Hard-core bosons in a zig-zag optical superlattice

Abstract

We study a system of hard-core bosons at half-filling in a one-dimensional optical superlattice. The bosons are allowed to hop to nearest and next-nearest neighbor sites. We obtain the ground state phase diagram as a function of microscopic parameters using the finite-size density matrix renormalization group (FS-DMRG) method. Depending on the sign of the next-nearest neighbor hopping and the strength of the superlattice potential the system exhibits three different phases, namely the bond-order (BO) solid, the superlattice induced Mott insulator (SLMI) and the superfluid (SF) phase. When the signs of both hopping amplitudes are the same (the "unfrustrated" case), the system undergoes a transition from the SF to the SLMI at a non-zero value of the superlattice potential. On the other hand, when the two amplitudes differ in sign (the "frustrated" case), the SF is unstable to switching on a superlattice potential and also exists only up to a finite value of the next nearest neighbor hopping. This part of the phase diagram is dominated by the BO phase which breaks translation symmetry spontaneously even in the absence of the superlattice potential and can thus be characterized by a bond order parameter. The transition from BO to SLMI appears to be first order.

One-dimensional sawtooth and zigzag lattices for ultracold atoms

“…Intriguingly, a nearly flat band can be also obtained by including the spin degrees of freedom in the presence of the spin-orbit coupling [22][23][24] or the dipolar interactions [25]. We note similar flattened quartic dispersion is also available in the shaken lattice [26].In this work, we describe a one-dimensional tunable optical zigzag lattice [27,28] and then analyse the geometric conversion from a zigzag into a sawtooth optical lattice that provides a nearly flat band [9,18]. Especially, a sawtooth lattice has attracted significant interest due to the flat band structure but the creation of tunable sawtooth geometry has not been proposed to our knowledge.…”

“…We analyse the band structure of the sawtooth and zigzag lattices for various lattice settings and provide a recipe for obtaining a nearly flat band in the sawtooth configuration. Besides the sawtooth lattice containing a flat band, a one-dimensional zigzag chain [27,28] also reveals particularly rich physics due to the interplay between frustration imposed by lattice geometry and two (three)-body interactions. Indeed, a chiral bosonic superfluid is expected in a zigzag lattice, which may become a Mott insulator even at small interactions [27,28].Creation of optical zigzag and sawtooth lattices An array of one-dimensional zigzag lattices can be created in twodimensional superlattice geometry.…”

“…In this work, we describe a one-dimensional tunable optical zigzag lattice [27,28] and then analyse the geometric conversion from a zigzag into a sawtooth optical lattice that provides a nearly flat band [9,18]. Especially, a sawtooth lattice has attracted significant interest due to the flat band structure but the creation of tunable sawtooth geometry has not been proposed to our knowledge.…”

Quantum phases of attractive bosons on a Bose-Hubbard ladder with three-body constraint

“…The extra coupling between the legs of the ladder makes these systems unique, as a result of which, the quantum phase transitions are influenced substantially even in a simple model like the Bose-Hubbard ladder [25][26][27]. Also, the effect of kinetic frustration along with various interactions can lead to interesting new phases in ladder systems [28][29][30][31][32][33][34][35][36], which are not possible in one dimensional lattice systems. In recent years, it has been shown that novel quantum phases such as a trimer liquid and the devil's staircase can arise from atoms and molecules possessing long range interactions [37,38].…”

Polar molecules in frustrated triangular ladders

“…The rich physics resulting from the interplay between frustration and interactions has attracted growing theoretical attention [15][16][17][18][19][20][21][22][23][24][25]. Recently, experiments on dynamically frustrated optical lattices in the presence of a synthetic gauge field have investigated the onset of chirality by observing the Meissner to vortex-phase transition [26].…”