Deconfined Gapless phases and criticalities in Shastry-Sutherland Antiferromagnet

Abstract

Antiferromagnets on the Shastry-Sutherland lattice have attracted lots of research interest due to the possible existence of deconfined criticality. In the present work, we study the $J_1$-$J_2$-$J_r$ model using Variational Monte Carlo (VMC) method, where $J_1$, $J_2$, $J_r$ stand for the nearest-neighbor, next nearest neighbor and ring exchange interactions respectively. An empty plaquette (EP) phase with spontaneous mirror symmetry breaking is reproduced. However, the EP phase in the VMC approach is $Z_2$ deconfined and have Majorana-type gapless spinon excitations, which is qualitatively different from the EP phase in literature. The central observation of the present study is the gapless $Z_2$ Quantum spin liquid phase resulting from the competition between the EP phase, the full plaquette (FP) phase and the antiferromagnetic Néel phase. While the phase transition from the $Z_2$ QSL phase to the EP phase is likely of Landau-Ginzburg type, the continuous transitions to the confined FP and Néel phases are exotic and need to be further explored.

Figures (13)

• Figure 1: Phase diagram of $J_1$-$J_2$-$J_r$ model on the Shastry-Sutherland lattice. The solid/dotted lines represent first-order/continuous phase transitions.
• Figure 2: (a) The SS lattice model with the translation $T_x, T_y$, rotation $C_4$, mirror $M_{x\pm y}$, and glide reflection $G_x, G_y$ symmetries. (b) The spin liquid ansatz Z2Azz13SS with $(t_{ij},\Delta_{ij})$ standing for the hopping and pairing parameters on the corresponding bonds.
• Figure 3: Energy difference between plaquette-ordered states and the QSL Z2Azz13SS, namely $E_{\rm PO}-E_{\rm QSL}$, for $J_1/J_2=0.71$.
• Figure 4: Spinon dispersion of the gapless $Z_2$ QSL phase. Four Majorana cones protected by the combined $IT$ symmetry are locating on the diagonal $(k_x\pm k_y)$-lines.
• Figure 5: (a)Two patterns of empty plaquette order in the EP phase (uper pattern: $\eta_x>1, \eta_y<1$; lower pattern: $\eta_x<1, \eta_y>1$). (b) Two patterns of full plaquette order in the FP phase (uper pattern: $\eta_x>1, \eta_y>1$; lower pattern: $\eta_x<1, \eta_y<1$). (c) Ansatz of the Néel phase having SSG symmetry, where the upper/lower graph respectively represents the hopping of the $f_\uparrow$/$f_\downarrow$ spinons, and the red lines indicate enhanced hopping amplitudes.