Phase diagram of hard-core bosons on a zigzag ladder

Abstract

We study hard-core bosons with unfrustrated nearest-neighbor hopping t and repulsive interaction V on a zig-zag ladder. As a function of the boson density ρ and V /t, the ground state displays different quantum phases. A standard one-component Tomonaga-Luttinger liquid is stable for ρ < 1/3 (and ρ > 2/3) at any value of V /t. At commensurate densities ρ = 1/3, 1/2, and 2/3 insulating (crystalline) phases are stabilized for a sufficiently large interaction V . For intermediate densities 1/3 < ρ < 2/3 and large V /t, the ground state shows a clear evidence of a bound state of two bosons, implying gapped single-particle excitations but gapless excitations of boson pairs. Here, the low-energy properties may be described by a two-component Tomonaga-Luttinger liquid with a finite gap in the antisymmetric sector. Finally, for the same range of boson densities and weak interactions, the system is again a one-component Tomonaga-Luttinger liquid with no evidence of any breaking of discrete symmetries, in contrast to the frustrated case, where a Z2 symmetry breaking has been predicted.

Supersolid in a one-dimensional model of hard-core bosons

“…Tracking the positions of the peaks yields k m = 2πρ. Similar feature has been studied before in a system of hardcore bosons in zig-zag ladder [29]. From Fig.…”

“…Similar feature has been studied before in a system of hardcore bosons in zig-zag ladder [29]. From Fig.…”

Polar molecules in frustrated triangular ladders

“…In contrast to the case of soft-core bosons, the SS phases in the hard-core case are characterized by a peak in S CDW at a value k max incommensurate with the lattice and dependent on the filling ρ [24,47]. As mentioned above, in the present case, there exist two CDW phases with S CDW peaked at k max = π (ρ = 1/2) and 2π/3 (ρ = 2/3).…”

Quantum phases and phase transitions of frustrated hard-core bosons on a triangular ladder

“…[15][16][17] Recently, a related model in one dimension with equal nearest-and next-nearest-neighbor hopping and nearestand next-nearest-neighbor interactions has also been studied. 18 In this paper, we study the model given by Eq. (1) at half filling numerically using the density matrix renormalizationgroup (DMRG) algorithm in the entire parameter space of t < 0 and V > 0 with t > 0.…”