31 problems

Let a Bethe ansatz state be specified by parameters satisfying a corresponding system of on-shell equations, and let its norm be the scalar product of the state with itself. The Ja…

Consider quantum many-body systems, such as spin-$1/2$ or fermionic systems, that lack a meaningful classical or semiclassical description. Restrict to sectors in which all local c…

Let $n$ bosonic particles have relativistic kinetic energy, and let $\mathcal{H}_{V\equiv 0}$ denote the pseudo-relativistic Hartree energy functional with vanishing external poten…

Let the energy be studied along the line $\gamma=2\pi\beta\kappa$, with real-valued minimizers and $\kappa=\pm 1$. Linear interpolation conjecture. The energy of the real-valued mi…

The standard-path insufficiency conjecture. The standard adiabatic path condition alone is insufficient to ensure the generalized area law.

Field-theoretic classification conjecture. At least a large class of $d$-dimensional topological phases of quantum many-body systems can be classified by field-theoretic methods.

For a weighted graph $G=(V,E,w)$, let … be the EPR Hamiltonian, and let $w(G)$ denote the total edge weight. Let $w(\operatorname{FM}_G)$ be the value of a maximum-weight fractiona…

Let $\mathbb T$ be the space-transfer matrix of a quantum circuit, and consider the system away from the dual-unitary point. Garratt's conjecture. The leading eigenvalues of…

Poulin–Hastings conjecture. The convergence of the Markov Entropy Decomposition is connected to the approximate saturation of strong subadditivity, also known as the decay of the c…

The extension conjecture. The displayed formula, with the stated contour prescription and singlet initial vector, holds for every $n\geq 3$ as well.

Limiting-distribution conjecture. The asymptotic behavior also holds for purely imaginary values of $\lambda$, and consequently $\mathcal{N}_+$ has an asymptotic limiting distribut…

Two-point correlation scaling conjecture. For arbitrary $\rho$ and $p$, the two-point correlation function satisfies

CA-EC applicability conjecture. CA-EC is expected to work for quantum systems involving more particles, as well as in conjunction with techniques other than complex scaling.

The W-state signature conjecture. If such a translation-invariant Hamiltonian is tuned so that the zero-mode $|W_1\rangle$-like state and the product state…

A symmetry is a property of the Hilbert space, while topological order is a ground-state property. Higher-dimensional topological-order conjecture. Symmetries should be related to…

Quantum many-body states obeying an entropy scaling law have entanglement entropies expressible as sums of terms scaling linearly with subsystem volume and area, together with a si…

Optimal convergence-rate conjecture. We conjecture that

Boundary Gibbs-state conjecture. The parent Hamiltonian of the PEPS is gapped if and only if the boundary states can be written as Gibbs states of one-dimensional short-range Hamil…

Emergence of the renormalized Gibbs measure. In the limit $\lambda=T^{-1}\to0$, one obtains the renormalized Gibbs measure in the sense that

Let $\Psi=(\psi)^{\otimes N/M}$ be a state of the periodic Heisenberg spin-1/2 chain, where $\psi$ has length $M$ and the chain length tends to infinity, $N\to\infty$. For each aux…

Let $M$ be even, and consider the $S_{M/2}\otimes S_{M/2}$ symmetric Jack polynomial eigenstates of the spinful Calogero–Sutherland model. The $(1,m+1)$ admissibility condition ref…

Let $\mathcal{L}_n(\gamma)$ be the degree-$n-1$ polynomial appearing in the conjectured decomposition of the $n$th-complexity contribution to the dimensionless Lieb–Liniger ground-…

Let $e(\gamma)=\sum_{n=0}^{+\infty}e_n(\gamma)$ be the dimensionless ground-state energy, decomposed into terms of complexity $n$, and let $e^{TG}=\pi^2/3$ denote its value in the…

Continuity and piecewise-smoothness conjecture. For every finite $N$, the ground-state curve is continuous in $\alpha$ and piecewise smooth, and the number of its smooth pieces gro…

Gibbs and generalised Gibbs ensemble thermalization conjecture. In a generic model, stationary values of local observables are described by Gibbs ensembles, whereas in an integrabl…