Family of Exactly Solvable Models with an Ultimate Quantum Paramagnetic Ground State

We present a family of two-dimensional frustrated quantum magnets solely based on pure nearest-neighbor Heisenberg interactions which can be solved quasiexactly. All lattices are constructed in terms of frustrated quantum cages containing a chiral degree of freedom protected by frustration. The ground states of these models are dubbed ultimate quantum paramagnets and exhibit an extensive entropy at zero temperature. We discuss the unusual and extensively degenerate excitations in such phases. Implications for thermodynamic properties as well as for decoherence free quantum computation are discussed.

Figure 1

(a) Heisenberg model with exchange $J$ on a periodically coupled chain of $N_t$ triangles. (b) Illustration of the two degenerate ground states. Thick (green) bonds represent singlet states. (c) The shortest segment of a Shastry-Sutherland chain consists of two vertical and one horizontal dimer. Note that the two dimers on the edges are part of the quantum cage.

Figure 2

Three representative lattice models with (a) $N_t=3$, (b) $N_t=4$, and (c) $N_t=6$. The left-hand side illustrates the chiral quantum cage of each lattice which contains a triangle chain shielded by surrounding dimers. The right-hand side represents 2D lattices made by adding dimers which couple cages. The dimer connecting two cages forms the shortest segment of a Shastry-Sutherland chain (illustrated in black).

Figure 3

Localized excitations on a chiral quantum cage with $N_t=3$ as a function of $x$. Thick gray line at energy $J$ corresponds to the exact triplet on the connecting dimer. Blue horizontal lines represent excitations inside the star. Dashed lines involve localized triplons on the outer shell which are the only single modes depending on $x$. The lowest of these modes is the energy of a single triplon. Other dashed lines correspond to a triplon plus an excitation inside the star. The number in square brackets gives the degeneracy on the cluster shown in the inset which has been diagonalized.

Figure 4

(a) The fully frustrated plaquette is the smallest inner star. (b) A direct coupling of stars ($N_t=3$ shown) leads to a different family of models. (c) Illustration of the two possible close packings of $N_t=6$ quantum cages on the kagome lattice. Left-hand figure represents the proposed valence bond solid ground state with the 36-site unit cell. Right-hand figure represents a diluted kagome lattice where sites marked by gray squares are removed.