Approximating the ground state of gapped quantum spin systems

Abstract

We consider quantum spin systems defined on finite sets $V$ equipped with a metric. In typical examples, $V$ is a large, but finite subset of Z^d. For finite range Hamiltonians with uniformly bounded interaction terms and a unique, gapped ground state, we demonstrate a locality property of the corresponding ground state projector. In such systems, this ground state projector can be approximated by the product of observables with quantifiable supports. In fact, given any subset, X, of V the ground state projector can be approximated by the product of two projections, one supported on X and one supported on X^c, and a bounded observable supported on a boundary region in such a way that as the boundary region increases, the approximation becomes better. Such an approximation was useful in proving an area law in one dimension, and this result corresponds to a multi-dimensional analogue.

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• Renormalization group constructions of topological quantum liquids and beyond
• Constraints on order and disorder parameters in quantum spin chains
• A class of asymmetric gapped Hamiltonians on quantum spin chains and its characterization I
• Tensor Networks for Lattice Gauge Theories beyond one dimension: a Roadmap
• Mathematical open problems in Projected Entangled Pair States
• Local Perturbations Perturb -Exponentially- Locally
• Non-equilibrium finite temperature dynamics of magnetic quantum systems: Applications to spin-polarized scanning tunneling microscopy
• On Hastings factorization for quantum many-body systems in the infinite volume setting