Related papers: Integrability from a single conservation law in qu…
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…
A bootstrap program is presented for algebraically solving the $R$-matrix of a generic integrable quantum spin chain from its Hamiltonian. The Yang-Baxter equation contains an infinite number of seemingly independent constraints on the…
A systematic method to construct the complete set of conserved quantities of the Haldane-Shastry type spin chains is proposed. The hidden relationship between the Yang-Baxter relation and the conservation laws of the long-range interacting…
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…
The integrability of a quantum many-body system, which is characterized by the presence or absence of local conserved quantities, drastically impacts the dynamics of isolated systems, including thermalization. Nevertheless, a rigorous and…
Using Reshetikhin's construction for multiparametric quantum algebras we obtain the associated multiparametric quantum spin chains. We show that under certain restrictions these models can be mapped to quantum spin chains with twisted…
There is a widespread perception that dynamical evolution of integrable systems should be simpler in a quantifiable sense than the evolution of generic systems, though demonstrating this relation between integrability and reduced complexity…
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…
In this contribution we review the theory of integrability of quantum systems in one spatial dimension. We introduce the basic concepts such as the Yang-Baxter equation, commuting currents, and the algebraic Bethe ansatz. Quite extensively…
Integrable quantum many-body systems host families of extensive conservation laws, some of which are fragile: even infinitesimal perturbations can qualitatively alter their dynamical constraints. Here we show that this fragility leaves a…
In integrable one-dimensional quantum systems an infinite set of local conserved quantities exists which can prevent a current from decaying completely. For cases like the spin current in the XXZ model at zero magnetic field or the charge…
In this paper we consider affine Toda systems defined on the half-plane and study the issue of integrability, i.e. the construction of higher-spin conserved currents in the presence of a boundary perturbation. First at the classical level…
We investigate conservation laws in the quantum mechanics of closed systems. We review an argument showing that exact decoherence implies the exact conservation of quantities that commute with the Hamiltonian including the total energy and…
We study S=1/2 quantum spin chains with shift-invariant and inversion-symmetric next-nearest-neighbor interaction, also known as zigzag spin chains. We completely classify the integrability and non-integrability of the above class of spin…
High-temperature spin transport in integrable quantum spin chains exhibits a rich dynamical phase diagram, including ballistic, superdiffusive, and diffusive regimes. While integrability is known to survive in static and periodically driven…
We show that the one dimensional, critical transverse field Ising model is Yang-Baxter integrable. This is done by constructing commuting transfer matrices built out of a $R$-matrix satisfying the Yang-Baxter equation with additive spectral…
In this paper we introduce a new property of two-dimensional integrable systems -- existence of infinitely many local three-dimensional conservation laws for pairs of integrable two-dimensional commuting flows. Infinitely many…
Quantum many-body states that frequently appear in physics often obey an entropy scaling law, meaning that an entanglement entropy of a subsystem can be expressed as a sum of terms that scale linearly with its volume and area, plus a…
In this paper, we address the problem of Yang-Baxter integrability of doubled quantum circuit of qubits (spins 1/2) with open boundary conditions where the two circuit replicas are only coupled at the left or right boundary. We investigate…
Conservation laws serve as the hallmark of integrability. The absence of conserved charges typically implies that the model is nonintegrable. The recently proposed Fredkin spin chain exhibits rich structures, and its ground state is…