Solving frustration-free spin systems

B. S. Shastry, B. Sutherland, Physica B 108

1981

Earlier work this paper cites.

M. Srednicki, Phys. Rev. Lett. 71

1993

Earlier work this paper cites.

J. Eisert and H. J. Briegel, Phys. Rev. A 64

2001

Earlier work this paper cites.

F. Verstraete, J. I. Cirac, and V. Murg, Adv. Phys. 57

2005

Cited alongside, same era.

K. M. R. Audenaert, J. Eisert, M. B. Plenio, and R. F. Werner, Phys. Rev. A 66

2007

Cited alongside, same era.

G. Vidal, Phys. Rev. Lett. 99

2007

Cited alongside, same era.

S. Bravyi, quant-ph/0602108

Cited in the paper.

R. Movassagh, E. Farhi, J. Goldstone, D. Nagaj, T. J. Osborne, and P. W. Shor, arXiv:1001.1006

Original

Cited in the paper.

We similarly accumulate any single-spin contributions in H U ′ H^{\prime}_{U} which arise from single-spin contributions in H U H_{U}

Cited in the paper.

While we effectively ignore single-spin terms in our analysis, such terms do impose constraints on the ground state manifold, and thus on whether the Hamiltonian is frustration free. However, these may be accounted for with little difficulty

Cited in the paper.

S. Bravyi, M. B. Hastings, and S. Michalakis, arXiv:1001.0344

Original

Cited in the paper.

However, for systems whose ground states have very localized correlations, estimating with respect to a subspace spanned by a small number of product states may scale poorly for large systems. For instance, when the variational set 𝒦 \mathcal{K} is the symmetric subspace Symm ⁡ ( ℂ N ) \Symm(\mathbb{C}^{N}) , the very symmetry of states in 𝒦 \mathcal{K} entails that correlations do not decay spatially but rather are constant

Cited in the paper.

The approach taken here is also expected to work for slightly frustrated Hamiltonians reminiscent of Shastry-Sutherland-type models

Cited in the paper.

One could also perform more sophisticated quantum circuits, such as constant-depth quantum circuits or partial MERA reductions: there will then exist a trade-off between accuracy of the simulation and the efficiency of the procedure

Cited in the paper.

P. Silvi, V. Giovannetti, S. Montangero, M. Rizzi, J. I. Cirac, and R. Fazio, arXiv:0912.0466

Original

Cited in the paper.

D. Aharonov, D. Gottesman, S. Irani, and J. Kempe, Comm. Math. Phys. 287

2009

Later among the works it cites.

J. Eisert, M. Cramer, and M. B. Plenio, Rev. Mod. Phys. 82

2010

Closest in time.

C. R. Laumann, A. M. Läuchli, R. Moessner, A. Scardicchio, and S. L. Sondhi, arXiv:0910.2058

Original

2058

Closest in time.