Computing local properties in the trivial phase

• URL: http://arxiv.org/abs/2001.10763v1
• Date: Wed, 29 Jan 2020 11:33:10 GMT
• Title: Computing local properties in the trivial phase
• Authors: Yichen Huang
• Abstract summary: A translation-invariant gapped local Hamiltonian is in the trivial phase if it can be connected to a completely decoupled Hamiltonian. We show that the expectation value of a local observable can be computed in time.
• Score: 2.741266294612776
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A translation-invariant gapped local Hamiltonian is in the trivial phase if it can be connected to a completely decoupled Hamiltonian with a smooth path of translation-invariant gapped local Hamiltonians. For the ground state of such a Hamiltonian, we show that the expectation value of a local observable can be computed in time $\text{poly}(1/\delta)$ in one spatial dimension and $e^{\text{poly}\log(1/\delta)}$ in two and higher dimensions, where $\delta$ is the desired (additive) accuracy. The algorithm applies to systems of finite size and in the thermodynamic limit. It only assumes the existence but not any knowledge of the path.

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