We study physical properties of a Luttinger liquid in a superlattice which is characterized by alternating two tunneling parameters. Employing the Bosonization approach, we describe the corresponding Hubbard model by the equivalent Tomonoga-Luttinger model. We analyze the spin-charge separation and transport property as the difference between the two tunneling parameter increases. We suggest that cold Fermi gases trapped in a bichromatic optical lattice and coupled quantum dots offer the opportunity to measure these effects in a convenient manner. We also study the classical Ising chain with two tunneling parameters. We found that the classical two-point correlator decreases as the difference between the two tunneling parameter increases.
We study physical properties of a Luttinger liquid in a superlattice which is characterized by alternating two tunneling parameters. Employing the Bosonization approach, we describe the corresponding Hubbard model by the equivalent Tomonoga-Luttinger model. We analyze the spin-charge separation and transport property as the difference between the two tunneling parameter increases. We suggest that cold Fermi gases trapped in a bichromatic optical lattice and coupled quantum dots offer the opportunity to measure these effects in a convenient manner. We also study the classical Ising chain with two tunneling parameters. We found that the classical two-point correlator decreases as the difference between the two tunneling parameter increases.
We investigate Luttinger liquid superlattices, periodic structures composed of two kinds of one-dimensional systems of interacting electrons. We calculate several properties of the low-energy sector: the effective charge and spin velocities, the compressibility, various correlation functions, the Landauer conductance, and the Drude weight. The low-energy properties are subsumed into effective parameters, much like homogeneous one-dimensional systems. A generic result is the weighted average nature of these parameters, in proportion to the spatial extent of the underlying subunits, pointing to the possibility of ``engineered'' structures. As a specific realization, we consider a one-dimensional Hubbard superlattice, which consists of a periodic arrangement of two long Hubbard chains with different coupling constants and different hopping amplitudes. This system exhibits a rich phase diagram with several phases, both metallic and insulating. We have found that gapless insulating phases are present over a wide range of parameters.
We calculate the correlation functions and the dc conductivity of Luttinger liquid superlattices, modelled by a repeated pattern of interacting and free Luttinger liquids. In a specific realization, where the interacting subsystem is a Hubbard chain, the system exhibits a rich phase diagram with four different phases: two metals and two compressible insulators. In general, we find that the effective low-energy description amalgamates features of both types of liquids in proportion to their spatial extent, suggesting the interesting possibility of `engineered' Luttinger liquids. In recent years, new experimental techniques have made it possible to grow nanostructures which are topologically one-dimensional, such as quantum wires and Carbon nanotubes. However, care must be taken when invoking existing models to discuss their electronic properties, since inhomogeneities must be taken into account in a fundamental way. Consider, for instance, the Luttinger liquid (LL), which is the standard model for low-energy phenomena involving interacting electrons in one dimension [1]. The absence of conductance renormalization in long high-mobility GaAs wires [2] has been explained in terms of a usual LL (representing the wire) in contact with a non-interacting LL at each of its ends (representing the Fermi liquid leads); that is, overall, the system can be thought of as an inhomogeneous Luttinger Liquid (ILL). LLs with different inhomogeneity profiles have also been used in the context of the fractional quantum Hall effect (FQHE), to describe transitions between edge states at different fillings [3, 4], or between an edge state connected to a Fermi liquid [5]. A different class of inhomogeneous systems is represented by superlattices (SLs) and multilayers. By varying the relative th...
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.
We consider the problem of tunneling between spinless one-dimensional (1D) Luttinger-liquid chains. We show how to map the problem onto the four-state chiral clock model together with a free boson for the total charge mode. We use a variety of results, some of them exact, from the integrable chiral Potts model and the study of commensurate/incommensurate transitions to deduce the physics of coupled Luttinger liquids. For those intrachain interaction strengths for which interchain tunneling is relevant, we find that it can lead to the formation of symmetric and antisymmetric bands with split Fermi surfaces, depending on the relative strengths of interchain tunneling and interchain interactions. With split Fermi surfaces, interchain transport is coherent. It is not possible to have two gapless Fermi surfaces with the same Fermi momentum when interchain tunneling is relevant. However, interchain interactions can drive the formation of a gap, in which case interchain transport will be incoherent. We comment on the possible relevance of our results to c-axis transport in high-Tc superconductors.
We calculate the correlation functions and the dc conductivity of Luttinger liquid superlattices, modelled by a repeated pattern of interacting and free Luttinger liquids. In a specific realization, where the interacting subsystem is a Hubbard chain, the system exhibits a rich phase diagram with four different phases: two metals and two compressible insulators. In general, we find that the effective low-energy description amalgamates features of both types of liquids in proportion to their spatial extent , suggesting the interesting possibility of `engineered' Luttinger liquids.