Quantum spin liquids represent a novel phase of magnetic matter where quantum fluctuations are large enough to suppress the formation of local order parameters, even down to zero temperature. Quantum spin liquid states can emerge from frustrated quantum magnets. These states show several peculiar properties, such as topological order, fractional excitations, and long-range entanglement.
The Kitaev spin model on the honeycomb lattice is one of the few models proposed which can exactly show the existence of a $\mathbb{Z}_2$ quantum spin liquid. The model describes spins featuring frustrated compass interactions, and it exhibits a quantum spin liquid ground state.
The model's ground state can be found exactly by representing spins in terms of Majorana fermions. It turns out that spin excitations fractionalize into two degrees of freedom: spinless matter fermions and flux excitations of the emergent $\mathbb{Z}_2$ gauge theory.
Recently, possible solid-state realizations of Kitaev quantum spin liquids have been proposed in a class of frustrated Mott insulators. Unfortunately, experiments can not unambiguously identify quantum spin liquids, due to their elusive nature.
Nevertheless, indirect observations on a spin liquid state can be done by looking at its excitations. Along this line, thermal transport investigations provide for an option to study heat-carrying excitations, and thus the properties of the related spin liquid state.
In this doctoral thesis work, I performed a study of longitudinal thermal transport properties in the two-dimensional Kitaev spin model. This study aims to advance the understanding of transport in prototypical frustrated quantum magnets that might harbor Kitaev physics, and in particular quantum spin liquid states. For this purpose, I explored the model for varying exchange coupling regimes $-$ to underline the impact of anisotropy on transport $-$ and I studied transport over a wide range of temperatures.
Transport properties have been explored within the formalism of the linear response theory. Based on the latter, thermal transport coefficients can be evaluated by calculating dynamical energy-current auto-correlation functions.
First, I performed an analytical study of the uniform gauge sector of the model $-$ where excitations of gauge degrees of freedom are neglected. Analytical findings for the energy-current correlations, and their related
transport coefficients, imply a finite-temperature ballistic heat conductor in terms of free matter fermion excitations $-$ independent of exchange couplings.
Second, thermal transport has been studied at finite temperatures, considering thermal gauge excitations off the uniform gauge sector. For this purpose, I made use of two complementary numerical methods able to treat finite-temperature systems.
On the one hand, I resorted on the exact diagonalization of the Kitaev Hamiltonian given in terms of fermions and a real-space dependent $\mathbb{Z}_2$ gauge potential, to study relatively small systems.
On the other hand, I used an approximate method based on a mean-field treatment of thermal gauge fluctuations. The method allowed to extend the study of thermal transport to systems with up to $\sim\mathcal{O}(10^4)$ spinful sites. It made possible the computation of correlation functions by reducing the exact trace over all gauge states to an average over dominant gauge states suited to a given temperature range.
The reliability of the method has been checked by comparing to numerically exact thermodynamics of systems. Based on the thermodynamic analysis, the method has been restricted to a temperature range where the mean-field treatment of gauge fluctuations is acceptable. Within such temperature range, the method succeeded in well reproducing exact results. The prime advantage of this method is its capability to reveal important features in the energy-current correlation spectra, not captured by the exact diagonalization approach because of finite-size effects.
I found that the energy-current correlation spectra, in the presence of thermal gauge excitations, show clear signatures of spin fractionalization. In particular, the low-energy part of spectra displays features arising from
a temperature-dependent matter-fermion density relaxation off an emergent thermal gauge disorder. This static gauge disorder also leads to the appearance of a pseudogap in the zero-frequency limit, which closes in the thermodynamic limit. The extracted dc heat conductivity is consequently influenced by this interplay between matter fermions and gauge degrees of freedom. The anisotropy in the exchange couplings moves Kitaev systems through gapless and gapped phases of the matter fermion sector.
Effects of anisotropy are visible in the dc conductivities which display a low-temperature dependence crossing over from power-law to exponentially activated behavior upon entering the gapped phase.
Therefore, I found that in the thermodynamic limit, two-dimensional Kitaev systems feature dissipative transport, regardless of exchange couplings. This finding is in contrast to the ballistic transport found discarding gauge excitations in the uniform gauge sector, which underlines the relevance of gauge degrees of freedom in thermal transport properties of Kitaev systems.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:36161 |
| Date | 15 November 2019 |
| Creators | Pidatella, Angelo |
| Contributors | Vojta, Matthias, Brenig, Wolfram, Technische Universität Dresden |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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