We study an organic Hydrogen bonded material $\rm{H_2SQ}$ analytically and map out the phase diagram as well as low energy excitations in the relevant parameter space. At zeroth order the dynamics is governed by plaquette interaction (product of $\sigma_z$ over a plaquette) which defines a $Z_2$ gauge theory and a deconfinement phase satisfying "ice rules". The system is studied under additional interactions such as an external Zeeman field (with strength $K$) in $x$-direction, a inter-molecular interaction (with strength $J_1$) and a dipole-dipole interaction with strength $J_2$ such that $K>J_1>J_2$. The effect of dipole-dipole interaction removes the local $Z_2$ symmetry and gives rise to four global degenerate states with Ferroeletric order. Using meanfield analysis we chart out the phase diagram for classical version of the model and find $K_c$ which defines the transition from disordered phase to ordered phase in $J_1, K$ plane for various values of $J_2$. We find that presence of $J_1$ and $J_2$ tends to stabilize the deconfined phases. Over the classical ground states we perform spin-wave analysis and surprisingly find that quantum fluctuations does not remove the classical degeneracy at all at quadratic level. The spin-wave spectrum is found for the four global degenerate ground states which shows both gapped spectrum and gapless spectrum (near the vicinity of CDT transition) for $J_2=0$. However for $J_2$ finite, the spectrum is always gapped. We perform PCUT analysis to improve the results of spin-wave analysis and calculate ground state energy and one particle dispersion and gap at high symmetry point. Using this we draw the phase boundary between confined and deconfined phase in the $K-J_1$ plane. The effect of $J_2$ is also discussed in the resulting phase boundary.
翻译:我们用分析方式研究有机氢质保质材料$\rm{H_2S ⁇ $, 并用分析方式绘制阶段图, 以及相关参数空间中的低能量引用。 在零顺序下, 动态由红色互动( 产产于 $\sigma_z$ z$ 以 plachate) 来调节。 该互动定义了 $2$ 的仪表理论 和满足“ 冰规则” 的解压缩阶段。 系统在额外的互动下进行着研究, 例如 外部Zeman 字段( 配有 $2K$ ), 并绘制了阶段图( 配有 $2K$ ) 。 分子互动( 配有 $ 1 美元 ), 平流动平价平价平价平价平价平价平价平价平价平价平价平价平价平价平价平价平流平流平流。 平流平流平流平流平流分析显示 平流平流平流平流平流平流平流平流平流平流平流平流平流平流平流平流平流平流平流平流平流平流平流平流平流平流平流平流。