XY模型的量子相变

通过解析和数值计算的方法研究了横场中具有周期性各向异性的一维XY自旋模型的量子相变和量子纠缠.主要讨论了周期为二的情况,即各向异性参数交替地取比值为α的两个值.结果表明,与横场中均匀XY模型相比,α=-1所对应的模型在参数空间的相图存在着明显的不同.原来的Ising相变仍然存在,没有了沿x和y方向的各向异性铁磁(FM_x,FM_y)相,即各向异性相变消失,出现了一个新的相,并且该相内沿x和y方向的长程关联函数相等且大于零,我们称新相为各向同性铁磁(FM_(xx))相.这是由于系统新的对称性所导致的.解析结果还说明系统在FM_(xx)相中的单粒子能谱有两个零点,是一个无能隙的相.最后,利用冯·诺依曼熵数值地研究了系统在新相内各点的量子纠缠,发现该相内每一点的冯·诺依曼熵的标度行为与均匀XY模型在各向异性相变处的相似,即S_L～1/3㏒_2L+Const.     

Quantum phase diagram of the half filled Hubbard model with bond-charge interaction

Using quantum field theory and bosonization, we determine the quantum phase diagram of the one-dimensional Hubbard model with bond-charge interaction X in addition to the usual Coulomb repulsion U at half-filling, for small values of the interactions. We show that it is essential to take into account formally irrelevant terms of order X  . They generate relevant terms proportional to X²$X^2$ in the flow of the renormalization group (RG). These terms are calculated using operator product expansions. The model shows three phases separated by a charge transition at U=Uc$U=U_c$ and a spin transition at U=Us>Uc$U=U_s>U_c$. For U<Uc$U<U_c$ singlet superconducting correlations dominate, while for U>Us$U>U_s$, the system is in the spin-density wave phase as in the usual Hubbard model. For intermediate values Uc<U<Us$U_c<U<U_s$, the system is in a spontaneously dimerized bond-ordered wave phase, which is absent in the ordinary Hubbard model with X=0$X=0$. We obtain that the charge transition remains at Uc=0$U_c=0$ for X≠0$X\ne 0$. Solving the RG equations for the spin sector, we provide an analytical expression for Us(X)$U_s(X)$. The results, with only one adjustable parameter, are in excellent agreement with numerical ones for X<t/2$X<t/2$ where t is the hopping.     

States and Structure of von Neumann Algebras

We summarize and deepen recent results on the interplay between properties of states and the structure of von Neumann algebras. We treat Jauch–Piron states and the concept of independence in noncommutative probability theory.     

依赖强度耦合双模Jaynes-Cummings 模型的纠缠和场熵演化

应用von Neumann熵研究了依赖强度耦合双模Jaynes-Cummings模型中原子与光场的纠缠度。给出了两模初始场均处于相干态和双模压缩真空态两种情况下熵演化的数值结果。讨论了初始场强度对原子―场纠缠度的影响。发现在强场条件下，原子与光场基本稳定在最大纠缠态但伴随着周期性的脉冲式解纠缠。     

Bethe ansatz results for Hubbard chains with toroidal boundary conditions

We solve exactly the problem of a one-dimensional repulsive-U Hubbard chain with toroidal boundary conditions (HTB) using the Bethe ansatz approach. We calculate analytically the finite-size corrections to the ground-state energy in the half-filled case and use this expression to derive charge and spin stiffnesses with no assumptions. We then use a particle-hole transformation to calculate the finite-size corrections for the half-filledattractive- U case, and again derive the resulting expressions for the charge and spin stiffnesses. Lastly, we discuss how the repulsive-U corrections relate to those of a Heisenberg model with toroidal boundary conditions.On leave from Departamento de Fisica, Universidade Federal de S. Carlos, S. Carlos, 13560, Brazil.     

Quantum Integrability of 1D Ionic Hubbard Model

The quantum integrability of the 1D ionic Hubbard model (IHM) is established using two independent numerical methods, namely i) energy level spacing statistics and ii) occupation profile of one-particle density matrix (OPDM) eigen-values. Both methods suggest that the 1D IHM is integrable. The calculations of energy level statistics reproduce the known results for the standard Hubbard model. Upon turning on the the ionic term, the energy level spacing distribution of this model continues to obey the Poissonian distribution. Occupation patterns as extracted from OPDM indicate that quasi-particles are sharpened upon increasing the ionic potential. This is evidenced by a larger jump in the occupation number distribution.     

Quantum Phase Transition and Local Entanglement in Extended Hubbard Model on Anisotropic Triangular Lattices

Using a mean-field theory based upon Hartree-Fock approximation, we theoretically investigate the competition between the metallic conductivity, spin order and charge order phases in a two-dimensional half-filled extended Hubbard model on anisotropic triangular lattice. Bond order, double occupancy, spin and charge structure factor are calculated, and the phase diagram of the extended Hubbard model is presented. It is found that the interplay of strong interaction and geometric frustration leads to exotic phases, the charge fluctuation is enhanced and three kinds of charge orders appear with the introduction of the nearest-neighbor interaction. Moreover, for different frustrations, it is also found that the antiferromagnetic insulating phase and nonmagnetic insulating phase are rapidly suppressed, and eventually disappeared as the ratio between the nearest-neighbor interaction and on-site interaction increases. This indicates that spin order is also sensitive to the nearest-neighbor interaction. Finally, the single-site entanglement is calculated and it is found that a clear discontinuous of the single-site entanglement appears at the critical points of the phase transition.     

De Morgan Property for Effect Algebras of von Neumann Algebras

It is shown that the unit interval of a von Neumann algebra is a Sum Brouwer–Zadeh algebra when equipped with another unary operation sending each element to the complement of its range projection. The main result of this Letter says that a von Neumann algebra is finite if and only if the corresponding Brouwer–Zadeh structure is de Morgan or, equivalently, if the range projection map preserves infima in the unit interval. This provides a new characterization of finiteness in the Murray–von Neumann structure theory of von Neumann algebras in terms of Brouwer–Zadeh structures.     

三带Hubbard模型中环形电流相的量子蒙特卡罗模拟

运用约束路径量子蒙特卡罗方法,对二维、三带Hubbard模型中的环形电流相进行数值模拟。在数值模拟过程中定义了表征环流相的不同算符及其关联函数,并且选用合理的模型Hamiltonian量中的参数。通过模拟发现,对应于闭合环形的关联函数在相同距离上要比其他所有没有闭合的关联函数大得多,因此证明在三带Hubbard模型中存在环形电流相。     

Rényi entropy and quantum phase transition in the Dicke model

The Rényi entropies of the Dicke model are presented. This quantum-optical model describes a single-mode bosonic field interacting with an ensemble of N two-level atoms. There is a quantum phase transition in the N→∞ limit. It is shown that there is an abrupt change in the Rényi entropy of order β at the transition point. Around the critical value of the coupling strength λc the Rényi entropy is proportional to the logarithm of the characteristic length and diverges as ln|λc−λ| for any order β. The pseudocapacity defined here in analogy with the heat capacity exhibits the phase transition. The critical exponent for the Dicke model is found to be 1 for any value of the parameter β.