F-electron spectral function of the Falicov-Kimball model and the Wiener-Hopf sum equation approach
We derive an alternative representation for the f-electron spectral function of the Falicov-Kimball model from the original one proposed by Brandt and Urbanek. In the new representation, all calculations are restricted to the real time axis, allowing us to go to arbitrarily low temperatures. The g...
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| Дата: | 2008 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут фізики конденсованих систем НАН України
2008
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| Назва видання: | Condensed Matter Physics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/119339 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | F-electron spectral function of the Falicov-Kimball model and the Wiener-Hopf sum equation approach / A.M. Shvaika, J.K. Freericks // Condensed Matter Physics. — 2008. — Т. 11, № 3(55). — С. 425-442. — Бібліогр.: 25 назв. — англ. |
Репозитарії
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irk-123456789-1193392017-06-07T03:03:09Z F-electron spectral function of the Falicov-Kimball model and the Wiener-Hopf sum equation approach Shvaika, A.M. Freericks, J.K. We derive an alternative representation for the f-electron spectral function of the Falicov-Kimball model from the original one proposed by Brandt and Urbanek. In the new representation, all calculations are restricted to the real time axis, allowing us to go to arbitrarily low temperatures. The general formula for the retarded Green's function involves two determinants of continuous matrix operators that have the Toeplitz form. By employing the Wiener-Hopf sum equation approach and Szeg¨ o's theorem, we can derive exact analytic formulas for the large-time limits of the Green's function; we illustrate this for cases when the logarithm of characteristic function (which de nes the continuous Toeplitz matrix) does and does not wind around the origin. We show how accurate these asymptotic formulas are to the exact solutions found from extrapolating matrix calculations to the zero discretization size limit. Отримано нове представлення для спектральної функцiї f-електронiв моделi Фалiкова-Кiмбала, яке альтернативне оригiнальному представленню Брандта i Урбанека. У новому представленнi усi розрахунки виконуються тiльки на дiйснiй часовiй осi, що дозволяє розглядати як завгодно низькi температури. Загальний вираз для запiзнюючої функцiї Ґрiна включає два детермiнанти неперервних матричних операторiв зi структурою типу Теплiца. Застосовуючи дискретний пiдхiд Вiнера-Гопфа i теорему Сеґо, отримано точнi аналiтичнi формули для довгочасової поведiнки функцiй Ґрiна; розглянуто випадки, коли логарифм характеристичної функцiї (яка визначає неперервну матрицю Теплiца) робить i не робить виток навколо початку координат. Показано наскiльки точними є данi асимптотичнi вирази у порiвняннi з точними розв’язками, якi отримуються при екстраполяцiї прямих матричних розрахункiв до границi нульової дискретизацiї. 2008 Article F-electron spectral function of the Falicov-Kimball model and the Wiener-Hopf sum equation approach / A.M. Shvaika, J.K. Freericks // Condensed Matter Physics. — 2008. — Т. 11, № 3(55). — С. 425-442. — Бібліогр.: 25 назв. — англ. 1607-324X PACS: 71.10.-w, 71.27.+a, 71.30.+h, 02.30.Rz DOI:10.5488/CMP.11.3.425 http://dspace.nbuv.gov.ua/handle/123456789/119339 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We derive an alternative representation for the f-electron spectral function of the Falicov-Kimball model from
the original one proposed by Brandt and Urbanek. In the new representation, all calculations are restricted
to the real time axis, allowing us to go to arbitrarily low temperatures. The general formula for the retarded
Green's function involves two determinants of continuous matrix operators that have the Toeplitz form. By employing
the Wiener-Hopf sum equation approach and Szeg¨ o's theorem, we can derive exact analytic formulas
for the large-time limits of the Green's function; we illustrate this for cases when the logarithm of characteristic
function (which de nes the continuous Toeplitz matrix) does and does not wind around the origin. We show
how accurate these asymptotic formulas are to the exact solutions found from extrapolating matrix calculations
to the zero discretization size limit. |
| format |
Article |
| author |
Shvaika, A.M. Freericks, J.K. |
| spellingShingle |
Shvaika, A.M. Freericks, J.K. F-electron spectral function of the Falicov-Kimball model and the Wiener-Hopf sum equation approach Condensed Matter Physics |
| author_facet |
Shvaika, A.M. Freericks, J.K. |
| author_sort |
Shvaika, A.M. |
| title |
F-electron spectral function of the Falicov-Kimball model and the Wiener-Hopf sum equation approach |
| title_short |
F-electron spectral function of the Falicov-Kimball model and the Wiener-Hopf sum equation approach |
| title_full |
F-electron spectral function of the Falicov-Kimball model and the Wiener-Hopf sum equation approach |
| title_fullStr |
F-electron spectral function of the Falicov-Kimball model and the Wiener-Hopf sum equation approach |
| title_full_unstemmed |
F-electron spectral function of the Falicov-Kimball model and the Wiener-Hopf sum equation approach |
| title_sort |
f-electron spectral function of the falicov-kimball model and the wiener-hopf sum equation approach |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/119339 |
| citation_txt |
F-electron spectral function of the Falicov-Kimball model and the Wiener-Hopf sum equation approach / A.M. Shvaika, J.K. Freericks // Condensed Matter Physics. — 2008. — Т. 11, № 3(55). — С. 425-442. — Бібліогр.: 25 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT shvaikaam felectronspectralfunctionofthefalicovkimballmodelandthewienerhopfsumequationapproach AT freericksjk felectronspectralfunctionofthefalicovkimballmodelandthewienerhopfsumequationapproach |
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2023-10-18T20:34:20Z |
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2023-10-18T20:34:20Z |
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1796150549895184384 |