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.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.
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 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.
This thesis concerns ultracold two-dimensional atomic gases and the associated novel superfluid phases in an optical lattice subjected to staggered rotations. In the first part, we study the Berezinskii-Kosterlitz-Thouless (BKT) transition in a two-dimensional Bose gas. Motivated by recent experiments on the cold gas in the BKT regime, we employ a modified Popov theory and a renormalization group theory to describe the system. The two-dimensional renormalization group flow equations display unique features, which we interpret as precursors of the BKT physics. We further calculate higher correlation functions close to the BKT transition, which can serve as observables for detecting effects beyond mean-field. Finally, we obtain the density profile under the conditions of the experiment performed in the group of Dalibard in Paris, France. In the second part of the thesis, we study a recent experimental proposal of a time-dependent optical lattice with staggered rotations. We show that in the tight-binding regime, the system can be effectively described by a (Bose-)Hubbard model subjected to an artificial staggered magnetic field. The staggered magnetic field (flux) in the lattice leads to conical points in the band structure which possesses distinct minima for different strength, and can give rise to Dirac-like dispersions. For bosons, we show that besides the homogenous superfluid phase, a staggered-vortex superfluid phase is stabilized for large flux values. We show that the staggered flux renormalizes the phase boundary and find a multi-critical point separating the two superfluid phases and the Mott insulating phase. Finally, the full phase diagram of the generalized Bose-Hubbard model at zero temperature is determined. We then generalize the model for a mixture of ultracold bosons and spin-1/2 fermions. By using the Bogoliubov theory for the bosonic sector, we show that the bosonic superfluid mediates attractive interactions between fermions up to the nearest-neighbor site. The resulting model is an extended Hubbard model in the presence of a staggered magnetic field, where the on-site and the nearest-neighbor attractive interactions can be tuned independently. We then employ the Bardeen-Cooper-Schrieffer theory for superconductivity, by considering an on-site pairing order parameter competing with a nearest-neighbor resonating-valence-bond order parameter. Due to conical points in the energy band, the system possesses quantum critical property and the resulting phase diagram displays features which are strikingly similar to that of high-critical-temperature superconductors or heavy-fermion superconductors.
In this thesis, we investigate several topics pertaining to emergent collective quantum phenomena in the domain of correlated fermions, using the quantum Monte Carlo method. They display exotic low temperature phases as well as phase transitions which are beyond the Landau–Ginzburg theory. The interplay between three key points is crucial for us: fermion statistics, many body effects and topology. We highlight the following several achievements: 1. Successful modeling of continuum field theories with lattice Hamiltonians, 2. their sign-problem-free Monte Carlo simulations of these models, 3. and numerical results beyond mean field descriptions. First, we consider a model of Dirac fermions with a spin rotational invariant inter- action term that dynamically generates a quantum spin Hall insulator. Surprisingly, an s-wave superconducting phase emerges due to the condensation of topological de- fects of the spin Hall order parameter. When particle-hole symmetry is present, the phase transition between the topological insulator and the superconducting phase is an example of a deconfined quantum critical point(DQCP). Although its low energy effec- tive field theory is purely bosonic, the exact conservation law of the skyrmion number operator rules out the possibility of realizing this critical point in lattice boson models. This work is published in Ref. [1]. Second, we dope the dynamically generated quantum spin Hall insulator mentioned above. Hence it is described by a field theory without Lorentz invariance due to the lack of particle-hole symmetry. This sheds light on the extremely hot topic of twisted bilayergraphene: Why is superconductivity generated when the repulsive Coulomb interaction is much stronger than the electron-phonon coupling energy scale? In our case, Cooper pairs come from the topological skyrmion defects of the spin current order parameter, which are charged. Remarkably, the nature of the phase transition is highly non-mean-field-like: one is not allowed to simply view pairs of electrons as single bosons in a superfluid-Mott insulator transition, since the spin-current order parameter can not be ignored. Again, due to the aforementioned skyrmions, the two order parameters are intertwined: One phase transition occurs between the two symmetry breaking states. This work is summarized in Ref. [2]. Third, we investigate the 2 + 1 dimensional O(5) nonlinear sigma model with a topological Wess-Zumino-Witten term. Remarkably, we are able to perform Monte Carlo calculations with a UV cutoff given by the Dirac Landau level quantization. It is a successful example of simulating a continuous field theory without lattice regularization which leads to an additional symmetry breaking. The Dirac background and the five anti-commuting Dirac mass terms naturally introduce the picture of a non-trivial Berry phase contribution in the parameter space of the five component order parameter. Using the finite size scaling method given by the flux quantization, we find a stable critical phase in the low stiffness region of the sigma model. This is a candidate ground state of DQCP when the O(5) symmetry breaking terms are irrelevant at the critical point. Again, it has a bosonic low energy field theory which is seemingly unable to be realized in pure boson Hamiltonians. This work is summarized in Ref. [3].