Lieb-Robinson bounds with exponential-in-volume tails
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915753883598848 |
|---|---|
| author | McDonough, Ben T. Yin, Chao Lucas, Andrew Zhang, Carolyn |
| author_facet | McDonough, Ben T. Yin, Chao Lucas, Andrew Zhang, Carolyn |
| contents | Lieb-Robinson bounds demonstrate the emergence of locality in many-body quantum systems. Intuitively, Lieb-Robinson bounds state that with local or exponentially decaying interactions, the correlation that can be built up between two sites separated by distance $r$ after a time $t$ decays as $\exp(vt-r)$, where $v$ is the emergent Lieb-Robinson velocity. In many problems, it is important to also capture how much of an operator grows to act on $r^d$ sites in $d$ spatial dimensions. Perturbation theory and cluster expansion methods suggest that at short times, these volume-filling operators are suppressed as $\exp(-r^d)$ at short times. We confirm this intuition, showing that for $r > vt$, the volume-filling operator is suppressed by $\exp(-(r-vt)^d/(vt)^{d-1})$. This closes a conceptual and practical gap between the cluster expansion and the Lieb-Robinson bound. We then present two very different applications of this new bound. Firstly, we obtain improved bounds on the classical computational resources necessary to simulate many-body dynamics with error tolerance $ε$ for any finite time $t$: as $ε$ becomes sufficiently small, only $ε^{-O(t^{d-1})}$ resources are needed. A protocol that likely saturates this bound is given. Secondly, we prove that disorder operators have volume-law suppression near the "solvable (Ising) point" in quantum phases with spontaneous symmetry breaking, which implies a new diagnostic for distinguishing many-body phases of quantum matter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02652 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lieb-Robinson bounds with exponential-in-volume tails McDonough, Ben T. Yin, Chao Lucas, Andrew Zhang, Carolyn Quantum Physics Statistical Mechanics Strongly Correlated Electrons Mathematical Physics Lieb-Robinson bounds demonstrate the emergence of locality in many-body quantum systems. Intuitively, Lieb-Robinson bounds state that with local or exponentially decaying interactions, the correlation that can be built up between two sites separated by distance $r$ after a time $t$ decays as $\exp(vt-r)$, where $v$ is the emergent Lieb-Robinson velocity. In many problems, it is important to also capture how much of an operator grows to act on $r^d$ sites in $d$ spatial dimensions. Perturbation theory and cluster expansion methods suggest that at short times, these volume-filling operators are suppressed as $\exp(-r^d)$ at short times. We confirm this intuition, showing that for $r > vt$, the volume-filling operator is suppressed by $\exp(-(r-vt)^d/(vt)^{d-1})$. This closes a conceptual and practical gap between the cluster expansion and the Lieb-Robinson bound. We then present two very different applications of this new bound. Firstly, we obtain improved bounds on the classical computational resources necessary to simulate many-body dynamics with error tolerance $ε$ for any finite time $t$: as $ε$ becomes sufficiently small, only $ε^{-O(t^{d-1})}$ resources are needed. A protocol that likely saturates this bound is given. Secondly, we prove that disorder operators have volume-law suppression near the "solvable (Ising) point" in quantum phases with spontaneous symmetry breaking, which implies a new diagnostic for distinguishing many-body phases of quantum matter. |
| title | Lieb-Robinson bounds with exponential-in-volume tails |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons Mathematical Physics |
| url | https://arxiv.org/abs/2502.02652 |