Integrability and PT-symmetry of $N$-Body Systems with Spin-coupling $δ$-Interactions
Shao-Ming Fei
研究了玻色子和费米子多体系统中与自旋相关的$δ$相互作用的PT对称边界条件和相应的可积性。详细讨论了自旋为1/2的粒子系统的能谱和束缚态。
We study the PT-symmetric boundary conditions for "spin"-related $δ$-interactions and the corresponding integrability for both bosonic and fermionic many-body systems. The spectra and bound states are discussed in detail for spin-1/2 particle systems.
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On Integrability of Many-Body Problems with Point Interactions
本文研究了具有一般点相互作用的一维量子力学多体系统的可积性，并给出了描述这种相互作用的边界条件，这些边界条件可以独立于粒子的自旋态，也可以依赖于粒子的自旋态。给出了相应的Bethe平衡解、束缚态和散射矩阵。讨论了与自旋相关的特殊边界条件对应的Hamilton算子。
Restoring integrability in one-dimensional quantum gases by two-particle correlations
我们发现，热化和局部三体弹性相互作用所造成的一维Lieb-Liniger模型的可积性的崩溃是抑制成对的量子关联时，接近强关联制度。如果相对动量$k$与两体耦合常数$c$相比很小，则三粒子散射态被抑制因子$(k/c)^{12}$。这表明，在一维量子系统中，不是两体碰撞的冻结，而是强量子关联确保了可积性。
On Integrability and Pseudo-Hermitian Systems with Spin-Coupling Point Interactions
研究了具有一般自旋耦合点相互作用的赝厄米系统，给出了PT对称系统相应边界条件的系统描述。研究了具有PT对称接触相互作用的玻色子和费米子多体系统的相应可积性。
From integrability to many-body quantum chaos through a Markovian bath
本文研究耦合马尔可夫浴的q体SYK模型，发现合适条件下环境可诱导多体量子混沌，为量子多体系统scrambling的调控提供了新途径。
Fragmented eigenstate thermalization versus robust integrability in long-range models
研究长程模型中积分性稳定性，揭示非广泛、广泛单体和广泛双体扰动对热化的影响，提出基于对称性的框架解释积分性稳定性。
PT-symmetry and Integrability
我们简要地解释了一些简单的论点的基础上的伪厄米性，超对称性和PT对称性，解释了一些非厄米哈密顿谱的现实。随后，我们利用PT对称性作为指导原则，构造了一些可积系统的形变，Calogero-Moser-Sutherland模型和Korteweg deVries方程.这些模型的一些性质进行了讨论。
Identifying quantum many-body integrability and chaos using eigenstates trace distances
本文提出基于本征态最近邻子系统迹距离的新指示器，用于识别量子多体可积性与混沌，并在多种典型模型中验证其可靠性，弥补了能级间距统计等现有方法的不足。
On the emergence of quantum many-body chaos for tunably-broken integrability
通过可调参数破坏可积性，在自由费米子电路中掺杂可积性破缺门，利用OTOC揭示从早期可积行为到晚期混沌的微观机制，并给出特征时空尺度及混沌特性对破缺参数的依赖。
There is developed a current algebra representation scheme for reconstructing algebraically factorized quantum Hamiltonian and symmetry operators in the Fock type space and its application to quantum Hamiltonian and symmetry operators in case of quantum integrable spatially many- and one-dimensional dynamical systems. As examples, we have studied in detail the factorized structure of Hamiltonian operators, describing such quantum integrable spatially many- and one-dimensional models as generalized oscillatory, Calogero-Sutherland, Coulomb type and nonlinear Schrödinger dynamical systems of spi…
Integrable quantum systems of finite size are generically robust against weak enough integrability-breaking perturbations, but become quantum chaotic and thermalizing if the integrability-breaking is strong enough. We argue that the onset of quantum chaos can be described as a Fock-space delocalization process, with the eigenstates of the integrable system being taken as the "Fock states". The integrability-breaking perturbation introduces hopping in this Fock space, and chaos sets in when this hopping delocalizes the many-body eigenstates in this space. Depending on the range of the dominant …
Uncovering Local Integrability in Quantum Many-Body Dynamics
本文利用最多124个可编程量子比特研究周期驱动自旋晶格，通过重构隐藏的局域运动积分算符，揭示无序诱导局域化区域中的可积动力学。
Quantum Quenches, Thermalization and Many-Body Localization
我们推测，强关联量子系统中量子猝灭后的热化与准粒子空间中的多体离域密切相关。在各向异性海森堡自旋链中，用不同类型的可积性破缺项来检验这种情况。我们首先通过分析能级间距统计和系统本征态的参与率倒数来量化可积性的偏差。然后，我们专注于热化，通过研究各向异性参数突然淬火后的动力学。我们的数值模拟清楚地支持该猜想，只要可积性破缺项均匀地作用在准粒子空间上，以这种方式诱导遍历所有相关的希尔伯特空间。
Transport and integrability-breaking in non-Hermitian many-body quantum systems
该研究针对非厄米开放量子系统的非幺正动力学问题，推广了线性响应关联函数，提出用动力学量子典型性高效计算，并结合XXZ链微扰模型与复能谱统计分析输运与可积性破缺。
Two mass-imbalanced atoms in a hard-wall trap: Deep learning integrability of many-body systems
本文通过能级统计和深度学习波函数研究硬壁阱中质量不平衡两体系统的可积性，利用卷积神经网络高精度识别可积转变点，并发现新的可积质量比1/3。
Integrability versus chaos in the steady state of many-body open quantum systems
本文研究开放多体量子系统中 Liouvillian 与稳态可积性的区别，提出结合能级间距统计、推广本征态热化假说及 Pauli 字符串算符尺寸分布来判别稳态混沌。
Partial symmetries are described by generalized group structures known as symmetric inverse semigroups. We use the algebras arising from these structures to realize supersymmetry in (0+1) dimensions and to build many-body quantum systems on a chain. This construction consists in associating appropriate supercharges to chain sites, in analogy to what is done in spin chains. For simple enough choices of supercharges, we show that the resulting states have a finite non-zero Witten index, which is invariant under perturbations, therefore defining supersymmetric phases of matter protected by the in…
This contributed conference proceeding reviews some results about a system of a few identical particles with spin trapped in one-dimensional potentials and experiencing two-body interactions. The focus is on how symmetry, integrability, and solvability depend on the trap shape, two-body interaction, the number of particles, and the number of spin components. A series of comments are presented that characterize the minimal symmetries possible for a composite system constructed from interacting single particles, with special focus on the contact interaction. For five and more particles with inte…
Exactly solvable dynamics and signatures of integrability in an infinite-range many-body Floquet spin system
本文研究无限范围伊辛相互作用量子比特在周期性磁场脉冲下的可积性，解析求解N=5至11情形并基于数值证据对N>11情形提出量子可积性猜想。
One-dimensional Bose chemistry: effects of non-integrability
分析了超冷全同玻色原子在紧圆柱约束下的三体碰撞。用两通道零程相互作用描述了两体碰撞中的费什巴赫共振。在三体问题中取消了封闭通道，将相互作用简化为一个具有能量依赖强度的单通道零程相互作用。与能量无关的相关问题（Lieb-Liniger-McGuire模型）有一个精确的解，并且禁止所有的化学过程，如三原子缔合和硅藻解离，以及原子-硅藻碰撞中的反射。共振的情况下进行了分析的Faddeev-Lovelace方程的数值解。结果表明，随着Lieb-Liniger-McGuire模型的内部对称性的提高，反射和化学反应变得允许，并且可以在实验中观察到。
Integrability of a family of clean SYK models from the critical Ising chain
本研究通过推导清洁SYK模型族的R矩阵，揭示了其与临界ISING链之间的深刻联系，展示了可积性与量子混沌的关联。
Interacting quantum systems in the chaotic domain are at the core of various ongoing studies of many-body physics, ranging from the scrambling of quantum information to the onset of thermalization. We propose a minimum model for chaos that can be experimentally realized with cold atoms trapped in one-dimensional multi-well potentials. We explore the emergence of chaos as the number of particles is increased, starting with as few as two, and as the number of wells is increased, ranging from a double well to a multi-well Kronig-Penney-like system. In this way, we illuminate the narrow boundary b…
In the time evolution of isolated quantum systems out of equilibrium, local observables generally relax to a long-time asymptotic value, governed by the expectation values (diagonal matrix elements) of the corresponding operator in the eigenstates of the system. The temporal fluctuations around this value, response to further perturbations, and the relaxation toward this asymptotic value, are all determined by the off-diagonal matrix elements. Motivated by this non-equilibrium role, we present generic statistical properties of off-diagonal matrix elements of local observables in two families o…
Symmetry and integrability in the anyon-Hubbard model
本文分析了有限长度任意子-哈伯德模型的对称性、可积性及其导致的简并，揭示了对称类随系统尺寸、粒子数和边界条件的切换，并发现周期性边界下两个任意子可积而开放边界下不可积。
Recently, we constructed the first-principle derivation of the holographic dual of N=4 SYM in the double-scaled $γ$-deformed limit directly from the CFT side. The dual fishchain model is a novel integrable chain of particles in AdS5. It can be viewed as a discretized string and revives earlier string-bit approaches. The original derivation was restricted to the operators built out of one of two types of scalar fields. In this paper, we extend our results to the general operators having any number of scalars of both types, except for a very special case when their numbers are equal. Interesting…
Generalized Spin Helix States as Quantum Many-Body Scars in Partially Integrable Models
提出一种通用机制构建具有任意大局部希尔伯特空间维度的部分可积模型，通过在Temperley-Lieb代数生成元组成的可积自旋链中引入可积性破缺项，在非可积子空间中识别出广义自旋螺旋态作为精确量子多体疤痕，揭示了可积性与多体疤痕的联系。
Entangling Power: A Probe of Symmetry and Integrability in Quantum Many-Body Systems
本文研究了量子多体系统中纠缠功率作为对称性和可积性探针的作用，通过计算各向异性Heisenberg链在不同模型和有限大小系统中的平均纠缠功率，以及在热力学极限下两磁子S矩阵的纠缠功率，揭示了纠缠极值在对称性增强点的特征。
Comment on "Integrability of the Rabi model"
在最近的一封信中，Braak提出拉比模型的正则谱是由超越函数$G_\pm(x)$的零点给出的。（3）-（5）），并强调了离散$\mathbb{Z}_2$ -对称性或奇偶性在确定$G_\pm(x)$中的作用。相反，我们在这里表明，人们可以定义一个超越函数$F_0(x)$，并得到拉比模型的正则谱作为$F_0(x)$的零点（见图1），而不必利用模型的基本$\mathbb{Z}_2$对称性。
We systematically investigate scrambling (or delocalizing) processes of quantum information encoded in quantum many-body systems by using numerical exact diagonalization. As a measure of scrambling, we adopt the tripartite mutual information (TMI) that becomes negative when quantum information is delocalized. We clarify that scrambling is an independent property of integrability of Hamiltonians; TMI can be negative or positive for both integrable and non-integrable systems. This implies that scrambling is a separate concept from conventional quantum chaos characterized by non-integrability. Fu…
Describing dynamics of quantum many-body systems is a formidable challenge due to rapid generation of quantum entanglement between remote degrees of freedom. A promising approach to tackle this challenge, which has been proposed recently, is to characterize the quantum dynamics of a many-body system and its properties as a bath via the Feynman-Vernon influence matrix (IM), which is an operator in the space of time trajectories of local degrees of freedom. Physical understanding of the general scaling of the IM's temporal entanglement and its relation to basic dynamical properties is highly inc…
Signatures of Integrability and Exactly Solvable Dynamics in an Infinite-Range Many-Body Floquet Spin System
该研究将无限程Ising相互作用的N自旋Floquet模型的相互作用强度推广为J，证明J=1/2时仅偶数量子比特系统存在量子可积性，解析求解小系统并通过数值证据推测大偶数N系统的可积性，揭示纠缠的多体特性并讨论实验验证方案。
We show that the onset of quantum chaos at infinite temperature in two many-body one-dimensional lattice models, the perturbed spin-1/2 XXZ and Anderson models, is characterized by universal behavior. Specifically, we show that the onset of quantum chaos is marked by maxima of the typical fidelity susceptibilities that scale with the square of the inverse average level spacing, saturating their upper bound, and that the strength of the integrability- or localization-breaking perturbation at these maxima decreases with increasing system size. We also show that the spectral function below the ``…
Systematic Construction of Kramers-Wannier-like Dualities in Quantum Lattice Models from Integrability
本文将临界横场 Ising 模型中的 Kramers-Wannier 对偶性推广到由可积性导出的广泛量子晶格模型，并给出可系统计算的对偶算子显式表达式。
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