Adrian E. Feiguin, Rolando D. Somma, Cristian D. Batista
We present a numerical method based on real-space renormalization that outputs the exact ground space of Hamiltonians that satisfy a frustration-free property. The complexity of our method is polynomial in the degeneracy of the ground spaces of the Hamiltonians involved in the renormalization steps. We apply the method to obtain the full ground spaces of two spin systems.The first system is a spin-1/2 Heisenberg model with four-spin cyclic-exchange interactions defined on a square lattice. In this case, we study systems up to 160 spins and find a triplet ground state that differs from the singlet states obtained in C.D. Batista and S. Trugman, Phys. Rev. Lett. 93, 217202 (2004). We characterize such a triplet state as consisting of two deconfined spinons that propagate in a background of fluctuating singlet dimers. The second system is a spin-1/2 Heisenberg chain with uniaxial exchange anisotropy and next-nearest-neighbor interactions. In this case, the method finds a ground-space degeneracy that scales quadratically with the system size and outputs the full ground space efficiently. Our method can substantially outperform methods based on exact diagonalization and is more efficient than methods based on renormalization groups when the ground-space degeneracy is large.
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http://arxiv.org/abs/1303.0305
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