In this thesis we present contributions in the field of the applications of quantum field theories techniques to condensed matter models. In chapter 3 we investigate on the non covariant fermionic determinant and its connection to Luttinger liquids. We address the problem of the regularization of the theory. In chapter 4 we treat spin flipping interactions in the non local Thirring model and we obtain an effective bosonic actions that describe separated spin and charge degrees of freedom. In chapter 4 we apply the self consistent harmonic approximation to previously derived bosonic action and we obtain potential depending equations for the spectrum gap. In chapter 5 we include spin-orbit couplings and compute correlations functions. We show that the spin orbit interactions modify the exponents and the phase diagram of the system and makes new susceptibilities diverge for low temperature. Finally in chapter 6 we summarize the main results and the conclusions.
In this thesis we present contributions in the field of the applications of quantum field theories techniques to condensed matter models. In chapter 3 we investigate on the non covariant fermionic determinant and its connection to Luttinger liquids. We address the problem of the regularization of the theory. In chapter 4 we treat spin flipping interactions in the non local Thirring model and we obtain an effective bosonic actions that describe separated spin and charge degrees of freedom. In chapter 4 we apply the self consistent harmonic approximation to previously derived bosonic action and we obtain potential depending equations for the spectrum gap. In chapter 5 we include spin-orbit couplings and compute correlations functions. We show that the spin orbit interactions modify the exponents and the phase diagram of the system and makes new susceptibilities diverge for low temperature. Finally in chapter 6 we summarize the main results and the conclusions.
In this thesis we present contributions in the field of the applications of quantum field theories techniques to condensed matter models. In chapter 3 we investigate on the non covariant fermionic determinant and its connection to Luttinger liquids. We address the problem of the regularization of the theory. In chapter 4 we treat spin flipping interactions in the non local Thirring model and we obtain an effective bosonic actions that describe separated spin and charge degrees of freedom. In chapter 4 we apply the self consistent harmonic approximation to previously derived bosonic action and we obtain potential depending equations for the spectrum gap. In chapter 5 we include spin-orbit couplings and compute correlations functions. We show that the spin orbit interactions modify the exponents and the phase diagram of the system and makes new susceptibilities diverge for low temperature. Finally in chapter 6 we summarize the main results and the conclusions.
In this thesis I present a theoretical study of three different\nstrongly correlated systems: Luttinger liquids, spin-1 chains and\nthe two-dimensional spin-1/2 Heisenberg model.\n\nFor every sub-field of our research I summarize the background and\nprovide further details to the work presented in the appended\npapers. Chapter 1 corresponds to paper I, Chapter 2 to paper II,\nChapter 3 and 4 to paper III and IV.\n\nIn paper I, we calculate with bosonization techniques the local\ndensity of states of a finite segment of Luttinger liquid. Besides of\nbeing of experimental relevance for Scanning Tunneling Microscopy\nexperiments on carbon nanotubes and cleaved overgrowth wires, the\nwave functions of a "Luttinger liquid in a box" very nicely\nvisualize the fundamental bosonic nature of the low energy\nexcitations.\n\nIn paper II, we analyze with field theory methods how the presence\nof a single-ion anisotropy affects the behavior of a spin-1 chain.\nWe determine in the framework of the Non Linear Sigma Model how the gaps\nof the anisotropic chain depend on an applied staggered magnetic\nfield. Our theoretical analysis is meant to model compounds like\nrmR2BaNiO5 that show coexistence of Haldane phase and\nlong-range order.\n\nIn paper III, we compute with quantum Monte Carlo simulations the\nlocal response to a uniform magnetic field around vacancies in the\ntwo-dimensional Heisenberg model. From the full understanding of the\nnumerical results, we can make quantitative predictions of relevance\nfor Nuclear Magnetic Resonance and susceptibility experiments. In\nparticular, we expect, even in the thermodynamic limit, a finite\nCurie contribution to the total susceptibility arising from the\nimpurities.\n\nFinally in paper IV, we consider interaction effects among\nimpurities. We compute the potential between static vacancies in\nseveral low-dimensional spin-1/2 antiferromagnets comparing\nthe numerics with exact results from conformal field theory and\nlinear spin wave theory. The potential is directly related to the\nlocal valence bond order and its magnitude is a loyal measure of the\namount of quantum correlations present into the system.
Strongly correlated systems show a variety of intriguing properties and have been extensively studied over the years. In this thesis two strongly correlated systems are discussed: the two-dimensional antiferromagnet and the Luttinger liquid. The Luttinger liquid has attracted much interest as a paradigm of non-Fermi liquid behavior. In the first part of the thesis, basic properties of Fermi liquids are briefly described while those of Luttinger liquids are considered in more detail. The differences in spectral properties of Luttinger liquids and Fermi liquids are discussed, as are the consequences for photoemission experiments. In this context Luttinger liquids with boundaries, treated in Papers I, II, and III, are introduced. The exact single-electron Green's function at finite temperature is calculated with bosonization methods, for both periodic and finite open-boundary systems. The corresponding local spectral density is analyzed. For a system with open boundaries, the well-known zero temperature bulk behavior always crosses over to a boundary dominated regime for small energies, while at finite temperature the low energy behavior becomes quadratic. For a periodic finite-size system we also calculate the Coulomb-blockade-like oscillations and study their dependence on interaction and temperature. The two-dimensional antiferromagnet has attracted much attention due to its connection to the undoped phase of the ceramic high-temperature superconductors. In the second part of the thesis including Papers IV and V, the two-dimensional Heisenberg antiferromagnet defined on the triangular and the honeycomb lattices is studied. We use the Schwinger-boson mean-field theory to investigate the stability of the ground state with respect to frustration. For the honeycomb lattice model we find an increased Néel stability as compared to the classical case. The dynamic structure factor is considered for various temperatures and the spin-wave velocity and the susceptibility are presented as functions of frustration for spin S=1/2. In the case of the intrinsically frustrated triangular lattice model we obtain, in the limit of infinite spin, results in complete agreement with the linear spin-wave theory. In contrast to the latter, however, two of the three modes acquire a mass for finite spin. The origin of this effect is discussed.
The Chapter 2 is devoted to the study of the transport properties of a quantum wire, described by the Tomonaga-Luttinger model, in the presence of a backscattering potential provided by several point-like or extended time-dependent impurities (barriers) and find regimes of conductance enhancement. In Chapte 3 we study a set of crossed 1D systems, which are coupled with each other via tunnelling at the crossings. Concentrating on the case of a single crossing, we were able to explain recent experiments on crossed metallic and semiconducting nanotubes, which showed the presence of localized states in the region of crossing. The Chapter 4 treats the effects of disorder and interactions in a quantum Hall ferromagnet. We study the problem by projecting the original fermionic Hamiltonian into magnon states, which behave as bosons in the vicinity of the ferromagnetic ground state. The approach permits the reformulation of a strongly interacting model into a non-interacting one. The latter is a non-perturbative scheme that consists in treating the two-particle neutral excitations of the electron system as a bosonic single-particle. Indeed, the employment of bosonization facilitates the inclusion of disorder in the study of the system. It has been shown previously that disorder may drive a quantum phase transition in the Hall ferromagnet. However, such studies have been either carried out in the framework of the nonlinear sigma model, as an effective low-energy theory, or included the long-range Coulomb interaction in a quantum description only up to the Hartree-Fock level. Here, we establish the occurrence of a disorder-driven quantum phase transition from a ferromagnetic 2DEG to a spin glass phase by taking into account interactions between electrons up to the random phase approximation level in a fully quantum description. In the Chapter 5 we derive and discuss an experimentally realistic model describing ultracold atoms in an optical lattice including a commensurate, but staggered, Zeeman field. The resulting band structure is quite exotic; fermions in the third band have an unusual rounded picture-frame Fermi surface (essentially two concentric squircles), leading to imperfect nesting. We develop a generalized theory describing the spin and charge degrees of freedom simultaneously, and show that the system can develop a coupled spin-charge-density wave order. This ordering is absent in studies of the Hubbard model that treat spin and charge density separately.
In this thesis we study the spin or pseudospin singlet pair condensation of two different kinds of polarized fermion systems.Using generalized BCS mean-field theories we study how pairing adapts to unequal spin or pseudospin populations.After briefly reviewing the basic physics of superconductivity in Chapter 2, in Chapter 3 the mean-field theory for electron-hole bilayer systems is derived to describe the condensation of excitons which is analogous to the Cooper pair condensation in superconductors.Self-consistent solution of the exciton system gap equation shows that the excitation energy spectrum is qualitatively the same as in superconductors.In Chapter 4 the role of the spin degree of freedom in the bilayer system is investigated by generalizing the two-component mean-field theory developed in Chapter vi 3 to four-component cases.The main consequence is that population polarization leads to ferromagnetism.The interplay between exciton condensation and spontaneous spin-order is the most important consequence of the presence of both spin and pseudospin degrees of freedom in excitonic condensates.In a sense that we explain in this Chapter, both normal and condensed fluids are present in the ferromagnetic excitonic state.Using the Rashba spin-orbit interaction model derived in the appendix, we show that an external electric field can alter the characteristics of the ferromagnetic condensate phase.The spin splitting by the spin-orbit interaction and its different spin state structures lead to qualitatively different magnetic properties for electron and hole layers.In Chapter 5 we turn our attention to a second class of polarized fermion systems that is of great current interest.A fully quantum mechanical treatment of a rotating fermion atom cloud is developed and implicit equations determining the critical temperatures for all center-of-mass Landau level pairings are obtained.In Chapter 6 the condition for the realization of higher center-of-mass Landau level pairing, which corresponds to FFLO state in spin split superconductors, is determined by calculating the critical temperatures for all possible pairing channels.It is shown that FFLO states can be realized in the strong interaction and low rotation frequency regimes in parameter space, where the pairing energy can survive the high polarization.
We present in this thesis a series of studies on the physical properties of some one dimensional systems. In particular we study the low energy properties of various spin chains and a junction of Luttinger wires. For spin chains we specifically look at the role of perturbations like frustrating interactions and dimerisation in a nearest neighbour chain and the formation of magnetisation plateaus in two kinds of models; one purely theoretical and the other motivated by experiments. In our second subject of interest we study using a renormalisation group analysis the effect of spin dependent scattering at a junction of Luttinger wires. We look at the physical effects caused by the interplay of electronic interactions in the wires and the scattering processes at the junction. The thesis begins with an introductory chapter which gives a brief glimpse of the ideas and techniques used in the specific problems that we have worked on. Our work on these problems is then described in detail in chapters 25. We now present a brief summary of each of those chapters.
In the second chapter we look at the ground state phase diagram of the mixed-spin sawtooth chain, i.e a system where the spins along the baseline are allowed to be different from the spins on the vertices. The spins S1 along the baseline interact with a coupling strength J1(> 0). The coupling of the spins on the vertex (S2) to the baseline spins has a strength J2. We study the phase diagram as a function of J2/J1 [1]. The model exhibits a rich variety of phases which we study using spinwave theory, exact diagonalisation and a semi-numerical perturbation theory leading to an effective Hamiltonian. The spinwave theory predicts a transition from a spiral state to a ferrimagnetic state at J2S2/2J1S1 = 1 as J2/J1 is increased. The spectrum has two branches one of which is gapless and dispersionless (at the linear order) in the spiral phase. This arises because of the infinite degeneracy of classical ground states in that phase. Numerically, we study the system using exact diagonalisation of up to 12 unit cells and S1 = 1 and S2 =1/2. We look at the variation of ground state energy, gap to the lowest excitations, and the relevant spin correlation functions in the model. This unearths a richer phase diagram than the spinwave calculation. Apart from revealing a possibility of the presence of more than one kind of spiral phases, numerical results tell us about a very interesting phase for small J2. The spin correlation function (for the spin1/2s) in this region have a property that the nextnearest-neighbour correlations are much larger than the nearest neighbour correlations. We call this phase the NNNAFM (nextnearest neighbour antiferromagnet) phase and provide an understanding of this phase by deriving an effective Hamiltonian between the spin1/2s. We also show the existence of macroscopic magnetisation jumps in the model when one looks at the system close to saturation fields.
The third chapter is concerned with the formation of magnetisation plateaus in two different spin…