High-order coupled cluster method calculations of spontaneous symmetry breaking in the spin-half one-dimensional J₁-J₂ model
In this article we present new formalism for high-order coupled cluster method (CCM) calculations for generalized ground-state expectation values and the excited states of quantum magnetic systems with spin quantum number s ≥ 1/2 . We use high-order CCM to demonstrate spontaneous symmetry break...
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| Дата: | 2009 |
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| Формат: | Стаття |
| Мова: | English |
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Інститут фізики конденсованих систем НАН України
2009
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| Назва видання: | Condensed Matter Physics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/120014 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | High-order coupled cluster method calculations of spontaneous symmetry breaking in the spin-half one-dimensional J₁-J₂ model / D.J.J. Farnell // Condensed Matter Physics. — 2009. — Т. 12, № 3. — С. 411-428. — Бібліогр.: 86 назв. — англ. |
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irk-123456789-1200142017-06-11T03:04:48Z High-order coupled cluster method calculations of spontaneous symmetry breaking in the spin-half one-dimensional J₁-J₂ model Farnell, D.J.J. In this article we present new formalism for high-order coupled cluster method (CCM) calculations for generalized ground-state expectation values and the excited states of quantum magnetic systems with spin quantum number s ≥ 1/2 . We use high-order CCM to demonstrate spontaneous symmetry breaking in the spin-half J₁ J₂ model for the linear chain using the coupled cluster method (CCM). We show that we are able to reproduce exactly the dimerized ground (ket) state at the Majumdar-Ghosh point (J₂/J₁ = 1/2 ) using a N´eel model state. We show that the onset of dimerized phase is indicated by a bifurcation of the nearest-neighbour ket- and bra-state correlation coefficients for the nearest-neighbour N´eel model state. We show that groundstate energies are in good agreement with the results of exact diagonalizations of nite-length chains across this entire regime (i. e., J₁ > 0 and J₂ ≤ 1/2 ). The effects of the bifurcation point are also observed for the sublattice magnetization for the nearest-neighbour model state. Finally, we use the new formalism for the excited state in order to obtain the excitation energy as a function of J₂/J₁ for the nearest-neighbour model state by solving up to the LSUB14 level of approximation. We obtain an extrapolated value for the excited-state energy gap of -0:0036 at J₂/J₁ = 0:0 and of 0:2310 at J₂/J₁ = 0:5. We show that an excitation energy gap opens up at J₂/J₁ ≈ 0:24, although the gap only becomes large at J₂/J₁ ≈ 0:4. У цiй статтi ми представляємо новий формалiзм розрахункiв методом взаємодiючих кластерiв (МВК) у вищих порядках для “узагальнених” середнiх значень в основному станi i збуджених станiв квантових магнiтних систем зi спiновим квантовим числом s ≥ 1/2. Ми використовуємо МВК у вищих наближеннях, щоб продемонструвати спонтанне порушення симетрiї у спiн-половина J₁-J₂ моделi на лiнiйному ланцюжку. Ми показуємо, що можна вiдтворити точно димеризований основний (кет) стан у точцi Маджумдара-Гоша (J₂/J₁ = 1/2), використовуючи як модельний стан стан Нiеля. Ми показуємо, що на встановлення димеризованої фази вказує бiфуркацiя кореляцiйних коефiцiєнтiв для кет- i бра-станiв для модельного стану Нiеля. Ми показуємо, що енергiя основного стану добре узгоджується iз результатами точної дiагоналiзацiї ланцюжкiв скiнченої довжини у цьому всьому режимi (тобто J₁ > 0 і J₂ ≤ 1/2). Ефекти точки бiфуркацiї також спостерiгаються у намагнiченостi пiдгратки для модельного стану Нiеля. Нарештi ми використовуємо новий формалiзм для збуджених станiв, щоб отримати енергiю збудження як функцiю J₂/J₁ для модельного стану Нiеля, шукаючи розв’язок аж до наближнення рiвня LSUB14. Ми отримуємо екстрапольоване значення для щiлини для енергiї збудження -0:0036 при J₂/J₁ = 0:0 i 0:2310 при J₂/J₁ = 0:5. Ми показуємо, що енергетична щiлина для збудження вiдкривається при J₂/J₁ ≈ 0:24, хоча щiлина стає великою лише при J₂/J₁ ≈ 0:4.. 2009 Article High-order coupled cluster method calculations of spontaneous symmetry breaking in the spin-half one-dimensional J₁-J₂ model / D.J.J. Farnell // Condensed Matter Physics. — 2009. — Т. 12, № 3. — С. 411-428. — Бібліогр.: 86 назв. — англ. 1607-324X PACS: 75.10.Jm, 75.10.Pq, 75.50.Ee DOI:10.5488/CMP.12.3.411 http://dspace.nbuv.gov.ua/handle/123456789/120014 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 |
In this article we present new formalism for high-order coupled cluster method (CCM) calculations for generalized
ground-state expectation values and the excited states of quantum magnetic systems with spin
quantum number s ≥ 1/2 . We use high-order CCM to demonstrate spontaneous symmetry breaking in the
spin-half J₁ J₂ model for the linear chain using the coupled cluster method (CCM). We show that we are able
to reproduce exactly the dimerized ground (ket) state at the Majumdar-Ghosh point (J₂/J₁ = 1/2 ) using a N´eel
model state. We show that the onset of dimerized phase is indicated by a bifurcation of the nearest-neighbour
ket- and bra-state correlation coefficients for the nearest-neighbour N´eel model state. We show that groundstate
energies are in good agreement with the results of exact diagonalizations of nite-length chains across
this entire regime (i. e., J₁ > 0 and J₂ ≤ 1/2 ). The effects of the bifurcation point are also observed for the sublattice
magnetization for the nearest-neighbour model state. Finally, we use the new formalism for the excited
state in order to obtain the excitation energy as a function of J₂/J₁ for the nearest-neighbour model state by
solving up to the LSUB14 level of approximation. We obtain an extrapolated value for the excited-state energy
gap of -0:0036 at J₂/J₁ = 0:0 and of 0:2310 at J₂/J₁ = 0:5. We show that an excitation energy gap opens
up at J₂/J₁ ≈ 0:24, although the gap only becomes large at J₂/J₁ ≈ 0:4. |
| format |
Article |
| author |
Farnell, D.J.J. |
| spellingShingle |
Farnell, D.J.J. High-order coupled cluster method calculations of spontaneous symmetry breaking in the spin-half one-dimensional J₁-J₂ model Condensed Matter Physics |
| author_facet |
Farnell, D.J.J. |
| author_sort |
Farnell, D.J.J. |
| title |
High-order coupled cluster method calculations of spontaneous symmetry breaking in the spin-half one-dimensional J₁-J₂ model |
| title_short |
High-order coupled cluster method calculations of spontaneous symmetry breaking in the spin-half one-dimensional J₁-J₂ model |
| title_full |
High-order coupled cluster method calculations of spontaneous symmetry breaking in the spin-half one-dimensional J₁-J₂ model |
| title_fullStr |
High-order coupled cluster method calculations of spontaneous symmetry breaking in the spin-half one-dimensional J₁-J₂ model |
| title_full_unstemmed |
High-order coupled cluster method calculations of spontaneous symmetry breaking in the spin-half one-dimensional J₁-J₂ model |
| title_sort |
high-order coupled cluster method calculations of spontaneous symmetry breaking in the spin-half one-dimensional j₁-j₂ model |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/120014 |
| citation_txt |
High-order coupled cluster method calculations of spontaneous symmetry breaking in the spin-half one-dimensional J₁-J₂ model / D.J.J. Farnell // Condensed Matter Physics. — 2009. — Т. 12, № 3. — С. 411-428. — Бібліогр.: 86 назв. — англ. |
| series |
Condensed Matter Physics |
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2023-10-18T20:36:01Z |
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