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Physical review. B, Condensed matter

Magnetization plateaus and Luttinger liquid behavior inXXZchains with superlattice structure

Jereson Silva-Valencia, E. Miranda

Published Dec 19, 2001• 13 citations
Publisher

Abstract

We study spin superlattices composed of a repeated pattern of two long spin-$\frac{1}{2}$ XXZ chains with different anisotropy parameters. They can be viewed as the limit of p-merized chains when the number of sites per cluster is very large. Magnetization plateaus are found, with magnetization values that depend on the relative sizes of the subchains. In certain regions of parameter space, the low-energy properties are described in terms of a Luttinger liquid superlattice parametrized by an effective velocity and an effective compactification radius.

DOI
10.1103/physrevb.65.024443

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We study spin superlattices composed of a repeated pattern of two long spin-12\frac{1}{2}21​ XXZ chains with different anisotropy parameters. They can be viewed as the limit of p-merized chains when the number of sites per cluster is very large. Magnetization plateaus are found, with magnetization values that depend on the relative sizes of the subchains. In certain regions of parameter space, the low-energy properties are described in terms of a Luttinger liquid superlattice parametrized by an effective velocity and an effective compactification radius.
Using the density matrix renormalization group technique, we study spin superlattices composed of a repeated pattern of two spin-12XXZ\frac{1}{2}\phantom{\rule{0.3em}{0ex}}XXZ21​XXZ chains with different anisotropy parameters. The magnetization curve can exhibit two plateaus, a nontrivial plateau with the magnetization value given by the relative sizes of the subchains and another trivial plateau with zero magnetization. We find good agreement of the value and the width of the plateaus with the analytical results obtained previously. In the gapless regions away from the plateaus, we compare the finite-size spin gap with the predictions based on bosonization and find reasonable agreement. These results confirm the validity of the Tomonaga-Luttinger liquid superlattice description of these systems.
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...
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 the present work, we provide a comprehensive numerical investigation of the magnetic properties and phase spectra of three types of spin-1/2 branched chains consisting of one, two and three side spins per unit block with intra-chain interaction and a uniform inter-chain interaction in the presence of an external magnetic field. In a specific magnetic field interval, the low-temperature magnetization of these chains shows a step-like behavior with a pronounced plateau depending on the strength and the type of intra-chain interaction being ferromagnetic or antiferromagnetic. We demonstrate that when inter-chain interaction J1 is antiferromagnetic and intra-chain interaction J2 is ferromagnetic, the magnetization of the models manifests a smooth increase without a plateau, which is evidence of the existence of a Luttinger-like spin liquid phase before reaching its saturation value. On the other hand, when J1 is ferromagnetic and J2 is antiferromagnetic, the low-temperature magnetization of the chain with two branches shows an intermediate plateau at one-half of the saturation magnetization that breaks a quantum spin liquid phase into two regions. The magnetization of the chain with three branches exhibits two intermediate plateaus and two regions of a quantum spin liquid. We demonstrate that the chains with more than one side spin illustrate in their ground-state phase diagram a Kosterlitz-Thouless transition from a gapful phase to a gapless spin liquid phase.
We calculate the spin gap of homogeneous and inhomogeneous spin chains, using the White's density matrix renormalization group technique. We found that the spin gap is related to the ration between the spin velocity and the correlation exponent. We consider a spin superlattice, which is composed of a repeated pattern of two spin-¹/2 XXZ chains with different anisotropy parameters. The behavior of the charge velocity as a function of the anisotropy parameter and the relative size of sub-chains was investigated. We found reasonable agreement between the bosonization results and the numerical ones.