5 problems

Upper-bound conjecture. The classical Hamiltonian satisfies the bound

Let $H_\Lambda$ be the Hamiltonian on the interval $\Lambda$, let $\kappa$ and $\lambda$ be its parameters, and let $\mathcal{D}_{l,r}^{(2)}$ be the invariant subspace associated w…

A state-sum Hamiltonian schema is obtained from a topological state-sum construction: for a cellulation $\Delta$ of a space manifold $Y$, the state-sum on $Y\times I$ defines an id…

Commuting quantum Dell Hamiltonians conjecture. The Hamiltonians $\hat {\mathfrak{H}}_a(w,u|q,t)$ commute with each other. The Hamiltonians are quantum counterparts of the Dell Ham…

Let $H=\frac{1}{m}\sum_{i=1}^m\Pi_i$ be a local Hamiltonian, where the terms $\Pi_i$ are local projectors, and let a quantum state be trivial if it can be obtained from a product s…