Generalized effective-potential Landau theory for bosonic quadratic superlattices

Abstract

We study the properties of the Bose-Hubbard model for square and cubic superlattices. To this end we generalize a recently established effective potential Landau theory for a single component to the case of multi components and find not only the characteristic incompressible solid phases with fractional filling, but also obtain the underlying quantum phase diagram in the whole parameter region at zero temperature. Comparing our analytic results with corresponding ones from quantum Monte Carlo simulations demonstrates the high accuracy of the generalized effective potential Landau theory (GEPLT). Finally, we comment on the advantages and disadvantages of the GEPLT in view of a direct comparison with a corresponding decoupled mean-field theory.

Tuning the quantum phase transition of bosons in optical lattices via periodic modulation of thes-wave scattering length

“…(23) follow from applying Rayleigh-Schrödinger perturbation theory by using a suitable diagrammatic representation [37,40]. By denoting the creation (annihilation) operator with an arrow line pointing into (out of) the site, each perturbative contribution of α (n) 2p can be sketched as an arrow-line diagram, which is composed of n oriented internal lines connecting the vertices and two external arrow lines.…”

“…Here we follow Refs. [37,40] and couple at first the annihilation and creation operators to external source fields with uniform strength j * and j:…”

“…In order to deal analytically with the spontaneous symmetry breaking of the inherent U(1) symmetry of bosons in an optical lattice the Effective Potential Landau Theory (EPLT) has turned out to be quite successful [37][38][39][40][41][42]. Whereas the lowest order of EPLT leads to similar results as mean-field theory [1], higher hopping orders have recently been evaluated via the process-chain approach [43], which determines the location of the quantum phase transition to a similar precision as demanding quantum Monte Carlo simulations [44].…”

Tunable anisotropic superfluidity in an optical kagome superlattice

“…With the rapid advances in experimental techniques [9] the many-body physics can now be analyzed on more complex lattice geometries. On the one hand, the lattice symmetry can be reduced by adding additional lasers or tuning their relative strength, leading to a superlattice structure [10][11][12][13], which can give rise to insulator phases with fractional fillings [14][15][16][17][18]. On the other hand, it is also possible to enhance the residual entropy of the many-body system by using frustrated lattices, which have recently been realized using sophisticated optical techniques [19][20][21].…”

“…In the following we will use the stochastic cluster series expansion algorithm [37][38][39] for unbiased quantum Monte Carlo (QMC) simulations of this model. In addition the Generalized Effective Potential Landau Theory (GEPLT) provides an analytic method to estimate the phase boundaries in an expansion of the hopping parameter t/U [18,40].…”