A Variational Approach to Understanding the Ground State of a Square-Lattice Heisenberg Antiferromagnet

Nakagawa, Shin-ichi; Hamada, Takehiko; Kane, J.; Natsume, Yuhei

doi:10.1143/jpsj.59.1131

Cited by 9 publications

(1 citation statement)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The RVB state has often been used as a variational wavefunction for approximating the ground states of the spin-1/2 Heisenberg model in square [82,83], triangular [84], and kagome lattices [85]. A numerical study on small clusters up to 26 spins [86] has shown that, by taking into account the Marshall's sign rule [87], the RVB state with only a few variational parameters can accurately represent the ground state of the spin-1/2 Heisenberg model in a square lattice, and that the (long-range) RVB state substantially improves the variational energy and the variational state as compared to the short-range RVB state.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Symmetry-adapted variational quantum eigensolver

Seki,

Shirakawa,

Yunoki

2019

Preprint

View full text Add to dashboard Cite

We propose a scheme to restore spatial symmetry of Hamiltonian in the variational-quantum-eigensolver (VQE) algorithm for which quantum circuit structures used usually break the Hamiltonian symmetry. The symmetry-adapted VQE scheme introduced here simply applies the projection operator, which is hermitian but not unitary, to restore the spatial symmetry in a desired irreducible representation of the spatial group. The entanglement of a quantum state is still represented in a quantum circuit but the nonunitarity of the projection operator is treated classically as postprocessing in the VQE framework. By numerical simulations for a spin-1/2 Heisenberg model on a one-dimensional ring, we demonstrate that the symmetry-adapted VQE scheme with a shallower quantum circuit can achieve significant improvement in terms of the fidelity of the ground state and has a great advantage in terms of the ground state energy with decent accuracy, as compared to the non-symmetry-adapted VQE scheme. We also demonstrate that the present scheme can approximate low-lying excited states that can be specified by symmetry sectors.

show abstract