Quantum phases, supersolids and quantum phase transitions of interacting bosons in frustrated lattices

Abstract

By using the dual vortex method (DVM), we develop systematically a simple and effective scheme to use the vortex degree of freedoms on dual lattices to characterize the symmetry breaking patterns of the boson insulating states in the direct lattices. Then we apply our scheme to study quantum phases and phase transitions in an extended boson Hubbard model slightly away from 1/3 ( 2/3 ) filling on frustrated lattices such as triangular and kagome lattice. In a triangular lattice at 1/3, we find a X-CDW, a stripe CDW phase which was found perviously by a density operator formalism (DOF). Most importantly, we also find a new CDW-VB phase which has both local CDW and local VB orders, in sharp contrast to a bubble CDW phase found previously by the DOF. In the Kagome lattice at 1/3, we find a VBS phase and a 6 fold-CDW phase. Most importantly, we also identify a CDW-VB phase which has both local CDW and local VB orders which was found in previous QMC simulations. We also study several other phases which are not found by the DVM. By analyzing carefully the saddle point structures of the dual gauge fields in the translational symmetry breaking sides and pushing the effective actions slightly away from the commensurate filling f = 1/3( 2/3 ), we classified all the possible types of supersolids and analyze their stability conditions. In a triangular lattice, there are X-CDW supersolid, stripe CDW supersolid, but absence of any valence bond supersolid ( VB-SS ). There are also a new kind of supersolid: CDW-VB supersolid. In a Kagome lattice, there are 6 fold-CDW supersolid, stripe CDW supersolid, but absence of any valence bond supersolid ( VB-SS ). There are also a new kind of supersolid: CDW-VB supersolid. We show that independent of the types of the SS, the quantum phase transitions from solids to supersolids driven by a chemical potential are in the same universality class as that from a Mott insulator to a superfluid, therefore have exact exponents z = 2, ν = 1/2, η = 0 ( with logarithmic corrections ). Excitation spectra of all these insulating phases and supersolid phases are also studied. Implications on QMC simulations with both nearest neighbor and next nearest neighbor interactions in both lattices are given. Some possible intrinsic problems of the DOF in identifying the insulating phases are also pointed out.

Quantum magnetism of spinor bosons in optical lattices with synthetic non-Abelian gauge fields

“…In Fig.7, we contrast the gauge field configurations in the U(1) basis with that quantum spin Hall effect realized in recent experiments [12][13][14]. [12][13][14][41][42][43][44]. Both are translational invariant along the y direction, so only one row is shown.…”

“…where the x is the x− coordinate [41][42][43][44] of the site i. For irrational β, this Hamiltonian completely breaks the lattice translational symmetry.…”

“…For irrational β, this Hamiltonian completely breaks the lattice translational symmetry. For a rational 2β = p/q, it contains q sites per unit cell (RBZ is 1/q of the original BZ, for details, see [41][42][43][44]). However, the U(1) basis Fig.7a only breaks the lattice into A and B sublattices for any ( irrational ) value β.…”

Topological Quantum Phase Transition in Synthetic Non-Abelian Gauge Potential: Gauge Invariance and Experimental Detections

“…Recently, there have been some experimental1920 and theoretical activities2122234243 in manipulating and controlling of ultracold atoms in a honeycomb optical lattice. Bermudez et al 24 studied Fermi gases trapped in a honeycomb optical lattice in the presence of a synthetic SU (2) gauge potential.…”

Сверхтвердая Магнитная Фаза В Двумерном Изингоподобном Антиферромагнетике С Большой Одноионной Анизотропией

“…Помимо газов в оптических решетках сверхтвердую магнитную фазу можно обнаружить и в других кван-товых магнетиках [5][6][7][8][9][10]. После того как была до-казана возможность реализации сверхтвердой фазы в двухподрешеточных спиновых системах [11,12], такие системы стали одними из перспективных кандидатов для обнаружения данного состояния [11,[13][14][15][16][17][18][19].…”