Traveling/non-traveling phase transition and non-ergodic properties in the random transverse-field Ising model on the Cayley tree
We study the random transverse field Ising model on a finite Cayley tree. This enables us to probe key questions arising in other important disordered quantum systems, in particular the Anderson transition and the problem of dirty bosons on the Cayley tree, or the emergence of non-ergodic properties...
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| Format: | Article |
| Language: | English |
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SciPost
2023-11-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.15.5.211 |
| _version_ | 1797449095556628480 |
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| author | Ankita Chakrabarti, Cyril Martins, Nicolas Laflorencie, Bertrand Georgeot, Éric Brunet, Gabriel Lemarié |
| author_facet | Ankita Chakrabarti, Cyril Martins, Nicolas Laflorencie, Bertrand Georgeot, Éric Brunet, Gabriel Lemarié |
| author_sort | Ankita Chakrabarti, Cyril Martins, Nicolas Laflorencie, Bertrand Georgeot, Éric Brunet, Gabriel Lemarié |
| collection | DOAJ |
| description | We study the random transverse field Ising model on a finite Cayley tree. This enables us to probe key questions arising in other important disordered quantum systems, in particular the Anderson transition and the problem of dirty bosons on the Cayley tree, or the emergence of non-ergodic properties in such systems. We numerically investigate this problem building on the cavity mean-field method complemented by state-of-the art finite-size scaling analysis. Our numerics agree very well with analytical results based on an analogy with the traveling wave problem of a branching random walk in the presence of an absorbing wall. Critical properties and finite-size corrections for the zero-temperature paramagnetic-ferromagnetic transition are studied both for constant (independent of the system volume) and algebraically vanishing (scaling as an inverse power law with the system volume) boundary conditions. In the later case, we reveal a regime which is reminiscent of the non-ergodic delocalized phase observed in other systems, thus shedding some light on critical issues in the context of disordered quantum systems, such as Anderson transitions, the many-body localization or disordered bosons in infinite dimensions. |
| first_indexed | 2024-03-09T14:19:54Z |
| format | Article |
| id | doaj.art-a97f3e7cfcc64f95ba8877ece655c26e |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-03-09T14:19:54Z |
| publishDate | 2023-11-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-a97f3e7cfcc64f95ba8877ece655c26e2023-11-28T16:10:00ZengSciPostSciPost Physics2542-46532023-11-0115521110.21468/SciPostPhys.15.5.211Traveling/non-traveling phase transition and non-ergodic properties in the random transverse-field Ising model on the Cayley treeAnkita Chakrabarti, Cyril Martins, Nicolas Laflorencie, Bertrand Georgeot, Éric Brunet, Gabriel LemariéWe study the random transverse field Ising model on a finite Cayley tree. This enables us to probe key questions arising in other important disordered quantum systems, in particular the Anderson transition and the problem of dirty bosons on the Cayley tree, or the emergence of non-ergodic properties in such systems. We numerically investigate this problem building on the cavity mean-field method complemented by state-of-the art finite-size scaling analysis. Our numerics agree very well with analytical results based on an analogy with the traveling wave problem of a branching random walk in the presence of an absorbing wall. Critical properties and finite-size corrections for the zero-temperature paramagnetic-ferromagnetic transition are studied both for constant (independent of the system volume) and algebraically vanishing (scaling as an inverse power law with the system volume) boundary conditions. In the later case, we reveal a regime which is reminiscent of the non-ergodic delocalized phase observed in other systems, thus shedding some light on critical issues in the context of disordered quantum systems, such as Anderson transitions, the many-body localization or disordered bosons in infinite dimensions.https://scipost.org/SciPostPhys.15.5.211 |
| spellingShingle | Ankita Chakrabarti, Cyril Martins, Nicolas Laflorencie, Bertrand Georgeot, Éric Brunet, Gabriel Lemarié Traveling/non-traveling phase transition and non-ergodic properties in the random transverse-field Ising model on the Cayley tree SciPost Physics |
| title | Traveling/non-traveling phase transition and non-ergodic properties in the random transverse-field Ising model on the Cayley tree |
| title_full | Traveling/non-traveling phase transition and non-ergodic properties in the random transverse-field Ising model on the Cayley tree |
| title_fullStr | Traveling/non-traveling phase transition and non-ergodic properties in the random transverse-field Ising model on the Cayley tree |
| title_full_unstemmed | Traveling/non-traveling phase transition and non-ergodic properties in the random transverse-field Ising model on the Cayley tree |
| title_short | Traveling/non-traveling phase transition and non-ergodic properties in the random transverse-field Ising model on the Cayley tree |
| title_sort | traveling non traveling phase transition and non ergodic properties in the random transverse field ising model on the cayley tree |
| url | https://scipost.org/SciPostPhys.15.5.211 |
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