Locality of dynamics in general harmonic quantum systems
Locality of dynamics in general harmonic quantum systems
复制标题
一般调和量子系统中动力学的局域性
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
J. Eisert
中科院分区：
文献类型：
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作者：
M. Cramer;A. Serafini;J. Eisert
Lieb-Robinson定理指出，量子晶格系统的动力学近似保持了局部性。只要有有限维成分，在局部哈密顿量下随时间演化的观测量基本上会在它们的支持下线性增长，直到指数抑制校正。在这项工作中，我们制定了一般的调和系统的Lieb-Robinson边界一般晶格，其中的成分是无限维的，作为系统代表离散版本的自由场或谐波近似的玻色-哈伯德模型。我们认为本地的相互作用以及无限范围的相互作用，显示如何修正本地继承的局部性的哈密顿量：本地的相互作用导致强于指数抑制的校正，而非本地的代数相互作用导致代数抑制。我们推导出的界限规范运营商，外尔运营商和大纲推广到任意运营商。作为一个例子，我们讨论了克莱因-戈登场，并看到如何在晶格模型中的近似局域性成为确切的因果关系的领域限制。我们讨论了这些结果的适用性淬火晶格系统远离平衡，量子相变的动力学。
The Lieb-Robinson theorem states that locality is approximately preserved in the dynamics of quantum lattice systems. Whenever one has finite-dimensional constituents, observables evolving in time under a local Hamiltonian will essentially grow linearly in their support, up to exponentially suppressed corrections. In this work, we formulate Lieb-Robinson bounds for general harmonic systems on general lattices, for which the constituents are infinite-dimensional, as systems representing discrete versions of free fields or the harmonic approximation to the Bose-Hubbard model. We consider both local interactions as well as infinite-ranged interactions, showing how corrections to locality are inherited from the locality of the Hamiltonian: Local interactions result in stronger than exponentially suppressed corrections, while non-local algebraic interactions result in algebraic suppression. We derive bounds for canonical operators, Weyl operators and outline generalization to arbitrary operators. As an example, we discuss the Klein-Gordon field, and see how the approximate locality in the lattice model becomes the exact causality in the field limit. We discuss the applicability of these results to quenched lattice systems far from equilibrium, and the dynamics of quantum phase transitions.