Spin Liquid Ground State of the Spin-1/2 Square $J_1$-$J_2$ Heisenberg Model

Details Spin Liquid Ground State of the Spin-1/2 Square $J_1$-$J_2$ Heisenberg Model Spin Liquid Ground State of the Spin-1/2 Square $J_1$-$J_2$ Heisenberg Model

2011-12-10

arxiv.org/abs/1112.2241v1

Physics

Condensed Matter

Strongly Correlated Electrons

11 pages, 5 figures in the main text, 1 figures in the Supplementary Information

Scientific paper

We perform highly accurate density matrix renormalization group (DMRG) simulations to investigate the ground state properties of the spin-1/2 antiferromagnetic square lattice Heisenberg $J_1$-$J_2$ model. Based on studies of numerous long cylinders with circumferences of up to 10 lattice spacings, we obtain strong evidence for a topological quantum spin liquid state in the region $0.41\leq J_2/J_1\leq 0.62$, separating conventional N\'eel and striped antiferromagnetic states for smaller and larger $J_2/J_1$, respectively. The quantum spin liquid is characterized numerically by the absence of magnetic or valence bond solid order, and non-zero singlet and triplet energy gaps. Furthermore, we positively identify its topological nature by measuring a non-zero topological entanglement entropy and a non-trivial finite size dimerization effect depending upon the parity of the circumference of the cylinder.

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