Exotic Phases and Supersymmetry in Quantum Magnets

爱德华·奥布莱恩将从理论上研究低维量子物质的奇异相和相变。他将把解析和数值技术应用到这些问题上。分析技术将包括统计力学中出现的传统技术，如分析可以准确找到基态的特殊耦合，以及超对称和共形场论等更现代的技术。数值技术将既包括精确对角化等传统方法，也包括量子信息世界中出现的新技术，特别是张量网络方法，如密度矩阵重正化群。最初的项目将涉及量子自旋链中出现的不寻常的“自双有序”相，其中铁磁有序的基态与完全无序的基态共存。奥布莱恩将分析这些相和邻近的三临界点，特别是寻找晶格的超对称性。更长期的目标包括在两个维度上分析拓扑有序阶段的相似结构。这项工作是在自然科学研究主题内进行的。主要研究领域是凝聚态物质：磁性和磁性材料，而解析工作与数学物理和量子光学与信息的数值工作有一些重叠。目前还没有牛津大学以外的公司或合作者参与这一项目。

Edward O'Brien will study theoretically exotic phases and phase transitions of quantum matter in low dimensions. He will apply both analytical and numerical techniques to these problems. The analytical techniques will include traditional ones arising in statistical mechanics, such as analysing special couplings where the ground state can be found exactly, along with more modern ones such as supersymmetry and conformal field theory. The numerical techniques will include both traditional ones such as exact diagonalisation, and new ones arising in the quantum information world, especially tensor-network methods such as the density-matrix renormalisation group. The initial project will concern the unusual "self-dual ordered" phases arising in quantum spin chains, where ferromagnetically ordered ground states coexist with completely disordered ground states. O'Brien will analyse these phases and the neighbouring tricritical points, and search in particular for lattice supersymmetry. Longer-term goals include analysing similar structure in topologically ordered phases in two dimensions. This work is within the Physical Sciences research theme. The main research area is Condensed matter: magnetism and magnetic materials, while the analytic work has some overlap with Mathematical Physics, and the numerical work with Quantum Optics and Information.There currently are no companies or collaborators outside the University of Oxford involved in this project.