Cluster expansion for ground states of local Hamiltonians

Peps as unique ground states of local hamiltonians

In this paper we consider projected entangled pair states (PEPS) on arbitrary lattices. We construct local parent Hamiltonians for each PEPS and isolate a condition under which the state is the unique ground state of the Hamiltonian. This condition, verified by generic PEPS and examples like the AKLT model, is an injective relation between the boundary and the bulk of any local region. While it...

Entanglement and Ground States of Gapped Hamiltonians

Ground State Connectivity of Local Hamiltonians

The study of ground spaces of local Hamiltonians is a fundamental task in condensed matter physics. In terms of computational complexity theory, a common focus has been to estimate a given Hamiltonian’s ground state energy. However, from a physics perspective, it is often more relevant to understand the structure of the ground space itself. In this paper, we pursue this latter direction by intr...

On preparing ground states of gapped Hamiltonians: An efficient Quantum Lovász Local Lemma

A frustration-free local Hamiltonian has the property that its ground state minimises the energy of all local terms simultaneously. In general, even deciding whether a Hamiltonian is frustration-free is a hard task, as it is closely related to the QMA1-complete quantum satisfiability problem (QSAT) – the quantum analogue of SAT, which is the archetypal NP-complete problem in classical computer ...

Homogeneous binary trees as ground states of quantum critical Hamiltonians

P. Silvi,1 V. Giovannetti,2 S. Montangero,3 M. Rizzi,4 J. I. Cirac,4 and R. Fazio2,5 1International School for Advanced Studies (SISSA), Via Bonomea 265, I-34136 Trieste, Italy 2NEST, Scuola Normale Superiore and Istituto di Nanoscienze-CNR, I-56127 Pisa, Italy 3Institut für Quanteninformationsverarbeitung, Universität Ulm, D-89069 Ulm, Germany 4Max-Planck-Institut für Quantenoptik, Hans-Kopfer...