Hardcore bosons in a zig-zag optical superlattice

TL;DR

This paper investigates the phase diagram of hard-core bosons in a zig-zag optical superlattice, revealing transitions among superfluid, Mott insulator, and bond-order phases depending on hopping signs and superlattice strength.

Contribution

It provides the first detailed phase diagram for hard-core bosons in a zig-zag lattice, highlighting the role of frustration and superlattice potential in phase transitions.

Findings

Identifies three phases: BO, SLMI, SF.

Shows phase transitions depend on hopping signs and superlattice strength.

Discovers a spontaneously broken translation symmetry in the BO phase.

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 producing a zig-zag geometry and 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.