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Register a new userThe quantum $J_1$-$J_1$-$J_2$ spin-1/2 Heisenberg model: Influence of the interchain coupling on the ground-state magnetic ordering in 2D
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We study the phase diagram of the 2D $J_1$-$J_1$-$J_2$ spin-1/2 Heisenberg model by means of the coupled cluster method. The effect of the coupling $J_1$ on the Neel and stripe states is investigated. We find that the quantum critical points for the Neel and stripe phases increase as the coupling strength $J_1$ is increased, and an intermediate phase emerges above the region at $J_1 approx 0.6$ when $J_1=1$. We find indications for a quantum triple point at $J_1 approx 0.60 pm 0.03$, $J_2 approx 0.33 pm 0.02$ for $J_1=1$.
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The spin-1/2 $J_1$-$J_2$ Heisenberg model on square lattices are investigated via the finite projected entangled pair states (PEPS) method. Using the recently developed gradient optimization method combining with Monte Carlo sampling techniques, we are able to obtain the ground states energies that are competitive to the best results. The calculations show that there is no Neel order, dimer order and plaquette order in the region of 0.42 $lesssim J_2/J_1lesssim$ 0.6, suggesting a single spin liquid phase in the intermediate region. Furthermore, the calculated staggered spin, dimer and plaquette correlation functions all have power law decay behaviours, which provide strong evidences that the intermediate nonmagnetic phase is a single gapless spin liquid state.
Liu et al. [Phys.Rev.B 98, 241109 (2018)] used Monte Carlo sampling of the physical degrees of freedom of a Projected Entangled Pair State (PEPS) type wave function for the $S=1/2$ frustrated $J_1$-$J_2$ Heisenberg model on the square lattice and found a non-magnetic state argued to be a gapless spin liquid when the coupling ratio $g=J_2/J_1$ is in the range $g in [0.42,0.6]$. Here we show that their definition of the order parameter for another candidate ground state within this coupling window---a spontaneously dimerized state---is problematic. The order parameter as defined will not detect dimer order when lattice symmeties are broken due to open boundaries or asymmetries originating from the calculation itself. Thus, a dimerized phase for some range of $g$ cannot be excluded (and is likely based on several other recent works).
Strongly correlated systems with geometric frustrations can host the emergent phases of matter with unconventional properties. Here, we study the spin $S = 1$ Heisenberg model on the honeycomb lattice with the antiferromagnetic first- ($J_1$) and second-neighbor ($J_2$) interactions ($0.0 leq J_2/J_1 leq 0.5$) by means of density matrix renormalization group (DMRG). In the parameter regime $J_2/J_1 lesssim 0.27$, the system sustains a N{e}el antiferromagnetic phase. At the large $J_2$ side $J_2/J_1 gtrsim 0.32$, a stripe antiferromagnetic phase is found. Between the two magnetic ordered phases $0.27 lesssim J_2/J_1 lesssim 0.32$, we find a textit{non-magnetic} intermediate region with a plaquette valence-bond order. Although our calculations are limited within $6$ unit-cell width on cylinder, we present evidence that this plaquette state could be a strong candidate for this non-magnetic region in the thermodynamic limit. We also briefly discuss the nature of the quantum phase transitions in the system. We gain further insight of the non-magnetic phases in the spin-$1$ system by comparing its phase diagram with the spin-$1/2$ system.
Using density-matrix renormalization-group calculations for infinite cylinders, we elucidate the properties of the spin-liquid phase of the spin-$frac{1}{2}$ $J_1$-$J_2$ Heisenberg model on the triangular lattice. We find four distinct ground-states characteristic of a non-chiral, $Z_2$ topologically ordered state with vison and spinon excitations. We shed light on the interplay of topological ordering and global symmetries in the model by detecting fractionalization of time-reversal and space-group dihedral symmetries in the anyonic sectors, which leads to coexistence of symmetry protected and intrinsic topological order. The anyonic sectors, and information on the particle statistics, can be characterized by degeneracy patterns and symmetries of the entanglement spectrum. We demonstrate the ground-states on finite-width cylinders are short-range correlated and gapped; however some features in the entanglement spectrum suggest that the system develops gapless spinon-like edge excitations in the large-width limit.
We study the phase diagram of the frustrated Heisenberg model on the triangular lattice with nearest and next-nearest neighbor spin exchange coupling, on 3-leg ladders. Using the density-matrix renormalization-group method, we obtain the complete phase diagram of the model, which includes quasi-long-range $120^circ$ and columnar order, and a Majumdar-Ghosh phase with short-ranged correlations. All these phases are non-chiral and planar. We also identify the nature of phase transitions.
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