Yuji Nozawa, Kouhei Fukai
We present a rigorous explicit expression for an extensive number of local conserved quantities in the XYZ spin-1/2 chain with general coupling constants. All the coefficients of operators in each local conserved quantity are calculated. We also confirm that our result can be applied to the case of the XXZ chain with a magnetic field in the z-axis direction.
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Matrix product operator representations for the local conserved quantities of the spin-$1/2$ XYZ chain
本文提出 spin-$1/2$ XYZ 链局部守恒量的 MPO 表示，揭示系数为 Catalan 数的多项式推广，并获得新的简单 Lax 算子。
Proof of the absence of local conserved quantities in the XYZ chain with a magnetic field
本文严格证明了带磁场的 spin-1/2 XYZ 链不存在局部守恒量，其任何非平凡守恒量必须至少覆盖半个系统，从而确立了具体模型中局部守恒量缺失的严格可证明性。
The $S=\frac{1}{2}$ XY and XYZ models on the two or higher dimensional hypercubic lattice do not possess nontrivial local conserved quantities
研究S=1/2量子自旋系统在二维或更高维超立方晶格上的非平凡局部守恒量问题，证明其仅存在平凡守恒量，表明模型非可积。
Current mean values in the XYZ model
针对缺乏全局U(1)对称性的可积自旋链XYZ模型，研究其守恒量流动的电流算符，推导了有限体积周期边界条件下任意本征态的电流平均值精确结果，为其输运性质的广义流体动力学研究提供基础。
Initially, we derive a nonlinear integral equation for the vacuum counting function of the spin 1/2-XYZ chain in the {\it disordered regime}, thus paralleling similar results by Klümper \cite{KLU}, achieved through a different technique in the {\it antiferroelectric regime}. In terms of the counting function we obtain the usual physical quantities, like the energy and the transfer matrix (eigenvalues). Then, we introduce a double scaling limit which appears to describe the sine-Gordon theory on cylindrical geometry, so generalising famous results in the plane by Luther \cite{LUT} and Johnson e…
Exact physical quantities of the XYZ spin chain in the thermodynamic limit
本文利用 $T-Q$ 关系、Bethe 根结构及相关多项式零点分布，求解周期或扭曲边界 XYZ 自旋链在热力学极限下的表面能与激发能，并通过 DMRG 验证。
We conjecture exact and simple formulas for physical quantities in two quantum chains. A classic result of this type is Onsager, Kaufman and Yang's formula for the spontaneous magnetization in the Ising model, subsequently generalized to the chiral Potts models. We conjecture that analogous results occur in the XYZ chain when the couplings obey J_xJ_y + J_yJ_z + J_x J_z=0, and in a related fermion chain with strong interactions and supersymmetry. We find exact formulas for the magnetization and gap in the former, and the staggered density in the latter, by exploiting the fact that certain quan…
XYZ integrability the easy way
本文通过矩阵乘积算符显式构造守恒荷，以更简单的方式证明了 XYZ 自旋链的可积性，并推广到任意边界磁场和杂质相互作用，得到有能隙体态的 Kondo 问题可积推广。
Proof of completeness of the local conserved quantities in the one-dimensional Hubbard model
本文严格证明了一维Hubbard模型中局部守恒量在每个局域性下唯一确定（至多差低阶项），并得出这些守恒量可由转移矩阵展开完全穷尽的结论。
We present the explicit expressions for the matrix product operator (MPO) representation for the local conserved quantities of the Heisenberg chain. The bond dimension of the MPO grows linearly with the locality of the charges. The MPO has more simple form than the local charges themselves, and their Catalan tree patterns naturally emerge from the matrix products. The MPO representation of local conserved quantities is generalized to the integrable $\mathrm{SU}(N)$ invariant spin chain.
Recently found spin-flip non-invariant (SFNI) conserved quantities play important roles in discussing nonequilibrium physics of the XXZ model. The representative examples are the generalized Gibbs ensemble (GGE) and the ballistic transport of the spin current. In spite of big progress in understanding nonequilibrium physics of integrable systems, the general framework to determine a minimal complete set of conserved quantities which describes the long-time steady state has not yet been found. This paper shows that the GGE of the gapless XXZ model consists of functionally independent conserved …
Energy transport can be influenced by the presence of other conserved quantities. We consider here diffusive systems where energy and the other conserved quantities evolve macroscopically on the same diffusive space-time scale. In these situations the Fourier law depends also from the gradient of the other conserved quantities. The rotor chain is a classical example of such systems, where energy and angular momentum are conserved. We review here some recent mathematical results about diffusive transport of energy and other conserved quantities, in particular for systems where the bulk Hamilton…
All Local Conserved Quantities of the One-Dimensional Hubbard Model
本文给出了一维Hubbard模型所有局域守恒量的精确表达式，确定了算符基并推导了高阶系数的递推方程，证明了所得局域荷的完备性。
Integrability of the XXZ model induces an extensive number of conserved quantities. In this paper we give a closed form expression for the series of local conserved charges of the XXZ model on a closed chain with or without a twist. We prove that each element of the series commutes with the Hamiltonian.
Conserved quantities in a bosonic tight-binding chain with non-Hermitian quartic terms
本文研究非厄米玻色子晶格中的局域守恒量，通过傅里叶变换和三角恒等式推导出相互对易的守恒量族，并扩展到多种相互作用形式，提供统一构造框架。
Absence of nontrivial local conserved quantities in the quantum compass model on the square lattice
本文通过扩展Shiraishi的方法，证明正方形晶格上的量子磁针模型除了哈密顿量本身外，不存在其他局域守恒量。
Proof of the absence of local conserved quantities in the Holstein model
本文证明了Holstein模型中除了哈密顿量和总费米子数算符外没有非平凡的局部守恒量，扩展了非积分性证明的范围到混合不同统计性质粒子的系统。
Proof of the absence of local conserved quantities in general spin-1/2 chains with symmetric nearest-neighbor interaction
该研究严格证明了除已知可积系统外，具有对称最近邻相互作用的一般自旋-1/2链无额外非平凡局域守恒量，排除了未发现可积系统及有限守恒量中间系统的可能，并厘清了非可积系统的短支撑守恒量。
Absence of nontrivial local conserved quantities in the Hubbard model on the two or higher dimensional hypercubic lattice
本文扩展Shiraishi策略，证明二维及以上超立方晶格Hubbard模型无局域守恒量，暗示其不可积，为首次推广至费米子模型，证明需三步且部分确定一维守恒量。
Rigorous Test for Quantum Integrability and Nonintegrability
针对量子多体系统可积性判定难题，本文提出有限范围相互作用量子自旋系统可积性与不可积性的严格可证检验方法，简化现有不可积性证明并首次证明多种模型不可积性，部分解决相关猜想且支持算法验证一维系统不可积性。
Absence of hidden analytic conserved quantities in harmonically confined rods
研究一维谐振子势阱中等长硬杆系统，通过限制守恒量形式，排除解析的额外隐藏守恒量，证明其依赖已知守恒量，特殊情况有更多解析守恒量，阐明守恒量结构并推动方法应用。
Absence of nontrivial local conserved quantities in a class of $U(1)$-symmetric spin-1 chains
该研究证明一类特殊U(1)对称自旋1链及周期Motzkin链不存在特定范围的局域守恒量，明确其连续对称性破缺源于无挫败结构而非守恒序参量。
We consider the isotropic spin-1/2 Heisenberg spin chain weakly perturbed by a local translationally- and SU(2)-invariant perturbation. Starting from the local integrals of motion of the unperturbed model, we modify them in order to obtain quasi-conserved integrals of motion (charges) for the perturbed model. Such quasi-conserved quantities are believed to be responsible for the existence of the prethermalization phase at intermediate timescales. We find that for a sufficiently local perturbation only the first few integrals of motion can be promoted to the quasi-conserved charges, whereas hig…
In statistical mechanics, a small system exchanges conserved quantities---heat, particles, electric charge, etc.---with a bath. The small system thermalizes to the canonical ensemble, or the grand canonical ensemble, etc., depending on the conserved quantities. The conserved quantities are represented by operators usually assumed to commute with each other. This assumption was removed within quantum-information-theoretic (QI-theoretic) thermodynamics recently. The small system's long-time state was dubbed ``the non-Abelian thermal state (NATS).'' We propose an experimental protocol for observi…
We outline a procedure for counting and identifying a complete set of local and quasilocal conserved operators in integrable lattice systems. The method yields a systematic generation of all independent, conserved quasilocal operators related to time-average of local operators with a support on up to M consecutive sites. As an example we study the anisotropic Heisenberg spin-1/2 chain and show that the number of independent conserved operators grows linearly with M. Besides the known local operators there exist novel quasilocal conserved quantities in all the parity sectors. The existence of q…
Emergent conserved quantities via irreversibility
本文研究了不可逆反应如何导致CRN和马尔可夫链中涌现的守恒律和断裂循环，提出通过'共生产指数'描述线性依赖电流，解决了非整数守恒律的困境。
We introduce a class of one dimensional deterministic models of energy-volume conserving interfaces. Numerical simulations show that these dynamics are genuinely super-diffusive. We then modify the dynamics by adding a conservative stochastic noise so that it becomes ergodic. System of conservation laws are derived as hydrodynamic limits of the modified dynamics. Numerical evidence shows these models are still super-diffusive. This is proven rigorously for harmonic potentials.
Quantum Dynamical Tunneling Breaks Classical Conserved Quantities
针对伪可积系统，本文证明量子动力学隧穿可破坏经典守恒量，并通过大规模本征态数值计算与随机矩阵模型揭示其普适统计及轨道叠加特征。
The $XYZ$ antiferromagnetic spin-$1/2$ chain with alternation of the exchange and anisotropy couplings in the presence of uniform and staggered axial magnetic fields is studied. The analysis is done using the effective quadratic fermionic Hamiltonian resulting from the Hartee-Fock approximation. Combining the exact and the mean-field methods, the local and string order parameters on the ground-state phase diagram of the model are identified and calculated. We found a topological phase with oscillating string order with a period of four lattice spacings, not reported before for this model. A de…
Conserved Quantities in Models of Classical Chaos
本文针对经典混沌模型中混沌与守恒量的关联问题，以无穷温度Heisenberg自旋链和随机介质中定向聚合物为对象，通过能量图景与磁化强度的类比开展研究，发现混沌与守恒量耦合会引发扰动轮廓转变，证实扩散守恒量可主导经典系统混沌演化。
Proof of absence of local conserved quantities in two- and higher-dimensional quantum Ising models
该研究将一维系统局域守恒量不存在性的证明技术推广，证明二维及以上超立方晶格带横向、纵向场的量子Ising模型（含梯状系统）除哈密顿量外无弱局域守恒量。
One-dimensional systems with short-range interactions cannot exhibit a long-range order at nonzero temperature. However, there are some particular one-dimensional models, such as the Ising-Heisenberg spin models with a variety of lattice geometries, which exhibit unexpected behavior similar to the discontinuous or continuous temperature-driven phase transition. Although these pseudo-transitions are not true temperature-driven transitions showing only abrupt changes or sharp peaks in thermodynamic quantities, they may be confused while interpreting experimental data. Here we consider the spin-$…
Proof of absence of local conserved quantities in the mixed-field Ising chain
本文严格证明了混合场伊辛链在非零耦合下除平凡量外不存在支撑集不超过系统一半的局域守恒量，并给出了周期与开放边界条件下的证明，为严格证明自旋模型非可积性提供了第二个实例。
We consider the diamond chain with S=1/2 XYZ vertical dimers which interact with the intermediate sites via the interaction of the Ising type. We also suppose all four spins form the diamond-shaped plaquette to have different g-factors. The non-uniform g-factors within the quantum spin dimer as well as the XY-anisotropy of the exchange interaction lead to the non-conserving magnetization for the chain. We analyze the effects of non-conserving magnetization as well as the effects of the appearance of negative g-factors among the spins from the unit cell. A number of unusual frustrated states fo…
Although one-dimensional systems that exhibit translational symmetry are generally believed to exhibit anomalous heat transport, previous work has shown that the model of coupled rotators on a one-dimensional lattice constitute a possible exception. We investigate the equilibrium spatiotemporal correlations of energy and momentum of the rotator model, and find that both these fields diffuse normally. The normal diffusion is explained within the framework of stochastic hydrodynamics by observing that the angle variables do not constitute a conserved field, which leads to the absence of long-wav…
The relaxation of out-of-time-ordered correlators (OTOCs) has been studied as a mean to characterize the scrambling properties of a quantum system. We show that the presence of local conserved quantities typically results in, at the fastest, an algebraic relaxation of the OTOC provided (i) the dynamics is local and (ii) the system follows the eigenstate thermalization hypothesis. Our result relies on the algebraic scaling of the infinite-time value of OTOCs with system size, which is typical in thermalizing systems with local conserved quantities, and on the existence of finite speed of propag…
The out-of-equilibrium dynamics of quantum systems is one of the most fascinating problems in physics, with outstanding open questions on issues such as relaxation to equilibrium. An area of particular interest concerns few-body systems, where quantum and thermal fluctuations are expected to be especially relevant. In this contribution, we present numerical results demonstrating the impact of conserved quantities (or 'charges') in the outcomes of out-of-equilibrium measurements starting from realistic equilibrium states on a few-body system implementing the Dicke model.
We show that the subregion entanglement Hamiltonians of excited eigenstates of a quantum many-body system are approximately linear combinations of subregionally (quasi)local approximate conserved quantities, with relative commutation errors $\mathcal{O}\left(\frac{\text{subregion boundary area}}{\text{subregion volume}}\right)$. By diagonalizing an entanglement Hamiltonian superdensity matrix (EHSM) for an ensemble of eigenstates, we can obtain these conserved quantities as the EHSM eigen-operators with nonzero eigenvalues. For free fermions, we find the number of nonzero EHSM eigenvalues is c…
For every conserved quantity written as a sum of local terms, there exists a corresponding current operator that satisfies the continuity equation. The expectation values of current operators at equilibrium define the persistent currents that characterize spontaneous flows in the system. In this work, we consider quantum many-body systems on a finite one-dimensional lattice and discuss the scaling of the persistent currents as a function of the system size. We show that, when the conserved quantities are given as the Noether charges associated with internal symmetries or the Hamiltonian itself…
Iterative construction of conserved quantities in dissipative nearly integrable systems
针对耗散近可积系统缺乏精确解析方法的挑战，提出一种迭代方案，利用破坏可积性的微扰确定主导守恒量，以实现高效的截断广义Gibbs系综描述，并为热力学大系统计算和构造未知守恒量提供新途径。
We numerically simulate mechanically stable packings of soft-core, frictionless, bidisperse disks in two dimensions, above the jamming packing fraction $ϕ_J$. For configurations with a fixed isotropic global stress tensor, we compute the averages, variances, and correlations of conserved quantities (stress $Γ_{\cal C}$, force-tile area $A_{\cal C}$, Voronoi volume $V_{\cal C}$, number of particles $N_{\cal C}$, and number of small particles $N_{s{\cal C}}$) on compact subclusters of particles ${\cal C}$, as a function of the cluster size and the global system stress. We find several significan…
Conserved quantities enable the quantum Mpemba effect in weakly open systems
研究弱开放多体量子系统中，初始距离更远的状态更快弛豫到稳态的条件，发现哈密顿量的守恒量数量起关键作用：仅当哈密顿量与其他广延算符对易或可积时，姆潘巴效应才可能发生。
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