ML Glasser, LM Nieto
A simple one dimensional model is introduced describing a two particle "atom" approaching a point at which the interaction between the particles is lost. The wave function is obtained analytically and analyzed to display the entangled nature of the subsequent state.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We investigate the correlations between different bipartitions of an exactly solvable one-dimensional many-body Moshinsky model consisting of Nn "nuclei" and Ne "electrons". We study the dependence of entanglement on the inter-particle interaction strength, on the number of particles, and on the particle masses. Consistent with kinematic intuition, the entanglement between two subsystems vanishes when the subsystems have very different masses, while it attains its maximal value for subsystems of comparable mass. We show how this entanglement feature can be inferred by means of the Born-Oppenhe…
We present a fully analytical solution of the dynamics of two strongly-driven atoms resonantly coupled to a dissipative cavity field mode. We show that an initial atom-atom entanglement cannot be increased. In fact, the atomic Hilbert space divides into two subspaces, one of which is decoherence free so that the initial atomic entanglement remains available for applications, even in presence of a low enough atomic decay rate. In the other subspace a measure of entanglement, decoherence, and also purity, are described by a similar functional behavior that can be monitored by joint atomic measur…
We have studied dynamical properties of an exactly solvable quantum coupled double-well (DW) systems with Razavy's hyperbolic potential. With the use of four kinds of initial wavepackets, the correlation function $Γ(t)$ and the concurrence $C(t)$ which is a typical measure of the entanglement in two qubits, are calculated. We obtain the orthogonality time $τ$ which signifies a time interval for an initial state to evolve to its orthogonal state, and the temporal average of $C(t)$, $C_{av}$ $(=\sqrt{\langle C(t)^2 \rangle})$. The coupling dependence of $τ$ and the concurrence [$C_{av}$ or $C(0)…
Lecture notes for the Brazilian School on Statistical Mechanics, Natal, Brazil, July 2011. The five lectures introduce to the description of entanglement in many-particle systems and review the ground-state entanglement features of standard solvable lattice models. This is done using a thermodynamic formulation in which the eigenvalue spectrum of a certain Hamiltonian determines the entanglement properties. The methods to obtain it are discussed and results, both analytical and numerical, for various cases including time evolution are presented.
We study Hamiltonian systems with point interactions and give a systematic description of the corresponding boundary conditions and the spectrum properties for self-adjoint, PT-symmetric systems and systems with real spectra. The integrability of one dimensional many body systems with these kinds of point (contact) interactions are investigated for both bosonic and fermionic statistics.
A solvable quantum many-body problem
该论文证明了一个指数型多体波函数是特定势能下薛定谔方程的解，并找到了平移不变的角动量本征态。
We study the non-Markovian effects on the dynamics of entanglement in an exactly-solvable model that involves two independent oscillators each coupled to its own stochastic noise source. First, we develop Lie algebraic and functional integral methods to find an exact solution to the single-oscillator problem which includes an analytic expression for the density matrix and the complete statistics, i.e., the probability distribution functions for observables. For long bath time-correlations, we see non-monotonic evolution of the uncertainties in observables. Further, we extend this exact solutio…
We compute the entanglement entropy of a wide class of exactly solvable models which may be characterized as describing matter coupled to gauge fields. Our principle result is an entanglement sum rule which states that entropy of the full system is the sum of the entropies of the two components. In the context of the exactly solvable models we consider, this result applies to the full entropy, but more generally it is a statement about the additivity of universal terms in the entropy. We also prove that the Renyi entropy is exactly additive and hence that the entanglement spectrum factorizes. …
Page curve entanglement dynamics in an analytically solvable model
本文提出一个自由费米子精确可解模型，再现纠缠熵先升后降并在晚期渐近消失的 Page 曲线，并揭示其伴随半经典图像破缺、纠缠 Hamilton 量相变和 Rényi 熵非解析性。
In this paper we investigate a open two-qubit model whose dynamics is not exactly solvable. When the initial state is the maximum entangled state, as the exactly solvable open two-qubit model [D. Tolkunov and V. Privman, Phys. Rev. A 71, 060308(R) (2005)], the decay of entanglement of formation of the model, expressed by concurrence is also governed by the product of suppression factors describing decoherence of the subsystems (qubits). However, if the initial state is not the maximum entangled state, its concurrence will decrease faster than the product of the suppression factors describing d…
A new exactly solvable alternative to the Calogero three-particle model is proposed. Sharing its confining long-range part, it contains the mere zero-range two-particle barriers. Their penetrability gives rise to a tunneling, tunable via their three independent strengths. Their variability can control the removal of the degeneracy of the energy levels in an innovative, non-perturbative manner.
There are several physically motivated density matrix functionals in the literature, built from the knowledge of the natural orbitals and the occupation numbers of the one-body reduced density matrix. With the help of the equivalent phase-space formalism, we thoroughly test some of the most popular of those functionals on a completely solvable model.
Newly, during an analytical calculation M. A. Yurischev [arXiv: 1302.5239 (2013)] prove that quantum discord (or entanglement) remains unchangeable for any centrosymmetric (CS) states that are converted to their corresponding mode X. In this paper, in addition to the above calculations, the conditions which geometric measure remains constant are presented. This work will be completed with discussion about two physical examples.
We calculate the entanglement-assisted and unassisted channel capacities of an exactly solvable spin star system, which models the quantum dephasing channel. The capacities for this non-Markovian model exhibit a strong dependence on the coupling strengths of the bath spins with the system, the bath temperature, and the number of bath spins. For equal couplings and bath frequencies, the channel becomes periodically noiseless.
The approach of multi-dimensional SUSY Quantum Mechanics is used in an explicit construction of exactly solvable 3-body (and quasi-exactly-solvable $N$-body) matrix problems on a line. From intertwining relations with time-dependent operators, we build exactly solvable non-stationary scalar and $2\times 2$ matrix 3-body models which are time-dependent extensions of the Calogero model. Finally, we investigate the invariant operators associated to these systems.
Non-equilibrium quantum dynamics represents an emerging paradigm for condensed matter physics, quantum information science, and statistical mechanics. Strongly interacting Rydberg atoms offer an attractive platform to study driven-dissipative dynamics of quantum spin models with long-range order. Here, we explore the conditions under which stationary many-body entanglement persists with near-unit fidelity and high scalability. In our approach, coherent many-body dynamics is driven by Rydberg-mediated laser transitions, while atoms at the lattice boundary reduce the entropy of the many-body sta…
We consider the spin k/2 analogue of the XXZ quantum spin chain. We compute the entanglement entropy S associated with splitting the infinite chain into two semi-infinite pieces. In the scaling limit, we find S ~ c_k/6 (ln(xi))+ln(g)+... . Here xi is the correlation length and c_k=3k/(k+2) is the central charge associated with the sl_2 WZW model at level k. ln(g) is the boundary entropy of the WZW model. Our result extends previous observations and suggests that this is a simple and perhaps rather general way both of extracting the central charge of the ultraviolet CFT associated with the scal…
We show how to detect entanglement with criteria built from simple two-body correlation terms. Since many natural Hamiltonians are sums of such correlation terms, our ideas can be used to detect entanglement by energy measurement. Our criteria can straightforwardly be applied for detecting different forms of multipartite entanglement in familiar spin models in thermal equilibrium.
With an easily applicable criterion based on permutation symmetries of (identically prepared) replicas of quantum states we identify distinct entanglement classes in high-dimensional multi- partite systems. The different symmetry properties of inequivalent states provide a rather intuitive picture of the otherwise very abstract classification of many-body entangled states.
Exactly solvable models that exhibit quantum signatures of classical chaos are both rare as well as important - more so in view of the fact that the mechanisms for ergodic behavior and thermalization in isolated quantum systems and its connections to non-integrability are under active investigation. In this work, we study quantum systems of few qubits collectively modeled as a kicked top, a textbook example of quantum chaos. In particular, we show that the 3 and 4 qubit cases are exactly solvable and yet, interestingly, can display signatures of ergodicity and thermalization. Deriving analytic…
We show a general approach for detecting genuine multipartite entanglement (GME) and partial inseparability in many-body-systems by means of macroscopic observables (such as the energy) only. We show that the obtained criteria, the "GME gap" and "the k-entanglement gap", detect large areas of genuine multipartite entanglement and partial entanglement in typical many body states, which are not detected by other criteria. As genuine multipartite entanglement is a necessary property for several quantum information theoretic applications such as e.g. secret sharing or certain kinds of quantum comp…
A genuine tripartite entanglement monotone is presented for $(2\otimes 2\otimes n)$-dimensional tripartite pure states by introducing a new entanglement measure for bipartite pure states. As an application, we consider the genuine tripartite entanglement of the ground state of the exactly solvable isotropic spin-1/2 chain with three-spin interaction. It is shown that the singular behavior of the genuine tripartite entanglement exactly signals a quantum phase transition.
We study the time evolution of the amount of entanglement generated by one dimensional spin-1/2 Ising-type Hamiltonians composed of many-body interactions. We investigate sets of states randomly selected during the time evolution generated by several types of time-independent Hamiltonians by analyzing the distributions of the amount of entanglement of the sets. We compare such entanglement distributions with that of typical entanglement, entanglement of a set of states randomly selected from a Hilbert space with respect to the unitarily invariant measure. We show that the entanglement distribu…
Using the quantum two-body system as a familiar model, this talk will describe how entanglement can be used to select preferred observables for interrogating a physical system. The symmetries and dynamics of the quantum two-body system provide a backdrop for testing the relativity of entanglement with respect to observable-induced tensor product structures. We believe this exploration leads us to a general statement: the physically-meaningful observable subalgebras are the ones that minimize entanglement in typical states.
We employ a nuclear magnetic resonance (NMR) quantum information processor to simulate the ground state of an XXZ spin chain and measure its NMR analog of entanglement, or pseudo-entanglement. The observed pseudo-entanglement for a small-size system already displays singularity, a signature which is qualitatively similar to that in the thermodynamical limit across quantum phase transitions, including an infinite-order critical point. The experimental results illustrate a successful approach to investigate quantum correlations in many-body systems using quantum simulators.
The Hall--Post inequalities provide lower bounds on $N$-body energies in terms of $N'$-body energies with $N'<N$. They are rewritten and generalized to be tested with exactly-solvable models of Calogero-Sutherland type in one and higher dimensions. The bound for $N$ spinless fermions in one dimension is better saturated at large coupling than for noninteracting fermions in an oscillator
We construct a family of quasi-solvable quantum many-body systems by an algebraic method. The models contain up to two-body interactions and have permutation symmetry. We classify these models under the consideration of invariance property. It turns out that this family includes the rational, hyperbolic (trigonometric) and elliptic Inozemtsev models as the particular cases.
This paper investigates the physical effects of Yang-Baxter equation (YBE) to quantum entanglements through the 3-body S-matrix in entangling parameter space. The explicit form of 3-body S-matrix $\breve{R}_{123}(θ,φ)$ based on the 2-body S-matrices is given due to the factorization condition of YBE. The corresponding chain Hamiltonian has been obtained and diagonalized, also the Berry phase for 3-body system is given. It turns out that by choosing different spectral parameters the $\breve{R}(θ,φ)$-matrix gives GHZ and W state respectively. The extended 1-D Kitaev toy model has been derived. E…
Multipartite entanglement plays an essential role in both quantum information science and many-body physics. Due to the exponentially large dimension and complex geometric structure of the state space, the detection of entanglement in many-body systems is extremely challenging in reality. Conventional means, like entanglement witness and entropy criterion, either highly depend on the prior knowledge of the studied systems or the detection capability is relatively weak. In this work, we propose a framework for designing multipartite entanglement criteria based on permutation moments, which have…
What correlations are present in the ground state of a many-body Hamiltonian? We study the relationship between ground-state correlations, especially entanglement, and the energy gap between the ground and first excited states. We prove several general inequalities which show quantitatively that ground-state correlations between systems not directly coupled by the Hamiltonian necessarily imply a small energy gap.
We propose a systematic method to construct quasi-solvable quantum many-body systems having permutation symmetry. By the introduction of elementary symmetric polynomials and suitable choice of a solvable sector, the algebraic structure of sl(M+1) naturally emerges. The procedure to solve the canonical-form condition for the two-body problem is presented in detail. It is shown that the resulting two-body quasi-solvable model can be uniquely generalized to the M-body system for arbitrary M under the consideration of the GL(2,K) symmetry. An intimate relation between quantum solvability and super…
In this paper we study the quantum phase transition and entanglement in s1=1/2 and s2=1 spin pair system by the exact diagonalization method. We show that, for this exactly solvable quantum bi-spin system, entanglement appears before quantum phase transition and disappears after it. Moreover, we show that the von Neumann entropy, as a measure of entanglement, can reveal quantum phase transition in this system.
In this work, we start from the well known Calogero-Wolfes type 3-body problems on a line and construct the corresponding exactly solvable rationally extended 3-body potentials. In particular, we obtain the corresponding energy eigenvalues and eigenfunctions which are in terms of the product of Xm Laguerre and Xp Jacobi exceptional orthogonal polynomials where both m,p = 1,2,3,....
Solvable Quantum Circuits from Spacetime Lattices
本文提出完全可约电路框架，通过分析信息流模式与纠缠动力学的关系，为非积分多体量子混沌提供新的统一解模型。
We introduce a general bipartite-like representation and Schmidt decomposition of an arbitrary pure state of $N$ indistinguishable fermions, based on states of $M<N$ and $(N-M)$ fermions. It is directly connected with the reduced $M$- and $(N-M)$-body density matrices (DMs), which have the same spectrum in such states. The concept of $M$-body entanglement emerges naturally in this scenario, generalizing that of one-body entanglement. Rigorous majorization relations satisfied by the normalized $M$-body DM are then derived, which imply that the associated entropy will not increase, on average, u…
We develop a novel approach aimed at solving the equations of motion of open quantum many-body systems. It is based on a combination of generalized wave function trajectories and matrix product states. We introduce an adaptive quantum stochastic propagator, which minimizes the expected entanglement in the many-body quantum state, thus minimizing the computational cost of the matrix product state representation of each trajectory. We illustrate this approach on the example of a one-dimensional open Brownian circuit. We show that this model displays an entanglement phase transition between area …
We establish a set of resource conversion relationships between quantum coherence and multipartite entanglement in many-body systems, where the operational measures of resource cost and distillation are focused. Under the multipartite incoherent operation, the initial coherence of single-party system bounds the maximal amounts of corresponding operational entanglement in an arbitrary bipartite partition as well as the genuine multipartite entanglement in many-body systems. Furthermore, the converted multipartite entanglement can be transferred to its subsystems and restored to coherence of a s…
We show that one-body entanglement, which is a measure of the deviation of a pure fermionic state from a Slater determinant (SD) and is determined by the mixedness of the single-particle density matrix (SPDM), can be considered as a quantum resource. The associated theory has SDs and their convex hull as free states, and number conserving fermion linear optics operations (FLO), which include one-body unitary transformations and measurements of the occupancy of single-particle modes, as the basic free operations. We first provide a bipartitelike formulation of one-body entanglement, based on a …
We construct optimal time-local control pulses based on a multipartite entanglement measure as target functional. The underlying control Hamiltonians are derived in a purely algebraic fashion, and the resulting pulses drive a composite quantum system rapidly into that highly entangled state which can be created most efficiently for a given interaction mechanism, and which bears entanglement that is robust against decoherence. Moreover, it is shown that the control scheme is insensitive to experimental imperfections in first order.
Entanglement transitions in a boundary-driven open quantum many-body system
该研究通过边界驱动的XXZ自旋链，展示了在开放量子多体系统中通过TTO近似态框架探测纠缠相变的能力，揭示了纠缠尺度与自旋电流之间的联系。
Exactly solvable models provide an opportunity to study different aspects of reduced quantum dynamics in detail. We consider the reduced dynamics of a single spin in finite XX and XY spin 1/2 chains. First we introduce a general expression describing the evolution of the reduced density matrix. This expression proves to be tractable when the combined closed system (i.e. open system plus environment) is integrable. Then we focus on comparing decoherence and thermalization timescales in the XX chain. We find that for a single spin these timescales are comparable, in contrast to what should be ex…
The evolution of a many-particle system on a one-dimensional lattice, subjected to a quantum walk can cause spatial entanglement in the lattice position, which can be exploited for quantum information/communication purposes. We demonstrate the evolution of spatial entanglement and its dependence on the quantum coin operation parameters, the number of particles present in the lattice and the number of steps of quantum walk on the system. Thus, spatial entanglement can be controlled and optimized using a many-particle discrete-time quantum walk.
The divergence in the interaction term of the Calogero model can be prevented introducing a cutoff length parameter, this modification leads to a quasi-exactly solvable model whose eigenfunctions can be written in terms of Heun's polynomials. It is shown both, analytical and numerically. that the reduced density matrix obtained tracing out one particle from the two-particle density operator can be obtained exactly as well as its entanglement spectrum. The number of non-zero eigenvalues in these cases is finite. Besides, it is shown that taking the limit in which the cutoff distance goes to zer…
The preparation of highly entangled many-body systems is one of the central challenges of both basic and applied science. The complexity of interparticle interaction and environment coupling increases rapidly with the number of to-be-entangled subsystems, rendering the requirements on the control of many-body quantum systems ever more restrictive. We propose an approach that allows to derive optimal control Hamiltonians in a purely algebraic fashion. These drive a composite quantum system rapidly into that highly entangled state which can be created most efficiently for a given interaction mec…
Two non--interacting quantum systems which couple to a common environment with many degrees of freedom initially in thermal equilibrium can become entangled due to the indirect interaction mediated through this heat bath. I examine here the dynamics of reservoir induced entanglement for a heat bath consisting of a thermal electro--magnetic radiation field, such as black body radiation or the cosmic microwave background, and show how the effect can be understood as result of an effective induced interaction.
We present several examples of quasi-exactly solvable $N$-body problems in one, two and higher dimensions. We study various aspects of these problems in some detail. In particular, we show that in some of these examples the corresponding polynomials form an orthogonal set and many of their properties are similar to those of the Bender-Dunne polynomials. We also discuss QES problems where the polynomials do not form an orthogonal set.
We analyze the quantum entanglement at the equilibrium in a class of exactly solvable one-dimensional spin models at finite temperatures and identify a region where the quantum fluctuations determine the behavior of the system. We probe the response of the system in this region by studying the spin dynamics after projective measurement of one local spin which leads to the appearance of the ``decoherence wave''. We investigate time-dependent spin correlation functions, the entanglement dynamics, and the fidelity of the quantum information transfer after the measurement.
We construct an entanglement witness for many-qubit systems, based on symmetric two-body correlations with two measurement settings. This witness is able to detect the entanglement of some Dicke states for any number of particles, and such detection exhibits some robustness against white noise and thermal noise under the Lipkin-Meshkov-Glick Hamiltonian. In addition, it detects the entanglement of spin-squeezed states, with a detection strength that approaches the maximal value for sufficiently large numbers of particles. As spin-squeezed states can be experimentally generated, the properties …
Exactly solvable models have played an important role in establishing the sophisticated modern understanding of equilibrium many-body physics. And conversely, the relative scarcity of solutions for non-equilibrium models greatly limits our understanding of systems away from thermal equilibrium. We study a family of non-equilibrium models, some of which can be viewed as dissipative analogues of the transverse-field Ising model, in that an effectively classical Hamiltonian is frustrated by dissipative processes that drive the system toward states that do not commute with the Hamiltonian. Surpris…
The entanglement membrane in exactly solvable lattice models
本文在广义对偶酉电路中精确计算了纠缠线张力，揭示了具有 $v_E<v_B$ 的速度层级，并构造了新的广义对偶酉门，验证了微观 Floquet 格点模型中的纠缠膜理论。
Notes on solvable models of many-body quantum chaos
本研究探讨与布朗SYK模型相关的多体混沌可解模型，利用涌现对称性映射为经典随机过程，研究有限N下算子尺寸增长等动力学性质，并展示大N极限下的普适行为。
We present a family of many-body models which are exactly solvable analytically. The models are an extended n-body interaction Lipkin-Meshkov-Glick model which considers spin-flip terms which are associated with the interaction of an external classical field which coherently manipulates the state of the system in order to, for example, process quantum information. The models also describe a two-mode Bose-Einstein condensate with a Josephson-type interaction which includes n-particle elastic and inelastic collisions. One of the models corresponds to the canonical two-mode Bose-Einstein Hamitoni…
Integrability conditions for systems of bosons or fermions with seniority conserving hamiltonians are derived. The conditions are shown to be invariant under a large class of transformations of the interaction matrix elements. Previously published integrable models are shown to satisfy these conditions and the existence of a new class of integrable models is demonstrated. The number of free parameters in the interaction in these models equals the number of single particle levels plus 3 . Equations for the energy eigenstates and eigenvalues are derived and the eigenvalues of the complete set of…
Solvable entanglement dynamics in quantum circuits with generalized space-time duality
本文利用三幺正与局部对偶幺正的广义时空对偶量子电路，精确刻画受激Ising模型的子系统马尔可夫影响矩阵，并求解任意时刻纠缠增长、饱和及非混沌准周期复现行为。
Entanglement breaking in self-referential quantum feedback: a record bound and an exactly solvable loop
该研究针对未来指向量子反馈的不动点，验证了同时满足相干、信息性、非纠缠破坏等性质的参数区域，为相关量子反馈协议的设计提供了可验证的原理性支撑。
Exactly solvable non-unitary time evolution in quantum critical systems I: Effect of complex spacetime metrics
本文利用可精确求解模型研究复时空度规导致的一维量子临界系统非幺正演化，揭示纠缠熵对数增长等普适行为，并数值分析含时驱动下的稳态纠缠结构。
Typically in many-body systems the correlation energy, which is defined as the difference between the exact ground state energy and the mean-field solution, has been a measure of the system's total correlations. However, under the quantum information context, it is possible to define some quantities in terms of the system's constituents that measure the classical and quantum correlations, such as the entanglement entropy, mutual information, quantum discord, one-body entropy, etc. In this work, we apply concepts of quantum information in fermionic systems in order to study traditional correlat…
The simple entanglement of N-body N-particle pure states is extended to the more general M-body or M-body N-particle states where $N\neq M$. Some new features of the M-body N-particle pure states are discussed. An application of the measure to quantify quantum correlations in a Bose-Einstien condensate model is demonstrated.
Non-equilibrium dynamics of charged dual-unitary circuits
本文研究带任意多个U(1)电荷的对偶幺正电路，构造可精确求解的非平衡动力学可解态，揭示其向广义吉布斯系综的弛豫、非最大纠缠饱和以及非可解态中的量子姆潘巴效应。
Short review on entanglement, as seen from a quantum information perspective, and some simple applications to many-body quantum systems. Special emphasis in area laws, cold atoms, and efficient descriptions using tensor network states.
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。