Probing exotic orders in quantum magnets through Berry phases

(1)我们提出了一种新的具有拓扑项的有效场论，它可以在2维和3维空间中探测反铁磁体的自旋能隙相和量子相变。我们期望这个理论--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--可以用于寻找奇异的自旋液态态。(2)与圣巴巴拉和犹他州的研究人员合作，我们中的一人(MK)解决了对实验观察到的二维化合物Cs_2CuCl4中自旋激发性质的理论理解问题。该理论将该系统模拟为由弱耦合的反铁磁自旋链组成，并很好地再现了实验结果。这一发现表明，这种化合物中的自旋最好被理解为存在于ID中的传统自旋激发的后代S。(3)与京都大学汤川研究所的K.Totsuka合作，该项目的首席研究员研究了反铁磁体在外部磁场中的磁化过程。我们发现，位于垂直于场的平面内的自旋分量的时空涡旋产生了非平凡的Berry相，这证明了低能物理的存在。Berry相效应重现了Ld的已知结果，提供了对2和3D的自然扩展，并在一定条件下将系统带入晶格规范理论，从而产生了以分数磁化平台为特征的新的质量相。

(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.