Refinement and extension of QC-DMRG based on recent quantum information concepts

基于最新量子信息概念的QC-DMRG的细化和扩展

• 批准号: 414324924
• 负责人: Dr. Christian Schilling
• 金额: --
• 依托单位: Center for Theoretical Physics
• 依托单位国家: 德国
• 项目类别: Independent Junior Research Groups
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/414324924?language=en
• 关键词: Refinement; extension; QC; DMRG; based

It is the main goal of my proposed research programme to explain the surprising success of DMRG in quantum chemistry (QC-DMRG) with the ultimate aim of overcoming its main limitations. As I plan to show in a concise way, it is the strong conflict between energy minimization and fermionic exchange symmetry in systems of confined fermions which enforces a reduction of particle and orbital/mode entanglement. Hence, similar to proper lattice systems, a local structure emerges in QC-DMRG on the underlying artificial one-dimensional lattice built from appropriate spatial orbitals. To elaborate on these general ideas, the following objectives are playing a crucial role. First, for systems of identical fermions, a solid foundation for particle and for mode/orbital entanglement shall be provided. Based on plausible axioms for fermionic entanglement measures, the flaws of common measures shall be sorted out: The artificial "correlations" due to the antisymmetry of the wave function shall no longer contribute to the particle entanglement. Furthermore, the application of mode/orbital entanglement measures in quantum chemistry must not violate the number parity superselection rule, reflecting the fact that nature never mixes even and odd fermion number states. To simplify their applicability to realistic fermionic systems, bounds and witnesses shall be constructed for those measures.Second, the conflict between energy minimization and fermionic exchange symmetry shall be concretized in the form of an exchange force constructed via reduced density matrix functional theory (RDMFT). For this, I will prove in a constructive way that the fermionic exchange symmetry manifests itself in RDMFT in the form of an effective "potential". The exchange force will then be introduced as the derivative of that potential with respect to the natural occupation numbers.Third, in a comprehensive QC-DMRG study, it shall be systematically verified for quantum chemical and harmonic trap systems that particle and orbital/mode entanglement are both significantly reduced in ground states compared to generic states. The expected strong relation between the reduction of entanglement and the strength of the exchange force shall be verified. To overcome the main limitation of QC-DMRG (recovering dynamic correlations), more general tensor network ansatzes will be exploited, higher virtual orbitals shall be merged to supersites and new insights from the exchange force and RDMFT will be used to improve systematically the choice of the "lattice sites" underlying QC-DMRG. Altogether, this shall eventually pave the way for QC-DMRG-blackbox calculations.

我提出的研究计划的主要目标是解释DMRG在量子化学(QC-DMRG)中取得的惊人成功，最终目的是克服其主要局限性。正如我计划用一种简洁的方式展示的那样，在受限费米子系统中，能量最小化和费米子交换对称性之间的强烈冲突迫使粒子和轨道/模纠缠的减少。因此，类似于适当的晶格系统，QC-DMRG在由适当的空间轨道建立的底层人工一维晶格上出现了局域结构。要详细阐述这些总体想法，以下目标起着至关重要的作用。首先，对于完全相同的费米子系统，应该为粒子和模/轨道纠缠提供坚实的基础。基于费米子纠缠测量的看似合理的公理，应该对常见测量的缺陷进行梳理：由于波函数的反对称而产生的人为“关联”将不再对粒子纠缠起作用。此外，模/轨道纠缠测量在量子化学中的应用不能违反数称超选择规则，这反映了自然界从不混合奇偶费米子数态的事实。其次，能量最小化和费米子交换对称性之间的冲突应具体化为通过约化密度矩阵泛函理论(RDMFT)构造的交换力的形式。为此，我将以一种建设性的方式证明，费米子交换对称性在RDMFT中以有效“势”的形式表现出来。第三，在一个全面的QC-DMRG研究中，对于量子化学和谐和陷阱系统，系统地验证了基态粒子和轨道/模的纠缠都比一般态显著减少。纠缠的减少与交换力的强弱之间的预期强烈关系将得到验证。为了克服QC-DMRG(恢复动态关联)的主要局限性，将利用更一般的张量网络变换，将更高的虚拟轨道合并为超位，并从交换力和RDMFT中获得新的见解，系统地改进QC-DMRG中“格点”的选择。总之，这最终将为QC-DMRG-Blackbox计算铺平道路。