Magnetic Field Induced Transition in a Quantum Magnet Described by the Quantum Dimer Model

The effect of a magnetic field on a gapped quantum magnet is described within the framework of the quantum dimer model. A minimal model describing the proliferation of itinerant spinons above a critical field is proposed and investigated by Lanczos exact diagonalizations and quantum Monte Carlo simulations. For both square and triangular lattices, it is shown that spinons are fully polarized and Bose condense. This offers a novel scenario of a quantum critical point in the dimer-liquid phase (triangular lattice) characterized by the continuous appearance of a spinon superfluid density, contrasting with the usual triplet condensation picture. The possible role of other spinon kinetic terms neglected in the model are discussed.

Figure 1

The four different kinetic processes of the effective Hamiltonian and their corresponding matrix elements in the case of a (nonfrustrated) Heisenberg quantum magnet. $\alpha =1/\sqrt{2}$ is the singlet normalization factor and $J$ the spin coupling. The sign convention for dimers is the one of Ref. 6.

Figure 2

The lowest-energy levels for four and six spinons on a $4\times 4$ square lattice in the subspace of zero momentum. The couplings are $t/J=0.2$ and $v/J=0.5$ and states are classified according to the total spin $S$.

Figure 3

Phase diagram of the QDM given by Eq. (1) as a function of magnetic field, for the square lattice (full squares) and the triangular lattice (empty triangles). The dashed and continuous lines indicate first- and second-order transitions, respectively.

Figure 4

(a) Spinon concentration for different values of $t$ as a function of the magnetic field $h$ (both in units of $J$) for the triangular lattice at $v=0.95$. (b) Same as (a) but for the square lattice and at $v=0.8$. The dashed lines show the locations of the first-order phase transitions. Error bars are of the size of the symbols. Inset: typical behaviors of $F(x)$ in the case of a first order phase transition (see text).