量子スピン系におけるLieb-Robinson Bounds ～厳密統計力学入門～（第60回物性若手夏の学校講義ノート）

We review recent progress on state-dependent Lieb--Robinson bounds for Bose--Hubbard Hamiltonians. In particular, Kuwahara, Vu, and Saito established that, for general bounded-density initial states, the Lieb--Robinson velocity is bounded by $t^{d-1}$ for large times, where $d$ denotes the lattice dimension. We present a shorter proof of the weaker, but still polynomial velocity bound $t^{d+ε}$ .We review recent progress on state-dependent Lieb--Robinson bounds for Bose--Hubbard Hamiltonians. In particular, Kuwahara, Vu, and Saito established that, for general bounded-density initial states, the Lieb--Robinson velocity is bounded by $t^{d-1}$ for large times, where $d$ denotes the lattice dimension. We present a shorter proof of the weaker, but still polynomial velocity bound $t^{d+ε}$.

math-phCross-listedarXiv:2603.26209Mar 30, 20260 citations

t^{d-1}

for large times, where

d

denotes the lattice dimension. We present a shorter proof of the weaker, but still polynomial velocity bound

t^{d+ε}