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Quantum phase transitions of two-species bosons

邱俊嘉

Published Jan 1, 2014• 0 citations
Publisher

Abstract

We investigate the phase of two-species bosons in square lattice by the quantum Monte Carlo simulations. The Mott insulator phase becomes solid by increasing the nearest-neighbor repulsion. The phase changing can be driven by increasing the strength of hopping. It is found that there is a direct first-order transition. There is also the transition form the superfluid phase to the supersolid phase by increasing the nearest-neighbor repulsion. And the transition can be found when we drive the strength of hopping. We found that there is a second-order transition.

DOI
10.6843/nthu.2014.00393

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We investigate the phase of two-species bosons in square lattice by the quantum Monte Carlo simulations. The Mott insulator phase becomes solid by increasing the nearest-neighbor repulsion. The phase changing can be driven by increasing the strength of hopping. It is found that there is a direct first-order transition. There is also the transition form the superfluid phase to the supersolid phase by increasing the nearest-neighbor repulsion. And the transition can be found when we drive the strength of hopping. We found that there is a second-order transition.
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We study a two-species bosonic Hubbard model on a two-dimensional square lattice by means of quantum Monte Carlo simulations. In addition to the usual contact repulsive interactions between the particles, the Hamiltonian has an interconversion term which allows the transformation of two particles from one species to the other. The phases are characterized by their solid or superfluid properties and by their polarization, i.e., the difference in the populations. When interspecies interactions are smaller than the intraspecies ones, the system is unpolarized, whereas in the opposite case the system is unpolarized in even Mott insulator lobes and polarized in odd Mott lobes and also in the superfluid phase. We show that in the latter case the transition between the Mott insulator of total density 2 and the superfluid can be of either second or first order depending on the relative values of the interactions, whereas the transitions are continuous in all other cases.
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Motivated by recent experiments [Y. J. Lin et al., Nature (London) 471, 83 (2011)], we study Mott phases and superfluid-insulator (SI) transitions of two-species ultracold bosonic atoms in a two-dimensional square optical lattice with nearest-neighbor hopping amplitude ttt and in the presence of a spin-orbit coupling characterized by a tunable strength $\ensuremath{\gamma}$. Using both strong-coupling expansion and Gutzwiller mean-field theory, we chart out the phase diagrams of the bosons in the presence of such spin-orbit interaction. We compute the momentum distribution of the bosons in the Mott phase near the SI transition point and show that it displays precursor peaks whose position in the Brillouin zone can be varied by tuning $\ensuremath{\gamma}$. Our analysis of the critical theory of the transition unravels the presence of unconventional quantum critical points at $t/\ensuremath{\gamma}=0$, which are accompanied by emergence of an additional gapless mode in the critical region. We also study the superfluid phases of the bosons near the SI transition using a Gutzwiller mean-field theory that reveals the existence of a twisted superfluid phase with an anisotropic twist angle which depends on $\ensuremath{\gamma}$. Finally, we compute the collective modes of the bosons and point out the presence of reentrant SI transitions as a function of $\ensuremath{\gamma}$ for nonzero ttt. We propose experiments to test our theory.
We present results of path-integral Monte Carlo simulations of bosons on a two-dimensional square lattice in a random potential of average strength V and with on-site repulsion U. We find that the superfluid density ${\mathrm{\ensuremath{\rho}}}_{\mathit{s}}$ is enhanced by increasing V and U in certain regions of parameter space. By combining the results of ${\mathrm{\ensuremath{\rho}}}_{\mathit{s}}$, with the behavior of the density-density correlation function on lattices of size up to 10\ifmmode\times\else\texttimes\fi{}10, we study the superfluid--to--Mott-insulator transition and the transition from a superfluid to a disorder-localized (``Bose glass'') phase.
We present the global phase diagram of the extended boson Hubbard model on a simple cubic lattice by quantum Monte Carlo simulation with the worm update algorithm. Four kinds of phases are supported by this model, including superfluid, supersolid, Mott, and charge density wave (CDW) states, which are identified in the phase diagram of chemical potential $\ensuremath{\mu}$ versus nearest-neighbor interaction VVV. By changing the chemical potential, a continuous transition is found from the Mott phase to a superfluid phase without breaking the translational symmetry. For an insulating CDW state, adding particles to it gives rise to a continuous transition to a supersolid phase, while removing particles usually leads to a first-order transition to either a supersolid or superfluid phase. By tuning the nearest-neighbor interaction, one can realize the transition between two insulating phases, Mott and CDW, with the same particle density, which turns out to be first order. We also confirm the result in Phys. Rev. B 79, 094503 (2009) that a supersolid phase with average particle density less than 1/2 can exist in a small region of the $\ensuremath{\mu}$-VVV phase diagram.