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Register a new userGapless spin liquid ground state of spin-1/2 $J_1$-$J_2$ Heisenberg model on square lattices
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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.
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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).
We use the state-of-the-art tensor network state method, specifically, the finite projected entangled pair state (PEPS) algorithm, to simulate the global phase diagram of spin-$1/2$ $J_1$-$J_2$ Heisenberg model on square lattices up to $24times 24$. We provide very solid evidences to show that the nature of the intermediate nonmagnetic phase is a gapless quantum spin liquid (QSL), whose spin-spin and dimer-dimer correlations both decay with a power law behavior. There also exists a valence-bond solid (VBS) phase in a very narrow region $0.56lesssim J_2/J_1leq0.61$ before the system enters the well known collinear antiferromagnetic phase. We stress that our work gives rise to the first solid PEPS results beyond the well established density matrix renormalization group (DMRG) through one-to-one direct benchmark for small system sizes. Thus our numerical evidences explicitly demonstrate the huge power of PEPS for solving long-standing 2D quantum many-body problems. The physical nature of the discovered gapless QSL and potential experimental implications are also addressed.
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 $J_1=1$.
We numerically study the Heisenberg models on triangular lattices by extending it from the simplest equilateral lattice with only the nearest-neighbor exchange interaction. We show that, by including an additional weak next-nearest-neighbor interaction, a quantum spin-liquid phase is stabilized against the antiferromagnetic order. The spin gap (triplet excitation gap) and spin correlation at long distances decay algebraically with increasing system size at the critical point between the antiferromagnetic phase and the spin-liquid phase. This algebraic behavior continues in the spin-liquid phase as well, indicating the presence of an unconventional critical (algebraic spin-liquid) phase characterized by the dynamical and anomalous critical exponents $z+etasim1$. Unusually small triplet and singlet excitation energies found in extended points of the Brillouin zone impose constraints on this algebraic spin liquid.
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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