Meron-cluster simulation of the quantum antiferromagnetic Heisenberg model in a magnetic field in one- and two-dimensions
Motivated by the numerical simulation of systems which display quantum phase transitions, we present a novel application of the meron-cluster algorithm to simulate the quantum antiferromagnetic Heisenberg model coupled to an external uniform magnetic field both in one and in two dimensions. In the i...
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| Дата: | 2015 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут фізики конденсованих систем НАН України
2015
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| Назва видання: | Condensed Matter Physics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/153515 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Meron-cluster simulation of the quantum antiferromagnetic Heisenberg model in a magnetic field in one- and two-dimensions / G. Palma, A. Riveros // Condensed Matter Physics. — 2015. — Т. 18, № 2. — С. 23002: 1–18. — Бібліогр.: 30 назв. — англ. |
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irk-123456789-1535152019-06-15T01:28:27Z Meron-cluster simulation of the quantum antiferromagnetic Heisenberg model in a magnetic field in one- and two-dimensions Palma, G. Riveros, A. Motivated by the numerical simulation of systems which display quantum phase transitions, we present a novel application of the meron-cluster algorithm to simulate the quantum antiferromagnetic Heisenberg model coupled to an external uniform magnetic field both in one and in two dimensions. In the infinite volume limit and at zero temperature we found numerical evidence that supports a quantum phase transition very close to the critical values $B_c=2$ and $B_c = 4$ for the system in one and two dimensions, respectively. For the one dimensional system, we have compared the numerical data obtained with analytical predictions for the magnetization density as a function of the external field obtained by scaling-behaviour analysis and Bethe Ansatz techniques. Since there is no analytical solution for the two dimensional case, we have compared our results with the magnetization density obtained by scaling relations for small lattice sizes and with the approximated thermodynamical limit at zero temperature guessed by scaling relations. Moreover, we have compared the numerical data with other numerical simulations performed by using different algorithms in one and two dimensions, like the directed loop method. The numerical data obtained are in perfect agreement with all these previous results, which confirms that the meron-algorithm is reliable for quantum Monte Carlo simulations and applicable both in one and two dimensions. Finally, we have computed the integrated autocorrelation time to measure the efficiency of the meron algorithm in one dimension. Будучи вмотивованими числовими симуляцiями систем, якi проявляють властивостi квантових фазових переходiв, представляємо нове застосування мерон-кластерного алгоритма з метою моделювання квантової антиферомагнiтної моделi Гайзенберга, що взаємодiє iз зовнiшнiм однорiдним магнiтним полем, як в одно- так i в двовимiрному випадках. В границi нескiнченного об’єму i при нульовiй температурi нами знайдено числовi докази, якi пiдтверджують наявнiсть квантового фазового переходу дуже близько до критичних значень Bc = 2 i Bc = 4 для системи, вiдповiдно, в одно- i двовимiрному випадках. Для одновимiрної системи нами здiйснено порiвняння числових даних, отриманих з аналiтичних результатiв для густини намагнiчування як функцiї зовнiшнього поля, отриманої за допомогою аналiзу скейлiнгової поведiнки та технiки анзацу Бете. Оскiльки не має аналiтичного розв’язку для двовимiрного випадку, автори порiвняли свої результати з густиною намагнiчування, отриманою за допомогою скейлiнгових спiввiдношень для невеликих розмiрiв граток i з апроксимованою термодинамiчною границею при нульовiй температурi, оцiненою зi скенйлiнгових спiввiдношень. Бiльше того, автори порiвняли числовi данi з iншими числовими симуляцiями, виконаними з використанням рiзних алгоритмiв в одному та у двох вимiрах, типу методу напрямлених петель. Отриманi числовi данi iдеально узгоджуються з усiма попереднiми рузультатами, а це в свою чергу пiдтверджує, що мерон-алгоритм є надiйним для проведення моделювання методом Монте Карло i його можна застосовувати в одному i двох вимiрах. I нарештi, нами обчислено сумарний автокореляцiний час з метою вимiрювання ефективностi мерон-алгоритма в одному вимiрi. 2015 Article Meron-cluster simulation of the quantum antiferromagnetic Heisenberg model in a magnetic field in one- and two-dimensions / G. Palma, A. Riveros // Condensed Matter Physics. — 2015. — Т. 18, № 2. — С. 23002: 1–18. — Бібліогр.: 30 назв. — англ. 1607-324X DOI:10.5488/CMP.18.23002 arXiv:1312.4915 PACS: 05.50.+q, 02.70.-c, 68.35.Rh, 75.40.Cx http://dspace.nbuv.gov.ua/handle/123456789/153515 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 |
Motivated by the numerical simulation of systems which display quantum phase transitions, we present a novel application of the meron-cluster algorithm to simulate the quantum antiferromagnetic Heisenberg model coupled to an external uniform magnetic field both in one and in two dimensions. In the infinite volume limit and at zero temperature we found numerical evidence that supports a quantum phase transition very close to the critical values $B_c=2$ and $B_c = 4$ for the system in one and two dimensions, respectively. For the one dimensional system, we have compared the numerical data obtained with analytical predictions for the magnetization density as a function of the external field obtained by scaling-behaviour analysis and Bethe Ansatz techniques. Since there is no analytical solution for the two dimensional case, we have compared our results with the magnetization density obtained by scaling relations for small lattice sizes and with the approximated thermodynamical limit at zero temperature guessed by scaling relations. Moreover, we have compared the numerical data with other numerical simulations performed by using different algorithms in one and two dimensions, like the directed loop method. The numerical data obtained are in perfect agreement with all these previous results, which confirms that the meron-algorithm is reliable for quantum Monte Carlo simulations and applicable both in one and two dimensions. Finally, we have computed the integrated autocorrelation time to measure the efficiency of the meron algorithm in one dimension. |
| format |
Article |
| author |
Palma, G. Riveros, A. |
| spellingShingle |
Palma, G. Riveros, A. Meron-cluster simulation of the quantum antiferromagnetic Heisenberg model in a magnetic field in one- and two-dimensions Condensed Matter Physics |
| author_facet |
Palma, G. Riveros, A. |
| author_sort |
Palma, G. |
| title |
Meron-cluster simulation of the quantum antiferromagnetic Heisenberg model in a magnetic field in one- and two-dimensions |
| title_short |
Meron-cluster simulation of the quantum antiferromagnetic Heisenberg model in a magnetic field in one- and two-dimensions |
| title_full |
Meron-cluster simulation of the quantum antiferromagnetic Heisenberg model in a magnetic field in one- and two-dimensions |
| title_fullStr |
Meron-cluster simulation of the quantum antiferromagnetic Heisenberg model in a magnetic field in one- and two-dimensions |
| title_full_unstemmed |
Meron-cluster simulation of the quantum antiferromagnetic Heisenberg model in a magnetic field in one- and two-dimensions |
| title_sort |
meron-cluster simulation of the quantum antiferromagnetic heisenberg model in a magnetic field in one- and two-dimensions |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/153515 |
| citation_txt |
Meron-cluster simulation of the quantum antiferromagnetic Heisenberg model in a magnetic field in one- and two-dimensions / G. Palma, A. Riveros // Condensed Matter Physics. — 2015. — Т. 18, № 2. — С. 23002: 1–18. — Бібліогр.: 30 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT palmag meronclustersimulationofthequantumantiferromagneticheisenbergmodelinamagneticfieldinoneandtwodimensions AT riverosa meronclustersimulationofthequantumantiferromagneticheisenbergmodelinamagneticfieldinoneandtwodimensions |
| first_indexed |
2023-05-20T17:41:44Z |
| last_indexed |
2023-05-20T17:41:44Z |
| _version_ |
1796153879706992640 |