论文标题
普遍的翻译不变性汉密尔顿人
Universal Translationally-Invariant Hamiltonians
论文作者
论文摘要
在这项工作中，我们将通用量子哈密顿量的概念扩展到了翻译不变的系统的设置。我们提出了一种结构，该结构允许具有最接近邻次相互作用，开放边界和翻译对称性的二维自旋晶格，以模拟任何本地目标哈密顿量----。在其低能子空间内重现整个目标系统以任意精确。由于这意味着能够模拟具有翻译不变耦合的非翻译不变的多体系统，因此任何效果，例如与外部混乱系统（例如多体定位也可能发生在翻译不变系统的低能希尔伯特太空领域。然后，我们绘制优化的通用晶格结构的变体，以模拟翻译不变的目标汉密尔顿人。最后，我们证明，由海森伯格或XY相互作用组成的Qubit Hamiltonians的互动强度仅限于嵌入$ \ Mathbb {r}^d $的连接翻译不变的图的边缘是通用的，并且可以有效地将Hamiltonian在$ \ MATHBB BB BB {d $}^d $}^d $ r}中有效地模拟。
In this work we extend the notion of universal quantum Hamiltonians to the setting of translationally-invariant systems. We present a construction that allows a two-dimensional spin lattice with nearest-neighbour interactions, open boundaries, and translational symmetry to simulate any local target Hamiltonian---i.e. to reproduce the whole of the target system within its low-energy subspace to arbitrarily-high precision. Since this implies the capability to simulate non-translationally-invariant many-body systems with translationally-invariant couplings, any effect such as characteristics commonly associated to systems with external disorder, e.g. many-body localization, can also occur within the low-energy Hilbert space sector of translationally-invariant systems. Then we sketch a variant of the universal lattice construction optimized for simulating translationally-invariant target Hamiltonians. Finally we prove that qubit Hamiltonians consisting of Heisenberg or XY interactions of varying interaction strengths restricted to the edges of a connected translationally-invariant graph embedded in $\mathbb{R}^D$ are universal, and can efficiently simulate any geometrically local Hamiltonian in $\mathbb{R}^D$.
