Statistics of correlations functions in the random Heisenberg chain
Ergodic quantum many-body systems satisfy the eigenstate thermalization hypothesis (ETH). However, strong disorder can destroy ergodicity through many-body localization (MBL) -- at least in one dimensional systems -- leading to a clear signal of the MBL transition in the probability distributions...
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| Format: | Article |
| Language: | English |
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SciPost
2019-11-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.7.5.064 |
| _version_ | 1818096958935400448 |
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| author | Luis Colmenarez, Paul A. McClarty, Masudul Haque, David J. Luitz |
| author_facet | Luis Colmenarez, Paul A. McClarty, Masudul Haque, David J. Luitz |
| author_sort | Luis Colmenarez, Paul A. McClarty, Masudul Haque, David J. Luitz |
| collection | DOAJ |
| description | Ergodic quantum many-body systems satisfy the eigenstate thermalization
hypothesis (ETH). However, strong disorder can destroy ergodicity through
many-body localization (MBL) -- at least in one dimensional systems -- leading
to a clear signal of the MBL transition in the probability distributions of
energy eigenstate expectation values of local operators. For a paradigmatic
model of MBL, namely the random-field Heisenberg spin chain, we consider the
full probability distribution of eigenstate correlation functions across the
entire phase diagram. We find gaussian distributions at weak disorder, as
predicted by pure ETH. At intermediate disorder -- in the thermal phase -- we
find further evidence for anomalous thermalization in the form of heavy tails
of the distributions. In the MBL phase, we observe peculiar features of the
correlator distributions: a strong asymmetry in $S_i^z S_{i+r}^z$ correlators
skewed towards negative values; and a multimodal distribution for spin-flip
correlators. A quantitative quasi-degenerate perturbation theory calculation of
these correlators yields a surprising agreement of the full distribution with
the exact results, revealing, in particular, the origin of the multiple peaks
in the spin-flip correlator distribution as arising from the resonant and
off-resonant admixture of spin configurations. The distribution of the
$S_i^zS_{i+r}^z$ correlator exhibits striking differences between the MBL and
Anderson insulator cases. |
| first_indexed | 2024-12-10T23:12:54Z |
| format | Article |
| id | doaj.art-ace6b27fd9834ac1b186039742fd39e1 |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-12-10T23:12:54Z |
| publishDate | 2019-11-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-ace6b27fd9834ac1b186039742fd39e12022-12-22T01:29:55ZengSciPostSciPost Physics2542-46532019-11-017506410.21468/SciPostPhys.7.5.064Statistics of correlations functions in the random Heisenberg chainLuis Colmenarez, Paul A. McClarty, Masudul Haque, David J. LuitzErgodic quantum many-body systems satisfy the eigenstate thermalization hypothesis (ETH). However, strong disorder can destroy ergodicity through many-body localization (MBL) -- at least in one dimensional systems -- leading to a clear signal of the MBL transition in the probability distributions of energy eigenstate expectation values of local operators. For a paradigmatic model of MBL, namely the random-field Heisenberg spin chain, we consider the full probability distribution of eigenstate correlation functions across the entire phase diagram. We find gaussian distributions at weak disorder, as predicted by pure ETH. At intermediate disorder -- in the thermal phase -- we find further evidence for anomalous thermalization in the form of heavy tails of the distributions. In the MBL phase, we observe peculiar features of the correlator distributions: a strong asymmetry in $S_i^z S_{i+r}^z$ correlators skewed towards negative values; and a multimodal distribution for spin-flip correlators. A quantitative quasi-degenerate perturbation theory calculation of these correlators yields a surprising agreement of the full distribution with the exact results, revealing, in particular, the origin of the multiple peaks in the spin-flip correlator distribution as arising from the resonant and off-resonant admixture of spin configurations. The distribution of the $S_i^zS_{i+r}^z$ correlator exhibits striking differences between the MBL and Anderson insulator cases.https://scipost.org/SciPostPhys.7.5.064 |
| spellingShingle | Luis Colmenarez, Paul A. McClarty, Masudul Haque, David J. Luitz Statistics of correlations functions in the random Heisenberg chain SciPost Physics |
| title | Statistics of correlations functions in the random Heisenberg chain |
| title_full | Statistics of correlations functions in the random Heisenberg chain |
| title_fullStr | Statistics of correlations functions in the random Heisenberg chain |
| title_full_unstemmed | Statistics of correlations functions in the random Heisenberg chain |
| title_short | Statistics of correlations functions in the random Heisenberg chain |
| title_sort | statistics of correlations functions in the random heisenberg chain |
| url | https://scipost.org/SciPostPhys.7.5.064 |
| work_keys_str_mv | AT luiscolmenarezpaulamcclartymasudulhaquedavidjluitz statisticsofcorrelationsfunctionsintherandomheisenbergchain |