论文标题
熵尺度定律和量子边缘问题
Entropy scaling law and the quantum marginal problem
论文作者
论文摘要
量子多体经常出现在物理学中经常遵守熵尺度定律，这意味着子系统的纠缠熵可以表示为与其体积和面积线性线性缩放的术语之和，以及与其大小无关的校正项。我们猜想这些状态在有界区域的一组边缘密度矩阵方面具有有效的双重描述，在本地遵守相同的熵缩放法。我们证明了在两个空间维度中的翻译不变系统的限制版本。具体而言，我们证明，翻译不变的边际服从三个非线性约束（所有这些都遵循直接的熵缩放法）必须与无限晶格上的某些全球状态一致。此外，我们得出了与那些边际兼容的最大熵密度兼容的封闭形式的表达，从而得出了在热力学自由能上的变异上限。我们的构造的主要假设完全可以通过拓扑顺序的可解决模型以及某些量子自旋汉密尔顿人的有限温度吉布斯状态满足。
Quantum many-body states that frequently appear in physics often obey an entropy scaling law, meaning that an entanglement entropy of a subsystem can be expressed as a sum of terms that scale linearly with its volume and area, plus a correction term that is independent of its size. We conjecture that these states have an efficient dual description in terms of a set of marginal density matrices on bounded regions, obeying the same entropy scaling law locally. We prove a restricted version of this conjecture for translationally invariant systems in two spatial dimensions. Specifically, we prove that a translationally invariant marginal obeying three non-linear constraints -- all of which follow from the entropy scaling law straightforwardly -- must be consistent with some global state on an infinite lattice. Moreover, we derive a closed-form expression for the maximum entropy density compatible with those marginals, deriving a variational upper bound on the thermodynamic free energy. Our construction's main assumptions are satisfied exactly by solvable models of topological order and approximately by finite-temperature Gibbs states of certain quantum spin Hamiltonians.
