SciPost Thesis Link
| Title: | Topological States of Matter in Frustrated Quantum Magnetism | |
| Author: | Alexander Wietek | |
| As Contributor: | (not claimed) | |
| Type: | Ph.D. | |
| Field: | Physics | |
| Specialties: |
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| Approach: | Computational | |
| URL: | https://diglib.uibk.ac.at/ulbtirolhs/content/titleinfo/2244867 | |
| Degree granting institution: | University of Innsbruck | |
| Supervisor(s): | Andreas M. Läuchli | |
| Defense date: | 2017-12-14 |
Abstract:
Frustrated quantum magnets may exhibit fascinating collective phenomena. The main goal of this dissertation is to provide conclusive evidence for the emergence of novel phases of matter like quantum spin liquids in local quantum spin models. After a general introduction to frustrated magnetism, spin liquids and the numerical methods employed in part I comprising chapter 1 and 2 we present the main results of the thesis in part II. We develop novel algorithms for large-scale Exact Diagonalization computations in chapter 3. So-called sublattice coding methods for efficient use of lattice symmetries in the procedure of diagonalizing the Hamiltonian matrix are proposed. Furthermore, we suggest a randomized distributed memory parallelization strategy. Benchmarks of computations on various supercomputers with system size up to 50 spin-1/2 particles have been performed. Results concerning the emergence of a chiral spin liquid in a frustrated kagome Heisenberg antiferromagnet are presented in chapter 4. We confirm previous findings obtained via DMRG calculations using Exact Diagonalization and propose that the chiral spin liquid phase in this model is well described by Gutzwiller-projected wave functions. Also, the stability and extent of this phase are discussed. In an extended Heisenberg model on the triangular lattice, we establish another chiral spin liquid phase in chapter 5 amongst several magnetically ordered phases. We discuss the special case of the Heisenberg J_1-J_2 model with nearest and next-nearest neighbor interactions and present a scenario where the critical point of phase transition from the 120-degree Néel to a putative Z_2 spin liquid is described by a Dirac spin liquid. A generalization of the SU(2) Heisenberg model with SU(N) degrees of freedom on the triangular lattice with an additional ring-exchange term is discussed in chapter 6. We present our contribution to the project and the final results that suggest a series of chiral spin liquid phases in an extended parameter range for N=3,...,10. Finally, we present preliminary data from a Quantum Monte Carlo study of an SU(N) version of the J-Q model on a square lattice in chapter 7. We study this model for N=2,...,10 and multi-column representations of SU(N) and establish the phase boundary between the Néel ordered phase and the disordered phases for J, Q >= 0. The disordered phase in the four-column representation is expected to be a two-dimensional analog of the Haldane phase for the spin-1 Heisenberg chain.