Quantum phase diagram of bosons in optical lattices

Abstract

We work out two different analytical methods for calculating the boundary of the Mott-insulatorsuperfluid (MI-SF) quantum phase transition for scalar bosons in cubic optical lattices of arbitrary dimension at zero temperature which improve upon the seminal mean-field result. The first one is a variational method, which is inspired by variational perturbation theory, whereas the second one is based on the field-theoretic concept of effective potential. Within both analytical approaches we achieve a considerable improvement of the location of the MI-SF quantum phase transition for the first Mott lobe in excellent agreement with recent numerical results from Quantum Monte-Carlo simulations in two and three dimensions. Thus, our analytical results for the whole quantum phase diagram can be regarded as being essentially exact for all practical purposes.

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

“…This hypothesis cannot directly be tested for a 3D lattice system as it is quite hard to get a satisfying quantum phase diagram from QMC. However, as EPLT is more accurate for higher-dimensional systems [37], it is suggestive that the error will even be smaller for a 3D cubic lattice. Now we use our second-order EPLT result in order to analyze the critical points of the Mott lobes in more detail.…”

“…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].…”

“…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:…”

Topological phases of lattice bosons with a dynamical gauge field

“…The values of the boundary do not correspond to the ones of the MF for the two-dimensional (2D) lattice, but they are closer to the ones of the one-dimensional case (see Ref. [35]). The structure of the GS state has revealed this to be closely related to the fact that the magnetic fields are in the Landau gauge.…”

Quantum magnetism of ultracold atoms with a dynamical pseudospin degree of freedom

“…The excitation spectra are obtained from the Green functions, which we evaluate within the first order of a resummed hopping expansion [25,26]. This approximation is equivalent to a mean-field treatment, which for the standard BoseHubbard model is known to give quantitatively good results in d > 1 dimensions.…”