Mean-field approaches to the Bose–Hubbard model with three-body local interaction

Abstract

The zero temperature properties of the generalized Bose-Hubbard model including three-body interactions are studied on a mean-field level. We obtain analytical results using the so-called perturbative mean-field method and more detailed numerical results using the Gutzwiller product state variational Ansatz. These two approaches yield equivalent results which compare well on a qualitative level with recent exact results obtained in the literature.

Emergent Phases in an Extended Bose-Hubbard Model with Three-body On-site Interaction

“…This model has been studied by various researchers using ED [18], perturbative mean-field theory and the Gutzwiller variational ansatz [17], DMRG [17,14] and the strong-coupling perturbation expansion technique [19]. The general results from these studies show that like the BHM, the phase diagram of this model exhibits the MI lobes for integer filling surrounded by an SF phase.…”

“…The non-trivial effect of the three-body Interaction, W , on the Second MI Lobe a typical phase diagram of the model variation with W/U = 1 shows that the BKT point for this lobe for W/U = 0 is at t/U = 0.3 while the BKT point for W/U = 1 is located at t/U = 0.38. [18,17,16,19].…”

“…Also, an extended variation of the BHM that includes a three-body onsite interaction has, for sometime now, been the focus of active research [4,15,17,19].…”

Origin and growth of the disorder within an ordered state of the spatially extended chemical reaction model

“…Кроме того, MFT нашло широкое применение в исследованиях квантовых явлений [Ayik, 2008;Horvath et al, 2008;Graefe et al, 2008;Akerlund et al, 2013;Sowinski, Chhajlany, 2014;Bighin, Salasnich, 2014;Hayami, Motome, 2015;Hinschberger et al, 2015;Leeuw et al, 2015;Ishihara, Nasu, 2015;Rosati et al, 2014;Serreau, Volpe, 2014;Vermersch, Garreau, 2015;Yilmaz et al, 2014;Yilmaz et al, 2015], в частности для описания динамики ядер [Ayik, 2008], получения динамики среднего поля на сфере Блоха для эрмитова и неэрмитова случаев [Graefe et al, 2008], изучения свойств обобщенной модели Бозе-Хаббарда, включающей трехмерные взаи-модействия при нулевой температуре [Sowinski, Chhajlany, 2014], получения наиболее обоб-щенных уравнений эволюции, описывающих распространение в среде (анти)нейтрино [Serreau, Volpe, 2014], исследования эволюции системы взаимодействия ультрахолодных бо-зонов, которые демонстрируют нелинейное хаотическое поведение в пределе большого числа частиц [Vermersch, Garreau, 2015].…”

One-dimensional Bose-Hubbard model with pure three-body interactions

“…Due to perturbative changes of single-particle wave functions, the effective three-body terms are attractive (for a repulsive gas) [7,8]. BH models with two-and three-body interactions have been studied in many different scenarios and using different numerical techniques [8][9][10][11][12][13][14][15][16][17][18]25]. Recently it was suggested that it is also possible to control three-body terms independently of the two-body ones.…”