Absence of Single-Particle Bose-Einstein Condensation at Low Densities for Bosons with Correlated Hopping

Motivated by the physics of mobile triplets in frustrated quantum magnets, the properties of a two-dimensional model of bosons with correlated hopping are investigated. A mean-field analysis reveals the presence of a pairing phase without single-particle Bose-Einstein condensation (BEC) at low densities for sufficiently strong correlated hopping, and of an Ising quantum phase transition towards a BEC phase at larger density. The physical arguments supporting the mean-field results and their implications for bosonic and quantum spin systems are discussed.

Figure 1

The diagonal bonds ($-t^{\prime }$) denote a correlated hopping process, and the nearest neighboring bonds denote the single-particle hopping ($-t$).

Figure 2

The mean-field quantum phase diagram. $n^{*}$ is the critical density at which, for a given $\alpha =t^{\prime }/(t+t^{\prime })$, the single-particle condensate density $n_c$ becomes zero. This marks the onset of the pairing phase with gapped quasiparticle excitations.

Figure 3

The variation of the quasiparticle gap and the mean-field order parameters as a function of $n$ for a fixed $\alpha$. While $n_c\ne 0$ only in the single-particle BEC phase ($n\gtrsim 0.072$), the pairing amplitude $\Delta \ne 0$ in both phases.

Figure 4

The behavior of different order parameters as a function of $\alpha$ for $n=0.05$. For $\alpha \gtrsim 0.78$, the condensate density ($n_c$) vanishes, and the system goes into the pairing ground state.

Figure 5

The temperature dependence of $\Delta$, $\kappa$, and $n$ for a given $\mu$ and $\alpha$. Inset: dependence of $T_c$ on the density.