Resolving superconductivity and pseudogap physics in oxides: beating the sign problem

超导材料无损耗传输电流，是先进医学成像和能量传输的基础。它们被广泛应用于电路、马达和发电机等领域，其效率远高于今天的任何产品。但是这些应用需要强烈的冷却——“最好”达到-160摄氏度——因为超导性需要电子对处于集体量子态，很容易被热能破坏。因此，材料理论的一个中心目标是系统地设计在更高温度下工作的超导体。然而，到目前为止，这是不可能的，因为今天基于氧化物陶瓷的最好的超导体，我们仍然不知道电子对是如何形成的。动态平均场理论（DMFT）可以预测氧化物中的SC特性，从而深入了解对的形成，从而允许设计更好的超导体。然而，DMFT目前无法做到这一点，因为它使用的量子蒙特卡罗（QMC）算法存在所谓的符号问题。该项目旨在解决SC氧化物的关键模型，特别是高温铜酸盐，以及钌酸锶。在比以前低得多的温度下处理更大的安德森杂质问题（AIPs）——DMFT的基础——将允许首次模拟这些氧化物的SC状态，以及神秘的假间隙（PG）和奇怪的金属（SM）状态，它们在更高温度下先于超导性。理解这些对于揭示为什么电子在氧化物中成对是至关重要的。该项目将建立在所谓的并行密度矩阵重整化群（pDMRG）数值的重大进展上，pDMRG是PI最近共同开发的。pDMRG代码在低温下的电子相互作用优于QMC，因为它没有符号问题。pDMRG也比常规的DMRG强大得多，它可以在超级计算机的许多计算节点上分配对单cpu计算要求太高的计算。因此，我们将使用pDMRG重新实现DMFT数字。结果将是DMFT不仅在数量上，而且在质量上优于以前的实现。利用它，我们将求解由扩展的铜酸盐Hubbard模型导出的AIPs以及钌酸锶的多轨道AIPs。对于钌酸锶，我们也将是第一个模拟从SM状态到25 K左右近乎完美的金属状态的交叉，这在QMC中也是不可能的。对于扩展的哈伯德模型，我们将寻求复制实验中发现的两个独立的假间隙的出现，一个大一个小。该项目将通过解决前所未有的系统尺寸和温度的扩展2D Hubbard模型，对高温氧化物超导体中电子配对的本质产生重要的见解。这可能是朝着有目的地设计高温超导体迈出的重要一步。这个项目可以进一步突破对超导的关键模型材料——钌酸锶的理解。目前还不知道它的SM状态，也不知道它是否能转化为完美的金属。因此，这个项目可以对这种模型材料的相互竞争的理论进行长期的“分类”，对超导理论有广泛的影响，因为这种特殊的材料是一种干净的、近乎理想的实验场地，可以对所有类型的现象进行测试。

Superconducting (SC) materials, which transport currents without losses, are the basis of advanced medical imaging and energy transmission. They are intensely researched for applications such as circuitry, motors and generators far more efficient than any today. But these applications need strong cooling - at 'best' to about -160 C - as superconductivity requires electron pairs in a collective quantum state, easily disrupted by thermal energy. A central goal of materials theory is thus to systematically design superconductors working at higher temperatures.Yet this has been impossible so far, as for the best superconductors today, based on oxide ceramics, we still do not understand how electron pairs form. Dynamical Mean Field Theory (DMFT) could predict SC properties in the oxides, yielding insight into pair formation, and thus allow designing better superconductors. Yet, DMFT currently cannot do so as it uses Quantum Monte Carlo (QMC) algorithms that suffer from the so-called sign-problem. This project aims to solve key models of SC oxides, especially the high-temperature cuprates, as well as strontium ruthenate. Treating much larger Anderson impurity problems (AIPs) - the basis of DMFT - at much lower temperatures than possible before will allow modelling these oxides in their SC state for the first time, as well as the mysterious pseudogap (PG) and strange metal (SM) states, which precede superconductivity at higher temperature. Understanding these as well is crucial for revealing why electrons pair in the oxides.The project will build on a major advance in so-called parallel density matrix renormalization group (pDMRG) numerics, co-developed by the PI recently. The pDMRG code outperforms QMC for interacting electrons at low temperatures as it does not suffer the sign-problem. The pDMRG is also much more powerful than regular DMRG, distributing a calculation too demanding for single-CPU calculations across many compute nodes of a supercomputer. We will thus re-implement DMFT numerics using pDMRG. The outcome will be a DMFT superior to previous implementations not just quantitatively, but qualitatively. Using it, we will solve AIPs derived from the extended Hubbard model of cuprates as well as multi-orbital AIPs for strontium ruthenate. For strontium ruthenate, we will also be the first to simulate the crossover from the SM state to a near-perfect metallic state around 25 K, which has also been impossible with QMC. For the extended Hubbard model, we will seek to replicate the experimentally found emergence of two separate pseudogaps, one large and one small. This project would yield important insight into the nature of electron-pairing in high-temperature oxide superconductors, by solving the extended 2D Hubbard model for unprecedented system sizes und temperatures. It could be a significant step towards being able to engineer high-temperature superconductors on purpose. This project could further deliver a breakthrough in the understanding of a key model-material for superconductivity, strontium ruthenate. Neither its SM state nor its crossover into a perfect metal is currently understood. This project could thus yield a long-necessary 'sorting' of the competing theories for this model material, with broad impact for the theory of superconductivity, due to this particular material being a clean, near-ideal testing ground for the whole class of phenomena.