Entanglement across scales: Quantics tensor trains as a natural framework for renormalization
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_ | 1866917154515845120 |
|---|---|
| author | Rohshap, Stefan Li, Jheng-Wei Lorenz, Alena Hasil, Serap Held, Karsten Kauch, Anna Wallerberger, Markus |
| author_facet | Rohshap, Stefan Li, Jheng-Wei Lorenz, Alena Hasil, Serap Held, Karsten Kauch, Anna Wallerberger, Markus |
| contents | Understanding entanglement remains one of the most intriguing problems in physics. While particle and site entanglement have been studied extensively, the investigation of length or energy scale entanglement, quantifying the information exchange between different length scales, has received far less attention. Here, we identify the quantics tensor train (QTT) technique, a matrix product state-inspired approach for overcoming computational bottlenecks in resource-intensive numerical calculations, as a renormalization group method by analytically expressing an exact cyclic reduction-based real-space renormalization scheme in QTT language, which serves as a natural formalism for the method. In doing so, we precisely match the QTT bond dimension, a measure of length scale entanglement, to the number of rescaled couplings generated in each coarse-graining renormalization step. While QTTs have so far been applied almost exclusively to numerical problems in physics, our analytical calculations demonstrate that they are also powerful tools for mitigating computational costs in semi-analytical treatments. We present our results for the one-dimensional tight-binding model with n-th-nearest-neighbor hopping, where the 2n rescaled couplings generated in the renormalization procedure precisely match the QTT bond dimension of the one-particle Green's function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19069 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Entanglement across scales: Quantics tensor trains as a natural framework for renormalization Rohshap, Stefan Li, Jheng-Wei Lorenz, Alena Hasil, Serap Held, Karsten Kauch, Anna Wallerberger, Markus Strongly Correlated Electrons Mathematical Physics Computational Physics Understanding entanglement remains one of the most intriguing problems in physics. While particle and site entanglement have been studied extensively, the investigation of length or energy scale entanglement, quantifying the information exchange between different length scales, has received far less attention. Here, we identify the quantics tensor train (QTT) technique, a matrix product state-inspired approach for overcoming computational bottlenecks in resource-intensive numerical calculations, as a renormalization group method by analytically expressing an exact cyclic reduction-based real-space renormalization scheme in QTT language, which serves as a natural formalism for the method. In doing so, we precisely match the QTT bond dimension, a measure of length scale entanglement, to the number of rescaled couplings generated in each coarse-graining renormalization step. While QTTs have so far been applied almost exclusively to numerical problems in physics, our analytical calculations demonstrate that they are also powerful tools for mitigating computational costs in semi-analytical treatments. We present our results for the one-dimensional tight-binding model with n-th-nearest-neighbor hopping, where the 2n rescaled couplings generated in the renormalization procedure precisely match the QTT bond dimension of the one-particle Green's function. |
| title | Entanglement across scales: Quantics tensor trains as a natural framework for renormalization |
| topic | Strongly Correlated Electrons Mathematical Physics Computational Physics |
| url | https://arxiv.org/abs/2507.19069 |