arXiv subjects

Mizuki Sanatani

Publications and source records attributed to Mizuki Sanatani.

8 recordsLinked to original sources

arXiv2026

Proof of the absence of local conserved quantities in the Holstein model

Absence of local conserved quantities, or nonintegrability, is often assumed when discussing various phenomena in quantum many-body systems, such as thermalization and transport. However, no concrete proof of this property is known in electron--phonon coupled systems, a typical setting for condensed matter physics. In this paper, we show that the one-dimensional Holstein model has no nontrivial local conserved quantities other than the Hamiltonian itself and the total fermion number operator. We further show that the absence of nontrivial local conserved quantities also holds for the more general Holstein--Hubbard model. We also establish the absence of nontrivial local conserved quantities in these models on higher-dimensional hypercubic lattices. Our result has accomplished an advance in nonintegrability proofs by expanding their scope to systems in which particles with different statistical properties are mixed.

cond-mat.stat-mech↗

arXiv2026

A Simple Necessary and Sufficient Condition for Yang--Baxter Integrability

Quantum integrability is a cornerstone of the exact theory of interacting quantum spin chains. In its standard formulation, however, one starts from R-matrices satisfying the Yang--Baxter equation, rather than from the Hamiltonian itself. It has therefore remained unclear how Yang--Baxter solvability can be characterized directly at the Hamiltonian level, and how it is related to the existence of local conservation laws. Here we prove that, in a broad standard setting, the Reshetikhin condition is not only necessary but also sufficient for Yang--Baxter integrability, thereby reducing the hidden algebraic structure of integrability to a Hamiltonian-level conservation law. Since the Reshetikhin condition is equivalent to conservation of the total energy current, this Hamiltonian-level criterion is also experimentally accessible. This result establishes a quantum counterpart of the Liouville--Arnold theorem for isotropic spin chains, stating that Yang--Baxter solvability is equivalent to an infinite hierarchy of local conserved quantities. Our result also simplifies substantially the search for integrable spin chains by replacing the search for R-matrices with a direct criterion on local Hamiltonians.

cond-mat.stat-mech↗

arXiv2026

Violating the All-or-Nothing Picture of Local Charges in Non-Hermitian Bosonic Chains

We present explicit counterexamples to a widespread empirical expectation that local commuting charges display all-or-nothing behavior. In the class of bosonic chains with symmetric nearest-neighbor hopping and arbitrary on-site terms (including non-Hermitian terms), we exhibit systems that possess k-local charges for some but not all k. Concretely, we construct non-Hermitian models with a 3-local charge but no other nontrivial local charges and models with k-local charges for all k except k = 4. These results show that the Grabowski--Mathieu integrability test based on 3-local charges is not universally applicable. We further give necessary and sufficient conditions for the existence of k-local charges in this class, yielding an exhaustive classification and uncovering additional integrable models.

cond-mat.stat-mech↗

arXiv2025

Absence of nontrivial local conserved quantities in the spin-1 bilinear-biquadratic chain and its anisotropic extensions

We provide a complete classification of the integrability and nonintegrability of the spin-1 bilinear-biquadratic model with a uniaxial anisotropic field, which includes the Heisenberg model and the Affleck-Kennedy-Lieb-Tasaki model. It is rigorously shown that, within this class, the only integrable systems are those that have been solved by the Bethe ansatz method, and that all other systems are nonintegrable, in the sense that they do not have nontrivial local conserved quantities. Here, "nontrivial" excludes quantities like the Hamiltonian or the total magnetization, and "local" refers to sums of operators that act only on sites within a finite distance. This result establishes the nonintegrability of the Affleck-Kennedy-Lieb-Tasaki model and, consequently, demonstrates that the quantum many-body scars observed in this model emerge independently of any conservation laws of local quantities. Furthermore, we extend the proof of nonintegrability to more general spin-1 models that encompass anisotropic extensions of the bilinear-biquadratic Hamiltonian and completely classify the integrability of generic Hamiltonians that possess translational symmetry, U(1) symmetry, time-reversal symmetry, and spin-flip symmetry. Our result accomplishes a breakthrough in nonintegrability proofs by expanding their scope to spin-1 systems.

cond-mat.stat-mech↗

arXiv2025

Dichotomy theorem separating complete integrability and non-integrability of isotropic spin chains

We investigate the integrability and non-integrability of isotropic spin chains with nearest-neighbor interaction with general spin $S$ in terms of the presence or absence of local conserved quantities. We prove a dichotomy theorem that whether a single quantity is zero or not sharply separates two scenarios: (i) this system has $k$-local conserved quantities for all $k$ (completely integrable), or (ii) this system has no nontrivial local conserved quantity (non-integrable). This result excludes the possibility of an intermediate system with some but not all local conserved quantities, which solves in the affirmative the Grabowski-Mathieu conjecture. This theorem also serves as a complete classification of integrability and non-integrability for $S\leq 13.5$, suggesting that all the integrable models are in the scope of the Yang-Baxter equation.

cond-mat.stat-mech↗

arXiv2024

Proof of the absence of local conserved quantities in general spin-1/2 chains with symmetric nearest-neighbor interaction

We provide a rigorous proof of the absence of nontrivial local conserved quantities in all spin-1/2 chains with symmetric nearest-neighbor interaction, except for known integrable systems. This result shows that there are no further integrable system that awaits to be discovered. Our finding also implies that there is no intermediate systems with a finite number of nontrivial local conserved quantities. In addition, we clarify all short-support conserved quantities in non-integrable systems, which we need to take into account in analyses of thermalization and level statistics.

cond-mat.stat-mech↗

arXiv2024

Complete Classification of Integrability and Non-integrability for Spin-1/2 Chain with Symmetric Nearest-Neighbor Interaction

General spin-1/2 chains with symmetric nearest-neighbor interaction are studied. We rigorously prove that all spin models in this class, except for known integrable systems, are non-integrable in the sense that they possess no nontrivial local conserved quantities. This result confirms that there are no missing integrable systems, i.e., integrable systems in this class are exactly those that are already known. In addition, this result excludes the possibility of intermediate systems which have a finite number of nontrivial local conserved quantities. Our findings support the expectation that integrable systems are exceptional in quantum many-body systems and most systems are non-integrable.

cond-mat.stat-mech↗

arXiv2024

Proof of avoidability of the quantum first-order transition in transverse magnetization in quantum annealing of finite-dimensional spin glasses

It is rigorously shown that an appropriate quantum annealing for any finite-dimensional spin system has no quantum first-order transition in transverse magnetization. This result can be applied to finite-dimensional spin-glass systems, where the ground state search problem is known to be hard to solve. Consequently, it is strongly suggested that the quantum first-order transition in transverse magnetization is not fatal to the difficulty of combinatorial optimization problems in quantum annealing.

quant-ph↗