Exact solution of the three-boson problem at vanishing energy

Matter-wave scattering from strongly interacting bosons in an optical lattice

We study the scattering of a matter-wave from an interacting system of bosons in an optical lattice, focusing on the strong-interaction regime. Analytical expressions for the many-body scattering cross section are derived from a strong-coupling expansion and a site-decoupling mean-field approximation, and compared to numerically obtained exact results. In the thermodynamic limit, we find a non-vanishing inelastic cross section throughout the Mott insulating regime, which decays quadratically as a function of the boson-boson interaction.

Exact quantum dynamics of a bosonic Josephson junction

The quantum dynamics of a one-dimensional bosonic Josephson junction is studied by solving the time-dependent many-boson Schrödinger equation numerically exactly. Already for weak interparticle interactions and on short time scales, the commonly-employed mean-field and many-body methods are found to deviate substantially from the exact dynamics. The system exhibits rich many-body dynamics like enhanced tunneling and a novel equilibration phenomenon of the junction depending on the interaction, attributed to a quick loss of coherence.

Effects Beyond Center-of-Mass Separability in a Trapped Bosonic Mixture: Exact Results

An exactly solvable model mimicking demixing of two Bose-Einstein condensates at the many-body level of theory is devised. Various properties are expressed in closed form along the demixing pathway and investigated. The connection between the center-of-mass coordinate and in particular the relative center-of-mass coordinate and demixing is explained. The model is also exactly solvable at the mean-field level of theory, allowing thereby comparison between many-body and mean-field properties. Applications are briefly discussed.

Describing systems of interacting fermions by boson models: exact mapping in arbitrary dimension and applications

We develop a new method that allows us to map models of interacting fermions onto bosonic models describing collective excitations in an arbitrary dimension. This mapping becomes exact in the thermodynamic continuous time limit. The boson models can be written either in the form of a model of non-interacting bosons in a fluctuating auxiliary field or in the form of a superfield theory of interacting bosons. We show how one can study the latter version using perturbation theory. Using the developed diagrammatic technique we compared the first two orders of perturbation theory with the correspon…

相互作用玻色子系统中具有非对角长程序的精确本征态

Exact eigenstates with off-diagonal long-range order for interacting bosonic systems

本研究针对环形晶格中带最近邻相互作用的费米子与硬核玻色子模型，构建了共振相互作用下硬核玻色子模型的精确本征态，证明其在热力学极限下存在非对角长程序，还通过数值模拟分析了周期性边界条件对凝聚态动力学的影响。

Exact solutions of a one-dimensional mixture of spinor bosons and spinor fermions

The exact solutions of a one-dimensional mixture of spinor bosons and spinor fermions with $δ$-function interactions are studied. Some new sets of Bethe ansatz equations are obtained by using the graded nest quantum inverse scattering method. Many interesting features appear in the system. For example, the wave function has the $SU(2|2)$ supersymmetry. It is also found that the ground state of the system is partial polarized, where the fermions form a spin singlet state and the bosons are totally polarized. From the solution of Bethe ansatz equations, it is shown that all the momentum, spin an…

Off-Diagonal Long-Range Order Implies Vanishing Charge Gap

For a large class of quantum many-body systems with U(1) symmetry, we prove a general inequality that relates the (off-diagonal) long-range order with the charge gap. For a system of bosons or fermions on a lattice or in the continuum, the inequality implies that a ground state with off-diagonal long-range order inevitably has a vanishing charge gap, and hence is characterized by nonzero charge susceptibility. For a quantum spin system, the inequality implies that a ground state within a magnetization plateau cannot have transverse long-range order.

相互作用玻色子模型的精确基态：一种统一方法

Models of interacting bosons with exact ground states: a unified approach

本文提出一种统一方法，构造一类无阻挫相互作用玻色子哈密顿量，其精确基态由经典晶格气体权重决定，涵盖多种已知可解模型及新奇的量子基态。

玻色哈伯德模型的精确SU(N)对称性分解：一般玻色-费米映射与平带单重态簇态

Exact SU($N$) symmetry resolution of bosonic Hubbard models: general boson-fermion mappings and flat-band singlet-cluster states

研究利用豪对偶性实现SU(N)对称玻色哈伯德模型的精确对角化，得出三个结构结论并推导吸引型SU(N)玻色子的有限温度相图，展示无挫跳跃产生的单重态簇态。

Exactly-solvable system of one-dimensional trapped bosons with short and long-range interactions

We consider trapped bosons with contact interactions as well as Coulomb repulsion or gravitational attraction in one spatial dimension. The exact ground state energy and wave function are identified in closed form together with a rich phase diagram, unveiled by Monte Carlo methods, with crossovers between different regimes. A trapped McGuire quantum soliton describes the attractive case. Weak repulsion results in an incompressible Laughlin-like fluid with flat density, well reproduced by a Gross-Pitaevskii equation with long-range interactions. Higher repulsion induces Friedel oscillation and …