Probing exotic orders in quantum magnets through Berry phases

(1)推导了一种新的具有拓扑项（theta项）的有效场理论，该理论可以在二维和三维空间中检测反铁磁体的自旋间隙相和量子相变。我们期望这个理论，作为一维反铁磁体的Haldane-Affleck映射到具有theta项的非线性sigma的自然推广，可以用于寻找奇异自旋液态。(2)我们中的一位（MK）与圣巴巴拉和犹他州的研究人员合作，解决了二维化合物Cs_2CuCl_4实验中观察到的自旋子激发性质的理论认识问题。该理论将系统建模为弱耦合反铁磁自旋链，并能很好地再现实验结果。这一发现表明，该化合物中的自旋子最好被理解为存在于Id中的传统自旋子激发的后代。系统。(3)本项目的首席研究员与京都大学汤川研究所的K. Totsuka合作，研究了反铁磁体在外加磁场中的磁化过程。我们发现，在与场垂直的平面内的自旋分量的时空涡贡献了非平凡的贝里相，它在低能物理中占主导地位。Berry相位效应再现了已知的ld结果，提供了2和3d的自然扩展，并且在某些条件下将系统映射到晶格规范理论中，从而产生了以分数磁化平台为特征的新型大质量相位。

(1) We have derived a new effective field theory with a topological term (theta-term) which can detect spin gap phases and quantum phase transitions in antiferromagnets in 2 and 3 spatial dimensions. We expect that this theory, which is a natural generalization of the Haldane-Affleck mapping of 1d antiferromagnets to a nonlinear sigma with a theta-term, can be utilized in the search for exotic spin liquid states.(2) In collaboration with researchers in Santa Barbara and Utah, one of us (MK) has resolved the issue on the theoretical understanding on the nature of the spinon excitations observed experimentally in the 2d compound Cs_2CuCl_4. The theory models the system as composed of weakly coupled antiferromagnetic spin chains, and reproduces well the experimental results. This finding implies that the spinons in this compound are best understood to be descendent s of the conventional spinon excitations which exist in Id. systems.(3) In collaboration with K. Totsuka of the Yukawa Institute, Kyoto University, the Head Investigator of this project investigated the magnetization process of antiferromagnets in an external magnetic field. We found that spacetime vortices of the spin components lying within the plane normal to the field contributes nontrivial Berry phases which doinate the low energy physics. The Berry phase effect reproduces known results for ld, provides natural extensions to 2 and 3d, and also under certain conditionsmaps the system into a lattice gauge theory which gives rise to a novel massive phase characterized by a fractional magnetization plateau.