Nonzero temperatures and emergent disorder in spin liquids

Abstract

At absolute zero temperature, spin liquids are known to exhibit a fascinating array of phenomena including topological order, emergent gauge fields, and the existence of exotic quasiparticles with fractional statistics. Meanwhile, at temperatures that are high compared to all characteristic interaction energy scales in the system, they often behave as trivial, uncorrelated paramagnets. This thesis aims to better understand the behaviour of spin liquids at temperatures that are intermediate, lying between these two extremes. At such intermediate temperatures, a finite density of defects are thermally excited, which inherit the peculiar properties of the proximate, zero temperature spin liquid state. Although the two limits are in most cases continuously connected via a crossover, these exotic defects have the potential to drastically alter the properties of the system. In spite of half a century of progress since the original ideas of Pauling and Anderson, quantum spin liquids have evaded unambiguous experimental detection. Therefore any precursor diagnostics in this temperature regime would be greatly beneficial before attempting to reach challengingly low temperatures where the effect of thermally excited defects is altogether negligible.

The thesis begins by considering the evolution of quantum mechanical entanglement with temperature in the toric code, utilising concepts borrowed from the field of quantum information theory. This highlights the importance of an intermediate temperature regime in which the ground state manifold does not have well-developed quantum coherence, but excitations out of the ground state sector are exponentially suppressed with temperature by their gap. The focus then moves to understanding how high-energy quasiparticles in the toric code propagate through a background of incoherent, thermally-generated gauge field excitations within this intermediate temperature regime. Analytical progress is made by making use of a mapping to the Bethe lattice, allowing predictions to be made about the experimentally measurable finite temperature dynamical structure factor. I then look at the propagation of quasiparticles in a different context: Classical spin ice. When spin ice is subjected to rapid cooling, the density of excitations (monopoles) form long-lived metastable plateaux as a result of the formation of noncontractible pairs. I develop a thorough understanding of the origin of these plateaux by formulating the problem in terms of reaction–diffusion processes and performing large-scale simulations, which both suggest that the long-range nature of the interactions between monopoles is the linchpin of the plateaux. Finally, I consider the nonequilibrium dynamics of quantum spin liquids in closed systems at finite energy density. In this context, the emergent (self-generated) nature of the disorder plays a crucial role, allowing the system to generically exist in a superposition of different disorder realisations. I show that this property gives rise to power law decay of the dynamical structure factor and unbounded logarithmic growth of entanglement in time, just as for many-body localised systems, despite the existence of a mapping to free fermions.