Quantum Gutzwiller approach for the two-component Bose-Hubbard model

Abstract

We study the effects of quantum fluctuations in the two-component Bose-Hubbard model generalizing to mixtures the quantum Gutzwiller approach introduced recently in [Phys. Rev. Research 2, 033276 (2020)]. As a basis for our study, we analyze the mean-field ground-state phase diagram and spectrum of elementary excitations, with particular emphasis on the quantum phase transitions of the model. Within the quantum critical regimes, we address both the superfluid transport properties and the linear response dynamics to density and spin probes of direct experimental relevance. Crucially, we find that quantum fluctuations have a dramatic effect on the drag between the superfluid species of the system, particularly in the vicinity of the paired and antipaired phases absent in the usual one-component Bose-Hubbard model. Additionally, we analyse the contributions of quantum corrections to the one-body coherence and density/spin fluctuations from the perspective of the collective modes of the system, providing results for the few-body correlations in all the regimes of the phase diagram.

Lattice polarons across the superfluid to Mott insulator transition

“…In this Letter, we consider a mobile impurity coupled to a BH bath in order to determine the properties of the lattice Bose polaron across the MI/SF phase transition. We study the problem using the quantum Gutzwiller (QGW) approach that we have recently developed [16,17]. This method allows the bath-impurity interaction to be recast in terms of elementary excitations, in a form which can be seen as an extension of the well-known Frölich model for polarons in crystals [18].…”

“…1(a), we employ the recently developed QGW method [19]. This approach has the advantage of providing a robust, semi-analytical description of both local and non-local quantum correlations in BH models, showing remarkable agreement with Quantum Monte Carlo predictions even in critical regimes where quantum fluctuations are strong [19,20]. Fluctuations δĉ n (r) on top of the mean-field Gutzwiller ground state r n c 0 n |n, r [21][22][23] are quantized in terms of the elementary many-body excitations of the system δĉ n (r…”

Magnetic supersolid phases of two-dimensional extended Bose–Hubbard model with spin–orbit coupling

“…Unlike the above mentioned computationally complex techniques that yield more accurate results, the IDGMF method ignore the details of correlation, and its computational simplicity is the main advantage, thus making it as the common method for the BH model. Moreover, apart from the ground-state phases, the dynamical transitions and thermalization effects at finite temperature [35,98,99] are also can be obtained using this Gutzwiller approach.…”

“…The two-species bosonic system can be realized by using 87 Rb and 41 K in the optical lattices in experiment [21][22][23], which can be described by the two-species BH model [24]. In two-species bosonic system, a rich variety of quantum phases are observed, such as the paired SF phase, supercounterfluid (SCF) phase, vortex-state MI phase, peculiar magnetic state, quantum droplet, ferromagnetic-and antiferromagnetic spin phases [25][26][27][28][29][30][31][32][33][34][35][36][37]. The experimental realization of two-species dipolar condensate mixtures of Er-Dy [38] stimulated the enthusiasm of researchers to study the two-species Bose gases in the extended optical lattices.…”

Fluctuations in multicomponent quantum fluids

“…However, a large variety of different perturbative and variational approaches are available for the study of many-body quantum systems, tailored to specific systems or physical regimes. Many variational approaches are based on a suitable factorization of the many-body wave function, among them Laughlin states [148], Dicke states [149,150] and Gutzwiller states [151][152][153]. For weakly entangled many-mode systems, a computationally efficient representation is offered by matrix product states [141,[154][155][156][157][158][159] and their generalization to tensor networks [160][161][162][163].…”