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تسجيل مستخدم جديدGapless 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 fou
nd 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.
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