Thesis Defense

Wen Jin

Friday, August 25, 2017 10:30AM (334 JFB)

Title: Low Dimensional Frustrated Quantum Magnets: a Playground for Novel Phases

Low-dimensionality, magnetic frustration, and quantum fluctuations are three ingredients that give rise to nontrivial magnetic orders or exotic ground states, such as spin nematic and spin liquid. In this thesis I discuss our efforts to find novel interesting magnetic phases by cooking up all these ingredients together.

First, a large fraction of the thesis is devoted to the behavior of quantum spin chains in the presence of a uniform Dzyaloshinskii-Moriya (DM) interaction. This problem is analyzed by the bosonization technique. Spin chain is the building block of many magnetic materials, such as K2CuSO4(Cl/Br)2 which strongly motivates our study. DM interaction originates from spin-orbit coupling, and is widely present in real materials. Theories of these systems are derived and described for both individual chain [1] and weakly coupled chains [2, 3] at zero and finite temperature and in the presence of external magnetic field. A special geometry of DM interactions—staggered between chains, but uniform within a given chain—leads to a peculiar type of frustration that effectively cancels the transverse inter-chain coupling and strongly reduces the ordering temperature. By taking advantage of this special geometry of DM interaction, one can construct a chiral spin liquid, which shares some basic features of fractional quantum Hall effect, such as gapped bulk and gapless chiral edge states, in arrays of spin chains. The second part of the thesis describes the investigation of the interplay between frustration, quantum fluctuations, and magnetic field in the phase diagram of quantum antiferromagnets on triangular lattice. For triangular antiferromagnets with spatial and/or exchange anisotropy and near the fully polarizing field, the competition between classical degeneracies and quantum fluctuations leads to multiple quantum phase transitions and highly nontrivial intermediate phases [4]. For a toy model of a zigzag chain—a spin chain with competing nearest and next-nearest exchange interactions—I investigate how quantum fluctuations and geometrical frustration establish a 1/3 magnetization plateau and a bond-nematic state. In this presentation, I will focus on the first part of the thesis and show how the interplay between DM interaction and magnetic field induces novel phases, such as an anisotropic Luttinger liquid, which is realized in a single quantum spin chain, and various two-dimensional spin density waves which appear due to a weak inter-chain exchange interaction.