Eigenstate thermalization hypothesis beyond standard indicators : Emergence of random-matrix behavior at small frequencies
Using numerical exact diagonalization, we study matrix elements of a local spin operator in the eigenbasis of two different nonintegrable quantum spin chains. Our emphasis is on the question to what extent local operators can be represented as random matrices and, in particular, to what extent matrix elements can be considered as uncorrelated. As a main result, we show that the eigenvalue distribution of band submatrices at a fixed energy density is a sensitive probe of the correlations between matrix elements. We find that, on the scales where the matrix elements are in a good agreement with all standard indicators of the eigenstate thermalization hypothesis, the eigenvalue distribution still exhibits clear signatures of the original operator, implying correlations between matrix elements. Moreover, we demonstrate that at much smaller energy scales, the eigenvalue distribution approximately assumes the universal semicircle shape, indicating transition to the random-matrix behavior, and in particular that matrix elements become uncorrelated.
| Medienart: |
E-Artikel |
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| Erscheinungsjahr: |
2020 |
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| Erschienen: |
2020 |
| Enthalten in: |
Zur Gesamtaufnahme - volume:102 |
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| Enthalten in: |
Physical review. E - 102(2020), 4-1 vom: 25. Okt., Seite 042127 |
| Sprache: |
Englisch |
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| Beteiligte Personen: |
Richter, Jonas [VerfasserIn] |
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| Links: |
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| Themen: |
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| Anmerkungen: |
Date Revised 20.11.2020 published: Print Citation Status PubMed-not-MEDLINE |
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| doi: |
10.1103/PhysRevE.102.042127 |
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| funding: |
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| Förderinstitution / Projekttitel: |
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| PPN (Katalog-ID): |
NLM317796917 |
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| 245 | 1 | 0 | |a Eigenstate thermalization hypothesis beyond standard indicators |b Emergence of random-matrix behavior at small frequencies |
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| 500 | |a Date Revised 20.11.2020 | ||
| 500 | |a published: Print | ||
| 500 | |a Citation Status PubMed-not-MEDLINE | ||
| 520 | |a Using numerical exact diagonalization, we study matrix elements of a local spin operator in the eigenbasis of two different nonintegrable quantum spin chains. Our emphasis is on the question to what extent local operators can be represented as random matrices and, in particular, to what extent matrix elements can be considered as uncorrelated. As a main result, we show that the eigenvalue distribution of band submatrices at a fixed energy density is a sensitive probe of the correlations between matrix elements. We find that, on the scales where the matrix elements are in a good agreement with all standard indicators of the eigenstate thermalization hypothesis, the eigenvalue distribution still exhibits clear signatures of the original operator, implying correlations between matrix elements. Moreover, we demonstrate that at much smaller energy scales, the eigenvalue distribution approximately assumes the universal semicircle shape, indicating transition to the random-matrix behavior, and in particular that matrix elements become uncorrelated | ||
| 650 | 4 | |a Journal Article | |
| 700 | 1 | |a Dymarsky, Anatoly |e verfasserin |4 aut | |
| 700 | 1 | |a Steinigeweg, Robin |e verfasserin |4 aut | |
| 700 | 1 | |a Gemmer, Jochen |e verfasserin |4 aut | |
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