Hidden Order in 1D Bose Insulators

We investigate the phase diagram of spinless bosons with long range ($\propto 1/r^3$) repulsive interactions, relevant to ultracold polarized atoms or molecules, using density matrix renormalization group. Between the two conventional insulating phases, the Mott and density wave phases, we find a new phase possessing hidden order revealed by nonlocal string correlations analogous to those characterizing the Haldane gapped phase of integer spin chains. We develop a mean field theory that describes the low-energy excitations in all three insulating phases. This is used to calculate the absorption spectrum due to oscillatory lattice modulation. We predict a sharp resonance in the spectrum due to a collective excitation of the new phase that would provide clear evidence for the existence of this phase.

Figure 1

Phase diagram of the Hamiltonian (1) in the ($U$, $V$) plane, obtained from DMRG. The phases that appear in the diagram are: superfluid (○), Mott insulator (□), density wave ($\mathrm{x}$) and Haldane insulator (▵). Inset: density wave (dashed line) and string (solid line) correlations at a particular ($U$, $V$) point [see (3, 4),]. This point is in the HI phase, as can be seen from the fact that string correlations do not decay, whereas DW correlations decay rapidly.

Figure 2

(a) DW order parameter (▵) and string order parameter (□) as a function of $V$ along the line $U=6t$. (b) Gaps to neutral and charged excitations, ${\Delta }_0$ (○) and ${\Delta }_1$ (⋄), respectively, (see text) along the same line.

Figure 3

Absorption spectrum (5) calculated from the mean field theory along the dotted line in the inset [mean field phase diagram of (7)]. The dotted line in the spectra marks the position of a quasiparticle peak seen only in the HI phase (b). The dashed and dash-dotted lines mark the edges of two particle continua.