7 problems

Optimal scaling conjecture. This bound has the best possible scaling in both $\varepsilon$ and $t$.

Consider a $d$-dimensional hypercubic lattice with translation-invariant Hamiltonians $H$ and $V$. For a sequence of lattices of increasing size, let $H(B)$ be the solution of the…

Let $\rho_0$ be a time-dependent initial state, and let $R$ denote the spatial scale of the information wave-front. Polynomial light-cone conjecture. An information wave-front of a…

Consider a $D$-dimensional long-range interacting system whose interactions decay with distance as a power law with exponent $\alpha$. The authors have proved that $\alpha>2D+1$ is…

A Lieb–Robinson bound is a bound controlling the spatial propagation of operators under Hamiltonian time evolution; its lightcone describes the region that can be significantly aff…

Conjecture on further LRB implications. The LRB encloses further theoretical implications, such as the clustering of correlations or the efficiency of time-dependent density matrix…

Let $A$ be any observable supported in a neighborhood of the sample, and let $U(t)$ be the time-evolution operator and $P_2^{(n)}$ the projection associated with the second lead be…