Reference data for phase diagrams of triangular and hexagonal bosonic lattices

Abstract

PACS 03.75.Lm -Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials PACS 64.70.Tg -Quantum phase transitions PACS 67.85.Hj -Bose-Einstein condensates in optical potentialsAbstract. -We investigate systems of bosonic particles at zero temperature in triangular and hexagonal optical lattice potentials in the framework of the Bose-Hubbard model. Employing the process-chain approach, we obtain accurate values for the boundaries between the Mott insulating phase and the superfluid phase. These results can serve as reference data for both other approximation schemes and upcoming experiments. Since arbitrary integer filling factors g are amenable to our technique, we are able to monitor the behavior of the critical hopping parameters with increasing filling. We also demonstrate that the g-dependence of these exact parameters is described almost perfectly by a scaling relation inferred from the mean-field approximation.

Quantum phase transitions of ultracold Bose systems in nonrectangular optical lattices

“…2. The tip of the first Mott lobe phase boundary of the hexagonal system is located at t c /U = 0.0787, deviating about 8.8% relatively from the numerical result [22].…”

“…Our third-order analytical result shows that the tip of the n = 1 Mott lobe phase boundary is located at t c /U = 0.034 06; it has a relative deviation of 9.7% from the systematic strong coupling expansion result [21] and 9.4% from the recent numerical result [22].…”

Hypergeometric continuation of divergent perturbation series: I. Critical exponents of the Bose–Hubbard model

“…Hence, the first term on the right-hand side gives the total repulsion energy, the second specifies the interaction with the given chemical potential, and the third corresponds to the kinetic energy of the particles. As usual in field theory, we couple this system (8) to external sources and drains which we choose to be spatially uniform with strength η, giving the extended system…”

“…In the present work we extend this basic scenario such that it captures the quantum phase transition from a Mott insulator to a superfluid in the pure two-dimensional Bose-Hubbard model at zero temperature. The Bose-Hubbard model is a paradigmatically simple lattice model of many-particle physics, involving spinless nonrelativistic Bose particles which move on a d-dimensional lattice of arbitrary geometry [6][7][8]. Neighboring lattice sites are connected by a tunneling link of strengthJ, and two particles occupying the same site repel each other with energyU; the dimensionless ratio J U then plays the role of the control parameterj.…”

“…The system is supposed to be open; its particle content being regulated by a chemical potentialμ. The phase diagram resulting for a two-dimensional square lattice in the J U -m U -plane is shown in figure 1; the corresponding diagrams for triangular or hexagonal lattices are available in the literature [8]. Within the so-called Mott lobes confined at low J U between successive integer valuesg 1 and g of the scaled chemical potential m U the system is in an incompressible Mott state with gparticles per site; when increasing J U at fixed m U it enters the superfluid phase at the phase boundary ( ) J U c .…”