Response theory for locally gapped systems
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912072578629632 |
|---|---|
| author | Henheik, Joscha Wessel, Tom |
| author_facet | Henheik, Joscha Wessel, Tom |
| contents | We introduce a notion of a \emph{local gap} for interacting many-body quantum lattice systems and prove the validity of response theory and Kubo's formula for localized perturbations in such settings.
On a high level, our result shows that the usual spectral gap condition, concerning the system as a whole, is not a necessary condition for understanding local properties of the system.
More precisely, we say that an equilibrium state $ρ_0$ of a Hamiltonian $H_0$ is locally gapped in $Λ^{\mathrm{gap}} \subset Λ$, whenever the Liouvillian $- \mathrm{i} \, [H_0, \, \cdot \, ]$ is almost invertible on local observables supported in $Λ^{\mathrm{gap}}$ when tested in $ρ_0$.
To put this into context, we provide other alternative notions of a local gap and discuss their relations.
The validity of response theory is based on the construction of \emph{non-equilibrium almost stationary states} (NEASSs).
By controlling locality properties of the NEASS construction, we show that response theory holds to any order, whenever the perturbation \(εV\) acts in a region which is further than $|\log ε|$ away from the non-gapped region $Λ\setminus Λ^{\mathrm{gap}}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_10809 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Response theory for locally gapped systems Henheik, Joscha Wessel, Tom Mathematical Physics Quantum Physics 81V70, 81Q15, 81Q99 We introduce a notion of a \emph{local gap} for interacting many-body quantum lattice systems and prove the validity of response theory and Kubo's formula for localized perturbations in such settings. On a high level, our result shows that the usual spectral gap condition, concerning the system as a whole, is not a necessary condition for understanding local properties of the system. More precisely, we say that an equilibrium state $ρ_0$ of a Hamiltonian $H_0$ is locally gapped in $Λ^{\mathrm{gap}} \subset Λ$, whenever the Liouvillian $- \mathrm{i} \, [H_0, \, \cdot \, ]$ is almost invertible on local observables supported in $Λ^{\mathrm{gap}}$ when tested in $ρ_0$. To put this into context, we provide other alternative notions of a local gap and discuss their relations. The validity of response theory is based on the construction of \emph{non-equilibrium almost stationary states} (NEASSs). By controlling locality properties of the NEASS construction, we show that response theory holds to any order, whenever the perturbation \(εV\) acts in a region which is further than $|\log ε|$ away from the non-gapped region $Λ\setminus Λ^{\mathrm{gap}}$. |
| title | Response theory for locally gapped systems |
| topic | Mathematical Physics Quantum Physics 81V70, 81Q15, 81Q99 |
| url | https://arxiv.org/abs/2410.10809 |