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

Peder Notto Galteland

Published Jan 1, 2016• 0 citations
OpenAlex

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.\n\nPaper 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.\n\nThe 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.

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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.\n\nPaper 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.\n\nThe 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.
This thesis presents four research papers in the field of condensed-matter theory. In all four papers, large-scale Monte Carlo simulations are used to investigate phases and phase transitions in two-component models of superconductors and superfluids with multiple broken symmetries. In Article I, a U(1) × U(1) lattice London superconductor with two different types of intercomponent interactions is investigated with focus on understanding the phases and the phase transitions of the model. Particularly, this model exhibits two different paired phases where proliferation of composite topological defects plays an important role.In Article II and III, a two-dimensional unconventional two-component Coulomb plasma with two distinct Coulomb interactions is investigated. The plasma relates to inner products of Ising-type quantum Hall states as well as to rotating two-component Bose- Einstein condensates with an intercomponent Andreev-Bashkin drag interaction. We investigate the phases and phase transitions of this plasma. Depending on the strength of the attractive intercomponent interaction, the plasma can undergo a Berezinskii- Kosterlitz-Thouless charge-unbinding transition. It can also undergo a two-dimensional melting transition when there is a strong intracomponent repulsion for one of the components. For the parameter values corresponding to the Ising-type quantum Hall states, the plasma is in a screening phase. This can be used to demonstrate that Ising-type quantum Hall states possess quasiparticles with exotic properties.In Article IV, the noncompact CP1 model is investigated. This model is proposed as a critical field theory of the continuous quantum phase transition between the N´eel state and the paramagnetic valence bond solid state in a quantum antiferromagnet. The model exhibits a direct transition line between a fully ordered phase with broken SU(2) symmetry and a fully disordered phase. By going to larger systems, we find that the bicritical point, which terminates the direct transition line, has been overestimated in earlier works. This may have important consequences for the determination of the character of the phase transition along the direct transition line.
This thesis presents four research papers in the field of condensed-matter theory. In all four papers, large-scale Monte Carlo simulations are used to investigate phases and phase transitions in two-component models of superconductors and superfluids with multiple broken symmetries. In Article I, a U(1) × U(1) lattice London superconductor with two different types of intercomponent interactions is investigated with focus on understanding the phases and the phase transitions of the model. Particularly, this model exhibits two different paired phases where proliferation of composite topological defects plays an important role.\n\nIn Article II and III, a two-dimensional unconventional two-component Coulomb plasma with two distinct Coulomb interactions is investigated. The plasma relates to inner products of Ising-type quantum Hall states as well as to rotating two-component Bose- Einstein condensates with an intercomponent Andreev-Bashkin drag interaction. We investigate the phases and phase transitions of this plasma. Depending on the strength of the attractive intercomponent interaction, the plasma can undergo a Berezinskii- Kosterlitz-Thouless charge-unbinding transition. It can also undergo a two-dimensional melting transition when there is a strong intracomponent repulsion for one of the components. For the parameter values corresponding to the Ising-type quantum Hall states, the plasma is in a screening phase. This can be used to demonstrate that Ising-type quantum Hall states possess quasiparticles with exotic properties.\n\nIn Article IV, the noncompact CP1 model is investigated. This model is proposed as a critical field theory of the continuous quantum phase transition between the N´eel state and the paramagnetic valence bond solid state in a quantum antiferromagnet. The model exhibits a direct transition line between a fully ordered phase with broken SU(2) symmetry and a fully disordered phase. By going to larger systems, we find that the bicritical point, which terminates the direct transition line, has been overestimated in earlier works. This may have important consequences for the determination of the character of the phase transition along the direct transition line.
This thesis presents four research papers in the field of condensed-matter theory. In all four papers, large-scale Monte Carlo simulations are used to investigate phases and phase transitions in two-component models of superconductors and superfluids with multiple broken symmetries. In Article I, a U(1) × U(1) lattice London superconductor with two different types of intercomponent interactions is investigated with focus on understanding the phases and the phase transitions of the model. Particularly, this model exhibits two different paired phases where proliferation of composite topological defects plays an important role.In Article II and III, a two-dimensional unconventional two-component Coulomb plasma with two distinct Coulomb interactions is investigated. The plasma relates to inner products of Ising-type quantum Hall states as well as to rotating two-component Bose- Einstein condensates with an intercomponent Andreev-Bashkin drag interaction. We investigate the phases and phase transitions of this plasma. Depending on the strength of the attractive intercomponent interaction, the plasma can undergo a Berezinskii- Kosterlitz-Thouless charge-unbinding transition. It can also undergo a two-dimensional melting transition when there is a strong intracomponent repulsion for one of the components. For the parameter values corresponding to the Ising-type quantum Hall states, the plasma is in a screening phase. This can be used to demonstrate that Ising-type quantum Hall states possess quasiparticles with exotic properties.In Article IV, the noncompact CP1 model is investigated. This model is proposed as a critical field theory of the continuous quantum phase transition between the N´eel state and the paramagnetic valence bond solid state in a quantum antiferromagnet. The model exhibits a direct transition line between a fully ordered phase with broken SU(2) symmetry and a fully disordered phase. By going to larger systems, we find that the bicritical point, which terminates the direct transition line, has been overestimated in earlier works. This may have important consequences for the determination of the character of the phase transition along the direct transition line.
Using a self-devised numerical approach, we developed a powerful tool to investigate vortex properties and interactions in mean-field theories for superconductors and superfluids, based on fixing the vortex phase distribution in the energy minimization process. The method was applied to (i) multi-component Bose-Einstein condensates (BECs) and (ii) superconductors with single- or multi-component superconducting condensates. In these systems, vortex-vortex interaction and other key vortex features are analytically described only in specific regimes, that do not account for a large part of vortex behavior observed experimentally. In multi-component BECs, for example, the vortex-vortex interaction is only known for inter-vortex distances much greater than the healing length, i.e. far from the vortex core. Under our approach, by assuming multi-vortex structures, within Gross-Pitaevskii theory, we report the vortex-vortex interaction in the full range of distances, capturing the mechanism behind unusual vortex conformations previously reported in literature, such as bound clusters with two or three vortices. Usually, these clusters emerge from a competition between intra- and inter-component vortex interaction, but we demonstrate they can also emerge from the phase-frustration between the components. In superconductors, the description of vortex-vortex interaction is usually restricted to bulk or very thin films, and most of the key vortex features, such as the spatial magnetic field and current density profiles, are known only in the limit of London theory, i.e. for coherence length negligible as compared to magnetic field penetration depth and other system dimensions. The parametric range outside this limit is actually relevant to many materials. We fill that gap by applying our method to Ginzburg-Landau theory. The vortex structure is investigated for single- and two-gap bulk superconductors, outside the London regime. This enables us to extend analytical expressions describing the condensate and magnetic profiles around the vortex available in literature by numerical calculations and suitable fitting functions. We expand our approach to account for films with finite thickness, to connect our findings to both bulk and Pearl’s description by adjusting the sample thickness. This also allowed us to describe how vortex configurations change for samples with intermediate thickness, where we observe the effective magnetic response of the superconductor changing between the textbook type-1 and type-2 behaviors, in a nontrivial manner, governed by the non-monotonic vortex interaction. As a result of a detailed analysis, we propose new critical parameters to define the crossover between different regimes and establish their relation with the superconducting critical fields.
In this thesis we investigate the properties of mixtures of Bose gases in one dimensions at zero temperature using quantum Monte-Carlo methods. First we investigate the limiting case of an impurity interacting with an atomic bath. We characterize the impurity, by calculating its effective mass, binding energy as well as the contact parameter between the impurity and the bath. In particular, we find that the effective mass rapidly increases to very large values when the impurity gets strongly coupled to an otherwise weakly repulsive bath. Then we describe uniform balanced mixtures with repulsive interactions. We investigate the miscibility phase diagram of the two components and find that correlations do not alter the phase diagram predicted by mean-field theories. We investigate the Andreev-Bashkin effect , a non-dissipative drag between the the two components of the gas and find that the drag becomes very large in the strongly interacting regime. In non-homogeneous systems we also investigate the frequency of the spin-dipole mode. Finally we describe mixtures with attractive inter-species interactions, where one can obtain a liquid ground state because of the competition between the inter-species attraction and intra-species repulsion. We characterize the the liquid and we find that the liquid state can be formed if the ratio of coupling strengths between inter-species attractive and intra-species repulsive interactions exceeds a critical value.
This thesis presents six research papers on topics in condensed-matter theory and one paper on a computational method.In two of the papers the focus is on the search for Deconfined Quantum Criticality in models describing quantum antiferromagnets on the square lattice. DQC is conjectured to be a quantum critical point between Neel and valence bond solid ordering in the models. If true, it would represent a schism with the Landau Ginzburg Wilson paradigm of phase transitions, inwhich such a critical point cannot be generic. Verification of the existence of DQC could have consequences not only for our understanding of phase transitions in general, but more specifically also for the understanding of the cuprate superconductors.Despite extensive Monte Carlo simulations, we are not able to reach a conclusion on the character of the phase transition for one of the proposed DQC models. In another, more fundamental model, no phase transition is found at all, severely undermining a lot of the theoretical framework assumed to be true in earlier work.Four of the papers investigate thermodynamical properties of superconductors with several (three or more) superconducting bands. This research is motivated by the multiband iron based superconductors, but the results should be quite general.Using large scale Monte Carlo simulations, we reveal that a new, time reversal symmetry broken non-superconducting phase should be viable for repulsive inter-band interactions. This is in contrast to mean field studies where no such phase is found, signifying the importance of fluctuations in these systems, even in three dimensions.In the last paper we present a multi-histogram reweighting method for nonequilibrium Markov chains with discrete energies.