Condensed ground states of frustrated Bose-Hubbard models

Abstract

We study theoretically the groundstates of two-dimensional Bose-Hubbard models which are frustrated by gauge fields. Motivated by recent proposals for the implementation of optically induced gauge potentials, we focus on the situation in which the imposed gauge fields give rise to a pattern of staggered fluxes, of magnitude α and alternating in sign along one of the principal axes. For α = 1/2 this model is equivalent to the case of uniform flux per plaquette n φ = 1/2, which, in the hard-core limit, realizes the "fully frustrated" spin-1/2 XY model. We show that the mean-field groundstates of this frustrated Bose-Hubbard model typically break translational symmetry. We introduce a general numerical technique to detect broken symmetry condensates in exact diagonalization studies. Using this technique we show that, for all cases studied, the groundstate of the Bose-Hubbard model with staggered flux α is condensed, and we obtain quantitative determinations of the condensate fraction. We discuss the experimental consequences of our results. In particular, we explain the meaning of gauge-invariance in ultracold atom systems subject to optically induced gauge potentials, and show how the ability to imprint phase patterns prior to expansion can allow very useful additional information to be extracted from expansion images.

Vortex and Meissner phases of strongly interacting bosons on a two-leg ladder

“…Note that the operators given in Eqs. (2)- (3) depend on the gauge, but the associated expectation values are gauge invariant [46], as can be explicitly seen in the definition of the Meissner current. For the data shown in the figures, j c is computed by restricting the sum to r ∈ [−L/4, L/4] to suppress boundary effects, since in DMRG simulations we use open boundary conditions.…”

“…Bosons on a ladder subjected to gauge fields have been the topic of previous theoretical work [37][38][39][40][41][42][43][44] (see also [45,46] for 2D lattices), yet complete quantitative phase diagrams are lacking. In our work, we use DMRG to systematically explore the full dependence on J ⊥ , φ, and filling and, as a main result, we observe both gapped and gapless Meissner and vortex phases for stronglyinteracting bosons.…”

Artificial Gauge Fields with Ultracold Atoms in Optical Lattices

“…It has been shown that such systems can feature interesting strongly-correlated phases as discussed in Ref. [171]. Other staggered flux distributions, arranged in a chequerboard-like pattern, were proposed using a time-dependent bichromatic optical potential [172].…”

“…5.1). The degeneracy of the ground state depends on the field strength [171] as well as the tunnel couplings and can be probed experimentally by measuring the momentum distribution (Sect. 5.5).…”

Nematic quantum liquid crystals of bosons in frustrated lattices

“…For exactly degenerate single particle spectrum, there is no preferred momentum state for the Bose condensation to occur. Depending on the specific model and parameter regime, bosonic ground states in such frustrated lattices may include chiral composite-fermion states of hard-core bosons [7][8][9] and chiral superfluid/Mott insulator states 10 which spontaneously break time-reversal symmetry, fractional Chern insulators 4,6 , and other exotic broken symmetry states [1][2][3]5,11,12 . From the experimental standpoint, rapid advance of artificial condensed matter systems such as cold atoms and interacting photons in circuit QED system have enabled not only the realization of geometrically frustrated lattices but also lattices subject to synthetic gauge fields [13][14][15][16][17][18][19][20][21][22][23][24] .…”