Classical mean-field, spin-wave, and perturbative continuous unitary transformation analyses of the squaric acid system H_2SQ

摘要

We study analytically an organic hydrogen-bonded material, H(2)SQ, whose dynamics is governed by (i) a four-spin plaquette interaction J(0), (ii) Ising-like intramolecular interaction J(1), (iii) a dipole-dipole interaction J(2), and (iv) an external transverse Zeeman field K; the symbols denote the strength of each interaction such that J(0) > J(1) > J(2), while K can be taken arbitrary. We chart out the classical phase diagram going to an ordered state from a disordered, degenerate ground state. Our spin-wave analysis above the classical ground states shows that there is no order-disorder transition associated with this. We argue that this happens due to the existence of a macroscopic number of symmetry operators. For finite J(2), the system shows a paraelectric to ferroelectric transition giving four global degenerate ferroelectric orders for which the high-field spin-wave spectrum is found to be gapless and linear near the phase transition point. In low-field, the spin-wave spectrum is gapped and quadratic. We perform a perturbative continuous unitary transformation (PCUT) to improve the results of spin-wave analysis and obtain the ground-state energy, the one-particle dispersion, and the gap and phase boundary in various parameter regimes. In the end, we briefly discuss the mapping of this model to a toric code model (TCM) for large J(0) and small field values K.