Supersolid Phase Induced by Correlated Hopping in Spin-$1/2$ Frustrated Quantum Magnets

We show that correlated hopping of triplets, which is often the dominant source of kinetic energy in dimer-based frustrated quantum magnets, produces a remarkably strong tendency to form supersolid phases in a magnetic field. These phases are characterized by simultaneous modulation and ordering of the longitudinal and transverse magnetization, respectively. Using quantum Monte Carlo and a semiclassical approach for an effective hard-core boson model with nearest-neighbor repulsion on a square lattice, we prove, in particular, that a supersolid phase can exist even if the repulsion is not strong enough to stabilize an insulating phase at half-filling. Experimental implications for frustrated quantum antiferromagnets in a magnetic field at zero and finite temperature are discussed.

Figure 1

Difference between single and correlated triplet hopping in a frustrated geometry. (a) Spin language: thick solid (dashed) lines stand for dimer triplet (singlet), thin solid lines for interdimer coupling. (b) Bosonic language: filled (open) circles denote hard-core boson sites that are occupied (empty).

Figure 2

Zero-temperature phase diagram for $t^{\prime }=0.95$ as a function of the $1/V$ versus $\mu /V$. Open squares (closed circles) denote first (second) order phase transitions deduced from QMC data. Thin dotted lines are SCA results. The other lines (solid and thick dashed lines for second and first order transitions, respectively) are obtained by interpolating between numerical data. The data for low densities including the paired superfluid (PSF) have been taken from Ref. 23.

Figure 3

Bosonic phases revealed by (a) the density $n$, (b) the static structure factor $S(\pi ,\pi )/N$, and (c) the superfluid stiffness $\rho$ as a function of the chemical potential for two representative cases. Left panel: $t^{\prime }=0.95$ and $V=2.2$ ($1/V=0.455$). Right panel: $t^{\prime }=0.75$ and $V=2.8$ ($1/V=0.36$). SF stands for superfluid, CB for checkerboard solid, and SS for supersolid.

Figure 4

Zero-temperature phase diagram for $V=2.8$ as a function of the correlated hopping $t^{\prime }$ versus the chemical potential $\mu$. Open squares (closed circles) denote first (second) order phase transitions deduced from QMC data. All the lines have been obtained by interpolating between numerical data. Thin dotted lines and the boundaries to the empty and full systems are SCA results.

Figure 5

(a) Thermal melting of the supersolid for $t^{\prime }=0.75$ and $V=2.8$: Binder ratio (empty black symbols) and superfluid stiffness (filled blue symbols) as a function of temperature for $\mu =6$ (upper panel) and $\mu =10$ (lower panel). The location of the melting transitions are marked by vertical dashed lines. (b) Finite-temperature phase diagram as a function of the chemical potential for $t^{\prime }=0.75$ and $V=2.8$ ($1/V=0.36$). (c) Same as (b) for $t^{\prime }=0.95$ and $V=2.2$ ($1/V=0.455$). In (b) and (c), lines are interpolations between numerical data, and error bars are smaller than the symbols.