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

解决氧化物中的超导性和赝能隙物理：解决符号问题

• 批准号: EP/W022982/1
• 负责人: Adrian Wasgen Daniel Kantian
• 金额: $ 50.14万
• 依托单位: Heriot-Watt University
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FW022982%2F1
• 关键词: Resolving; superconductivity; pseudogap; physics; oxides

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.

超导（SC）材料是不损失的电流的，是先进的医学成像和能量传播的基础。他们对诸如电路，电动机和发电机等应用的应用进行了深入研究，效率要比当今的任何一个要高得多。但是这些应用需要强烈的冷却 - 在“最佳”至约-160 c的情况下 - 超导性需要以集体量子状态的电子对，很容易被热能破坏。因此，材料理论的一个核心目标是系统地设计在较高温度下工作的超导体。到目前为止，这是不可能的，至于当今最好的超导体，基于氧化物陶瓷，我们仍然不了解电子对的形式。动力学平均场理论（DMFT）可以预测氧化物中的SC特性，从而深入了解成对形成，从而允许设计更好的超导体。但是，DMFT目前无法这样做，因为它使用了遇到所谓标志问题的量子蒙特卡洛（QMC）算法。该项目旨在解决SC氧化物的关键模型，尤其是高温铜酸盐以及松酸盐的关键模型。治疗更大的安德森杂质问题（AIP） - DMFT的基础 - 在温度远低于以前的温度下，将首次以其SC状态建模这些氧化物，以及在较高温度下超过超导性之前的神秘伪PSEUDOGAP（PG）和奇怪的金属（SM）状态。也了解这些对于揭示为什么氧化物中的电子对至关重要。该项目将以最近由PI共同开发的所谓平行密度基质矩阵重新归一化组（PDMRG）数字的重大进展为基础。 PDMRG代码在低温下与QMC相互作用的QMC优于QMC，因为它没有符号问题。 PDMRG也比常规DMRG强大得多，在超级计算机的许多计算节点上分发了对单CPU计算的计算。因此，我们将使用PDMRG重新实现DMFT数字。结果将不仅在定量上，而且在定性上都优于以前的实现。使用它，我们将解决源自层状甲酸盐的扩展哈伯德模型的AIP，以及用于扁平酸中酸盐的多轨AIP。对于缎形牙印酸盐，我们也将是第一个模拟从SM状态到近乎25 K的金属状态的交叉的人，QMC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发现的两个单独的伪群的出现，一个大且一个很小。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，从而对高温氧化物超导体中电子配对的性质进行重要洞察力。这可能是迈向能够故意设计高温超导体的重要一步。该项目可以进一步在理解超导性的关键模型材料（牙酸滨酸盐）方面取得突破。目前，它的SM状态和跨界均未被理解为完美的金属。因此，该项目可以为该模型材料提供竞争性理论的长期“分类”，并对超导性理论产生广泛的影响，因为这种特殊的材料是整个现象类别的干净，近乎理想的测试地面。