This PhD thesis focuses on the mutual interplay of frustration and quenched disorder in magnetic insulators. Frustrated quantum magnets are known to host a plethora of interesting many-body phenomena ranging from noncollinear N\'el ordering to spin liquid phases. In this thesis, the consequences of the breakdown of translation symmetry, a widely occurring phenomenon in real materials, are studied in several examples of frustrated spin systems. The thesis is split into two parts dedicated to different kinds of frustrated magnets and the effects of quenched random perturbations in them. In the first part, bond randomness in frustrated noncollinear ordering is considered. Noncollinear magnetic orders originating from the spontaneous breakdown of continuous spin rotation symmetries at zero temperature are found to be unstable in the presence of exchange randomness. It is shown that in this case, the frustrated N\'{e}el ordering is destroyed for any magnitude of random exchange disorder. The resulting disordered ground states, however, possess interesting distinctions depending on the precise nature of the broken spin rotation symmetry. For SU(2) Heisenberg spins, it is demonstrated that the weak disordered ground describes a classical spin glass at zero temperature with a finite correlation length. At higher disorder, enhanced quantum fluctuations are predicted to modify that ground state into a random-singlet-like form. On the other hand, for noncollinear XY spin systems with U(1) or SO(2) symmetry which have stable integer-valued vortex topological defects, it is instead found that the weak disorder and the strong disorder ground states are distinct even at the classical level. The former has a quasi-long range order spin arrangement, while the latter exhibits a truly short-range ordered state. These two phases are shown to be separated by a Kosterlitz-Thouless-like phase transition point where vortex unbinding takes place. The spontaneously broken chiral degeneracy of noncollinear N\'el ordering is witnessed to be robust up to the point of the vortex-driven phase transition.
In the second part of the thesis, the focus is switched to the effects of quenched disorder on quantum spin liquids. These are quantum disordered phases of matter with long-range entanglement, topological order, and fractionalised excitations that often arise in frustrated spin systems. The U(1) Dirac spin liquid with its magnetic monopole excitations has been identified as a parent state for N\'{e}el, valence-bond solid, and algebraic spin liquid phases. In this thesis, the fate of this state is studied in the presence of quenched random perturbations. It is demonstrated that a wide class of random perturbations induce monopole-driven confinement of the fractionalised quasi-particles of the spin liquid, leading to the onset of a spin glass-like order. Finally, dilution effects in the $\rm Z_2$ spin liquid phase of the Kitaev model are discussed in the presence of generic symmetry allowed interactions. The spin-liquid state remains stable when the non-Kitaev perturbations and dilution are small. However, the low-energy properties of the ground state are altered. It is shown that the degeneracies from the Majorana zero modes, which are known to localise at defect sites of the Kitaev spin liquid, are generically lifted by the non-Kitaev perturbations. Consequently, a dilution-tuned impurity band with a finite density of states is found to emerge.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:76963 |
| Date | 13 December 2021 |
| Creators | Dey, Santanu |
| Contributors | Vojta, Matthias, Schmidt, Kai Phillip, Technische Universität Dresden |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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