39 problems

A time-dependent quantum Hamiltonian is called quantum integrable when it possesses nontrivial parameter-dependent commuting partners. Quantum-integrability necessity conjecture. Q…

Let a quantum chain have translation-invariant nearest-neighbor interactions and periodic boundary conditions. A conserved charge is independent if it is not generated by the Hamil…

The claim concerns a particular class of integrable systems, including closed Toda chains, elliptic Calogero–Moser systems, and their relativistic versions, together with observabl…

Let $H$ be a quantum Hamiltonian whose classical counterpart is integrable, and consider the point spectrum of $H$ (or its normalized energy differences). Berry's conjecture. The p…

Let $h$ be a local Hamiltonian density, and let the Reshetikhin condition denote the lowest-order nontrivial constraint obtained by expanding the Yang–Baxter equation around a regu…

Let a six-dimensional Chern–Simons theory have surface defects supporting algebras of local operators, and let the intersection of surface operators produce the mixed coproduct … w…

In six-dimensional holomorphic Chern–Simons theory on twistor space, consider intersecting surface operators whose correlation function defines a local operator. A rational, spectr…

Let the finite spin-$1/2$ Heisenberg chain have Bethe roots and a ground state, and let their algebraic degrees denote the degrees of the corresponding algebraic numbers over the r…

RG-trajectory conjecture. Any quantum integrable model with constant coupling strengths should retain integrability when its coupling strengths are made time dependent, provided th…

For an integrable Hamiltonian with time-dependent interaction strengths, let the interaction strengths evolve along temporal trajectories coinciding with the renormalization-group…

For a short-range interacting quantum spin chain, let the Reshetikhin condition be the local condition on the Hamiltonian terms introduced in the paper, and let integrability in th…

A quantum spin system is integrable when it possesses local conserved quantities. In a one-dimensional system with translational symmetry and nearest-neighbor interactions, a conse…

Let $H_i(t)$, for $i=1,\ldots,n$, be mutually commuting Hamiltonians associated with a Landau-Zener model, and let $\Psi(\vec{z})$ be a wavefunction depending on multi-time variabl…

Consider the spin-$\frac{1}{2}$ XXX chain weakly perturbed by an isotropic next-to-nearest-neighbor exchange interaction. The unperturbed XXX chain is integrable and has infinitely…

Consider the spin-$\frac{1}{2}$ isotropic Heisenberg chain (the XXX model) weakly perturbed by an isotropic next-to-nearest-neighbor exchange interaction. A quasiconserved charge i…

The two-step Temperley–Lieb algebraic Floquet protocol has evolution operators generated by two time steps $T_1$ and $T_2$, with $\beta$ denoting the Temperley–Lieb parameter. Inte…

Let $\mathfrak A_{\mathrm{ql}}$ be the algebra of quasilocal operators and let…

R-matrix conjecture. An intertwining R matrix $\mathsf{R}^{\rm FM}_{(a,b)(c,d)}(z,w,\theta)$ exists and satisfies

Integrability conjecture. The Hamiltonian $\mathsf{H}^{\rm FM}(r,\theta)$ is integrable for arbitrary $r\in\mathbb{Z}_{>0}$ and $0\leq\theta<2\pi$. This proposes an integrable inte…

Let an on-shell overlap be the overlap between a two-site state and a Bethe eigenstate, and let the $Q$-system be the system of Baxter $Q$-functions associated with the integrable…

The paper studies wave functions from the Calogero–Moser/Ruijsenaars–Schneider family in QQ-dual form, represented as sums over colored paths in a discrete stochastic model. Genera…

Let $H_i$ be the commuting operators … acting in the nil-DAHA representation, and let $\Lambda_i(x)$ denote the eigenvalue of $H_i$. Consider the classical open Toda chain with can…

The paper considers a quantum mechanical system represented through an auxiliary statistical stochastic model. A wave function $\Psi_E(x)$ admits a Feynman representation as a sum…

Three-dimensional quantum crystal melting conjecture. The three-dimensional quantum crystal melting model is integrable and has the same mass gap as its one- and two-dimensional co…

Q-function factorization conjecture. For class I configurations,