Monte-Carlo studies of multi-component Ginzburg-Landau theories with competing interactions

Abstract

This thesis presents four research papers in the field of condensed-matter theory. Three of the papers make use of large-scale Monte-Carlo simulations to explore various aspects of Bose-Einstein condensates with multiple superfluid components. Papers I and II relate to a two-component Bose-Einstein condensate in three spatial dimensions under rotation. They explore the phase diagram and phase transitions of the model in two regimes, where either inter- or intra-component interactions dominates, as well as at a special SU(2)-symmetric point where all density-density interactions are of equal strength. We find that this rich phase diagram, in the coexisting regime, exhibits co-centered vortex lattices with hexagonal symmetry when the inter-component interaction is attractive. These lattices evolve into intercalated hexagonal lattices as the inter-component interaction is made repulsive, and further into intercalated square lattices as the repulsive interaction is increased in strength. In the phase-separated regime, we find striped vortex lattices for intermediate inter-component coupling strengths. For sufficiently strong inter-component coupling strengths one of the condensates is completely depleted, while the other develops a hexagonal vortex line lattice, as it is effectively a single-component condensate.

Paper III investigates the phases and phase transitions of a similar model of a two-component condensate, now in two spatial dimensions with spin-orbit coupling and zero rotation. Here we find, for low inter-component coupling strength, that the effect of the spin-orbit interaction is to modulate the condensate fields by a single q-vector, a plane wave state. For increased inter-component couplings, but with intermediate spin-orbit coupling, we again find that one of the condensates will be depleted, making the remaining condensate effectively a single-component condensate. This completely removes the effect of the spin-orbit interaction. For both high inter-component and high spin-orbit interaction strengths, we find that the condensate forgoes the energy gained by depleting one condensate. It will rather modulate the condensate, but now with staggered condensate amplitudes. This state is a superposition of two states with modulation vectors q and - q, a standing wave state. We also explore the thermal phase transitions in the absence of spin-orbit couplings, here we find Kosterlitz-Thouless transitions in all components regardless of whether or not one component has collapsed, and independent on the value of the inter-component density-density interaction strength.

The last paper explores, in a purely analytical treatment, the effect of inter-band Josephson couplings on an N-component London superconductor. It utilizes a mathematical identity to re-express the model in terms of integer-valued superconducting currents, and we show that the inclusion of inter-band couplings introduces instanton-like events in these currents. These events effectively removes the current conservation in each individual superconducting current, as is expected when introducing the Josephson coupling. However, one particular combination of current, the sum of all the currents, remains conserved even with the Josepshon coupling. We argue that this converts the phase transitions of the neutral sector into crossovers, while leaving the charged phase transition unaffected. The fluctuations of the neutral sector will weaken, but may still influence the charged fluctuations sufficiently to preempt the remaining inverted-3DXY transition, making it first order. We also re-express the onset of the Higgs mass when entering the superconducting state as a blowout of loops of superconducting current.