Spin and Charge Dynamics: Competing Orders and Quasi-Particle Formation

描述量子材料的性质及其不同的量子相是至关重要的，以便能够开发出超越半导体范式的新的替代技术，用于能量转换，电子设备和光收集。该奖项支持的研究和教育不仅具有技术影响，而且还将解决物理学中的基本问题，这些问题可能会带来意想不到的发现。对具有新功能的材料的追求是由对量子系统的研究推动的，其中组成电子之间的相互作用非常强。这些相互作用可以引起复杂和有趣的现象，当物理学主要由材料内部电子的集体行为控制时，就会发生这种现象。 一个特别的例子发生在考虑电子被限制在低空间维度时：限制迫使电子通过“推动”而不是相互传递来移动。与弦的振荡一样，这种受限电子系统的自然激发可以用波来更好地理解。结果，电子失去了它们作为粒子的个体身份。该项目的重点是了解电子如何失去或恢复其作为单个激发的身份，以及它们的行为如何随后转变，从而在材料中产生不同的相。尽管这些问题由于其潜在的复杂性而在理论上非常具有挑战性，但它们可以通过数值方法进行处理。研究的重点是计算性的，还将涉及基于量子信息和机器学习思想的新创新算法的开发。科学发现的新工具将被开发，并将作为开源软件提供给社区，这些软件可能会在凝聚态物理学之外的其他学科中找到应用。技术总结该奖项将支持研究和教育，重点是解决由于反铁磁长程有序和货车霍韦奇点的存在而导致的强相关材料中不同不稳定性的紧迫问题。这个项目从一个新的角度解决了凝聚态物质的一个范式问题。为了克服Mermin-Wagner定理的局限性，我们将在长程相互作用的存在下研究链和梯子，这些长程相互作用可以实现实际的自发对称性破缺和真正的反铁磁有序。这项研究将解决一个非常基本的问题：i）自旋子如何演变成磁振子，它们在激发光谱中的特征是什么？ii）是否有可能在布里渊区的不同区域中同时实现分数激发和相干激发？（3）在长程有序的情况下，相干准粒子是如何形成的（如果有的话）？我们还能在光谱中观察到自旋-电荷分离的特征吗？（iv）长程反铁磁有序和配对之间的相互作用是什么？（5）哈密顿量中的哪些项会引起超导铜氧化物中观察到的竞争不稳定性？选择的方法将是密度矩阵重整化群及其时间依赖变体，这是由PI共同开发的，并且已经成功地将我们对相关效应的知识扩展到时域。这项工作通过开发新的计算方法来解决高维系统来补充，这些方法基于连接量子信息和机器学习的新的原创思想：i）使用在真实的和动量空间表示之间插值的重叠正交轨道，ii）量子解缠器和自然轨道来构造基本准粒子激发的波函数，以及iii）使用受限玻尔兹曼机来计算单粒子绿色函数，从而重建量子多体问题的整个激发谱。这些新工具将作为开源软件提供给社区，这些软件可能会在凝聚态物理学之外的其他学科中找到应用。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

NONTECHNICAL SUMMARYCharacterizing the properties of quantum materials and their different quantum phases is paramount in order to be able to develop new alternative technologies beyond the semiconductor paradigm for applications in energy conversion, electronic devices, and light harvesting. This award supports research and education that will not only have technological implications but will also tackle fundamental questions in physics that could lead to unanticipated discoveries.The quest for materials with novel functionality is driven by the study of quantum systems where interactions among the constituent electrons are very strong. These interactions can give rise to complex and intriguing phenomena that take place when the physics is mostly governed by the collective behavior of the electrons inside the material. One particular example occurs when considering electrons confined in low spatial dimensions: the confinement forces electrons to move by "pushing" instead of passing around each other. Same as oscillations of a string, the natural excitations of such a confined system of electrons can be better understood in terms of waves. As a consequence, electrons lose their individual identities as particles. This project focuses on understanding how electrons lose or recover their identities as individual excitations and how their behavior is subsequently transformed, giving rise to different phases in the material.Even though these problems are theoretically very challenging due to their underlying complexity, they are amenable to numerical methods. The focus of the research is computational in nature and will also involve the development of new innovative algorithms based on quantum information and machine-learning ideas. New tools for scientific discovery will be developed and will be made available to the community as open-source software that may find applications in other disciplines beyond condensed matter physics.TECHNICAL SUMMARYThis award will support research and education focused on tackling urgent questions concerning different instabilities in strongly correlated materials due to the presence of antiferromagnetic long-range order and van Hove singularities. This project tackles a paradigmatic problem in condensed matter from a new perspective. In order to overcome the limitations of the Mermin-Wagner theorem, chains and ladders will be studied in the presence of long-range interactions that can realize actual spontaneous symmetry breaking and true antiferromagnetic order. The research will address questions of a very fundamental nature: i) How do spinons evolve into magnons and what are their signatures in the excitation spectrum? ii) Is it possible to realize fractionalized excitations and coherent excitations simultaneously in different regions of the Brillouin zone? iii) How do coherent quasiparticles form (if at all), in the presence of long-range order? Will we still observe signatures of spin-charge separation in the spectrum? iv) What is the interplay between long-range antiferromagnetic order and pairing? v) What terms in the Hamiltonian would give rise to competing instabilities such as those observed in superconducting cuprates? The method of choice will be the density matrix renormalization group and its time-dependent variants, which were co-developed by the PI and have had a remarkable success expanding our knowledge of correlation effects to the time domain.This work is complemented by the development of novel computational approaches to tackle higher-dimensional systems based on new original ideas that bridge quantum information and machine learning: i) The use of lapped orthogonal orbitals that interpolate between real- and momentum-space representations, ii) Quantum disentanglers and natural orbitals to construct the wave functions of the elementary quasiparticle excitations, and iii) Using restricted Boltzmann machines to calculate the single-particle Green's functions, and therefore reconstruct the entire excitation spectrum of the quantum many-body problem. These new tools will be made available to the community as open-source software that may find applications in other disciplines beyond condensed matter physics.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.