19 problems

Finite-temperature length-scale conjecture. A finite temperature introduces the additional length scale

Critical scaling conjecture. In any dimension $d$, in the critical regime,

Free-fermion solvability conjecture. The circuits defined by $\mathcal{V}^{({\rm III})}_M$ are solvable by free-fermion decomposition (FFD).

Let $T(u)$ denote the transfer matrix of the spin-chain model, depending on the spectral parameter $u$. The authors seek a factorization of $T(u)$ for generic values of $u$. Generi…

The cited quantum circuit is a product of three-site operators obtained from a transfer matrix of the free-fermions-in-disguise model at a special spectral parameter. Free-fermioni…

Let $\mathcal H=\ell^2(\mathbb Z^2)$ and let $P$ be the Fermi projection of a gapped Hamiltonian $H$ satisfying exponential locality. Let $\omega_P$ be the associated quasi-free st…

Logarithmically enhanced area-law conjecture. As $L\to\infty$ and $B\to0$,

Let $\mathcal A$ be the linear subspace of polynomials vanishing at $0$ and $1$ such that, for every Lipschitz domain $\Lambda$, the error term in the asymptotic expansion for…

Sharp variance asymptotics conjecture. The variance of the free-fermion linear statistic satisfies the two-sided bound above as $\hbar\to0$.

Let $S(x)$ be the entanglement entropy of the interval $[x,\infty)$ near the right edge, let $x_{\rm e}$ denote the edge position, and let $\ell_\Delta$ be the edge length scale. L…

The topological vertex is denoted by $\langle \lambda,\nu,\mu\rangle$, and Kodaira–Spencer theory refers to the deformation theory associated with the topological vertex. Fermionic…

Let $V_{fer}$ denote the free fermion vertex operator superalgebra, let $k$ be an even positive integer, and let $V_{\mathbb{Z}\alpha}$ be the rank-one lattice vertex operator supe…

Hypermaximal neutrality conjecture. The space of solutions of the Dirac equation in a sufficiently regular spacetime region should be a hypermaximal neutral subspace of the space o…

Fix $k_F$, an order $N$, and a positive window parameter $\Xi$. Let $\xi_m$ be the spectral variables determined by the eigenvalue quantization condition, and let…

Spectrum expansion conjecture. The expansion above holds asymptotically as $L\to\infty$. The coefficients have been checked explicitly through tenth order, but the series is not pr…

Let $\chi(\kappa,k_F,L)$ be the generating function with Fisher–Hartwig expansion … whose two parts are given by equations (1) and (2). The parameter $\kappa$ may have half-integer…

Let $F_1(k_F,\lambda)$ denote the coefficient of $L^{-1}$ in the expansion … for the full-counting-statistics generating function of one-dimensional free fermions. The cubic coeffi…

Let ${\cal M}_N$ be the configuration space of gauge-inequivalent configurations of an $N\times N$ complex matrix, and let $G_2$ and $G_3$ be the differential operators associated…

Let ${\cal M}_N$ be the configuration space of gauge-inequivalent configurations of an $N\times N$ complex matrix, and let $G_2$ and $G_3$ denote the differential operators associa…