标题： PEPS作为局域哈密顿量的独特基态 显示英文标题

标题： PEPS as unique ground states of local Hamiltonians

摘要： 本文中我们研究了任意格点上的投影纠缠对态（PEPS）。 我们为每个PEPS构建局域母哈密顿量，并找出一个条件，在此条件下该态是哈密顿量的唯一基态。 这个条件被一般的PEPS以及像AKLT模型这样的例子所验证，它是在任意局域区域的边界与体之间的一种单射关系。 虽然这表明在一维情况下存在能隙，但我们将会展示在某些情况（例如，在二维蜂窝状格点上）下，母哈密顿量可以是无能隙的，并具有临界基态。 为了证明这一点，我们引入经典模型和量子模型之间的映射，并证明在这种情况下边界与体之间的单射关系仅依赖于晶格几何结构。 显示英文摘要

摘要： 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 implies the existence of an energy gap in the 1D case we will show that in certain cases (e.g., on a 2D hexagonal lattice) the parent Hamiltonian can be gapless with a critical ground state. To show this we invoke a mapping between classical and quantum models and prove that in these cases the injectivity relation between boundary and bulk solely depends on the lattice geometry.