A Numerical Renormalization Group for Low Dimensional Field Theories
低维场论的数值重正化群
基本信息
- 批准号:1208521
- 负责人:
- 金额:$ 21.01万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2012
- 资助国家:美国
- 起止时间:2012-08-15 至 2016-05-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
This program will extend and apply a numerical technique developed by the PI and CO-PI by which the properties of a wide range of interacting field theories in low dimensions can be studied in a nonperturbative fashion. The approach takes as input already available data, in the form of spectra together with matrix elements, arising from integrable and conformal field theoretical treatments of a wide class of strongly interacting zero and one dimensional systems. Using this as a foundation, more complicated field theories, built by either perturbing or coupling together such systems, are analyzed numerically through a controlled truncation of the Hilbert space guided by a renormalization group procedure. This is the renormalization group improved truncated spectrum approach (RGTSA). The strongest interactions are taken into account at the very start. Using it one can study arbitrary perturbations of 1+1 dimensional integrable and conformal field theories as well as study large arrays of coupled one-dimensional field theories, permitting the extension of the approach to 2+1 dimensions. The numerical renormalization group technique borrows ideas from the study of quantum impurity problems and density matrix renormalization group approaches to one dimensional lattice models. This technique is sufficiently versatile to extract the spectrum, correlation functions and non-equilibrium phenomena such as the dynamics following a quantum quench. This technique is able to characterize the properties of real materials. As a proof of principle of the technique, the excitonic spectrum of semi-conducting carbon nanotubes has been studied and it has been shown that the modeling well describes experimental data. This technique will be used to study the optical properties of hybrid nanosystems with the aim of better understanding this hybrid's potential as a solar energy device. Two graduate students will receive extensive training in low dimensional quantum field theories as well as their application in condensed matter settings. They will conduct original research and develop theoretical methods with cross-field applicability. The results will be presented in journals and through seminars, colloquia, and conference presentations.
该计划将扩展和应用PI和CO-PI开发的数值技术,通过该技术,可以以非微扰的方式研究低维相互作用场理论的广泛性质。该方法需要作为输入已经可用的数据,在频谱的形式连同矩阵元素,所产生的广泛的一类强相互作用的零维和一维系统的可积和共形场理论治疗。以此为基础,更复杂的场论,建立在扰动或耦合在一起,这样的系统,数值分析通过控制截断的希尔伯特空间的重整化群程序的指导下。这就是重整化群改进的截断谱方法(RGTSA)。在一开始就考虑最强的相互作用。使用它可以研究1+1维可积和共形场论的任意扰动,以及研究耦合一维场论的大阵列,允许将方法扩展到2+1维。数值重整化群技术借鉴了量子杂质问题的研究和一维格点模型的密度矩阵重整化群方法。这种技术是足够通用的提取光谱,相关函数和非平衡现象,如量子淬火后的动力学。该技术能够表征真实的材料的性质。作为该技术的原理的证明,半导体碳纳米管的激子光谱已被研究,它已被证明是很好地描述了实验数据的建模。这项技术将用于研究混合纳米系统的光学特性,目的是更好地了解这种混合物作为太阳能设备的潜力。两名研究生将接受低维量子场论及其在凝聚态环境中的应用的广泛培训。他们将进行原创性研究,并开发具有跨领域适用性的理论方法。研究结果将发表在期刊上,并通过研讨会,座谈会和会议报告。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Robert Konik其他文献
Quantum coherence confined
量子相干局限
- DOI:
10.1038/s41567-021-01211-5 - 发表时间:
2021-03-18 - 期刊:
- 影响因子:18.400
- 作者:
Robert Konik - 通讯作者:
Robert Konik
Robert Konik的其他文献
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