Exotic Phases and Supersymmetry in Quantum Magnets

Edward O'Brien将从理论上研究低维量子物质的奇异相和相变。他将运用分析和数值技术来解决这些问题。分析技术将包括统计力学中出现的传统方法，例如分析可以精确找到基态的特殊耦合，以及更现代的方法，例如超对称和共形场论。数值技术将包括传统的方法，如精确对角化，以及量子信息世界中出现的新方法，特别是张量网络方法，如密度矩阵重整化群。最初的项目将关注量子自旋链中出现的不寻常的“自对偶有序”相，其中铁磁有序基态与完全无序基态共存。O'Brien将分析这些相和邻近的三临界点，并特别寻找晶格超对称。长期目标包括在两个维度上分析拓扑有序相的相似结构。这项工作属于物理科学研究主题。主要研究领域为凝聚态物质、磁学和磁性材料，分析工作与数学物理有一定的重叠，数值工作与量子光学和信息学有一定的重叠。目前，牛津大学之外没有公司或合作者参与这个项目。

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.