Constructing a Gapless Spin-Liquid State for the Spin-1/2 J1-J2 Heisenberg Model on a Square Lattice

Category: Scientific Highlights

Published in Physical Review Letters

ABSTRACT:

We construct a class of projected entangled pair states which is exactly the resonating valence bond wave functions endowed with both short range and long range valence bonds. With an energetically preferred resonating valence bond pattern, the wave function is simplified to live in a one-parameter variational space. We tune this variational parameter to minimize the energy for the frustrated spin-1/2 J1−J2 antiferromagnetic Heisenberg model on the square lattice. Taking a cylindrical geometry, we are able to construct four topological sectors with an even or odd number of fluxes penetrating the cylinder and an even or odd number of spinons on the boundary. The energy splitting in different topological sectors is exponentially small with the cylinder perimeter. We find a power law decay of the dimer correlation function on a torus, and a lnL correction to the entanglement entropy, indicating a gapless spin-liquid phase at the optimum parameter.

 

		Figure: Renyi entanglement entropy S2(L) for an area L×L on a torus of size 2L×L with L=4,…,20. The fitted solid red line is of form S2(L)=a1L-(1/2)ln⁡L+b1 for L∈[6:20]; the fitted dashed green line is S2(L)=a2L+b2 for L∈[6:14] and b2=-0.68(1).

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