Formation of quantum magnetization plateaux in mixed-spin Ising chains with single-ion anisotropy

We investigate the physical processes which give rise to a multi-plateau ground-state magnetization curve in ferrimagnetic Ising chains with alternating spins (S,s) and different single-ion anisotropies on each sublattice of the system under an applied magnetic field, by using an elaboration of the molecular-field theory. Our analysis is started with the system () for which we use the transfer-matrix technique for comparison. In this system, we find a double-plateau structure (initial and saturation) in the magnetization curve for all values of , independent of anisotropies. Then we study two more elaborate systems, comparing the results with density-matrix renormalization group calculations, and finally generalize our argument to the general case. We find that for a specified range of the anisotropy parameters, the system exhibits 2s+1 plateaux, including the two classical and all those allowed for general quantum spin chains. This follows a similar rule as that known for spin-S(S≥1) Ising chains with single-ion anisotropy, for which 2S+1 plateaux appear in the ground-state magnetization curve, surviving even at low temperatures.     

On the critical behavior of the magnetization in high-dimensional Ising models

We derive rigorously general results on the critical behavior of the magnetization in Ising models, as a function of the temperature and the external field. For the nearest-neighbor models it is shown that ind4 dimensions the magnetization is continuous atT _c and its critical exponents take the classical values=3 and=1/2, with possible logarithmic corrections atd=4. The continuity, and other explicit bounds, formally extend tod>3 1/2. Other systems to which the results apply include long-range models ind=1 dimension, with 1/|x–y| couplings, for which 2/(–1) replacesd in the above summary. The results are obtained by means of differential inequalities derived here using the random current representation, which is discussed in detail for the case of a nonvanishing magnetic field.Research supported in part by NSF grant PHY-8301493 A02, and by a John S. Guggenheim Foundation fellowship (M.A.).     

Low-energy properties of aperiodic quantum spin chains

We investigate the low-energy properties of antiferromagnetic quantum XXZ spin chains with couplings following two-letter aperiodic sequences, by an adaptation of the Ma-Dasgupta-Hu renormalization-group method. For a given aperiodic sequence, we argue that, in the easy-plane anisotropy regime, intermediate between the XX and Heisenberg limits, the general scaling form of the thermodynamic properties is essentially given by the exactly known XX behavior, providing a classification of the effects of aperiodicity on XXZ chains. As representative illustrations, we present analytical and numerical results for the low-temperature thermodynamics and the ground-state correlations for couplings following the Fibonacci quasiperiodic structure and a binary Rudin-Shapiro sequence, whose geometrical fluctuations are similar to those induced by randomness.     

Branching chains and critical clusters of Ising spins

Ising critical clusters are related to the excess of neighbor spins of similar, over anti-similar, orientation. The clusters are approximately described by self-avoiding branching chains. γ, ν andalso a “time” (of growth from the origin) and a “perimeter/bulk” exponent are measured with the help of Monte-Carlo sampling.     

Scaling and front dynamics in Ising quantum chains

We study the relaxation behaviour of the quantum Ising chain, focusing our attention onto the non-equilibrium dynamics of the transverse magnetization. The initial states, from which the magnetization relaxes, are product states such as those generated by setting in contact several systems, each initially equilibrated at a given temperature. Due to the free fermionic structure of the chain, the dynamics of the transverse magnetization is easily expressed in a compact form. In the completely factorized initial state, corresponding to a situation where all the spins are thermalized independently, we obtain in the scaling limit the Green function associated to the transverse magnetization. The relaxation behaviour is also considered in the system-bath case, where part of the chain called the system is thermalized at a temperature T_s and the remaining part is at a temperature T_b. The magnetization profiles show a scaling behaviour. Moreover, in the extreme case T_b=∞ and T_s=0, it is shown that the magnetization relaxes in quantized steps in the strong transverse field region.     

Entanglement entropy fluctuations in quantum Ising chains

The behavior of Ising chains with the spin-spin interaction value λ in a transverse magnetic field of constant intensity (h = 1) is considered. For a chain of infinite length, exact analytical formulas are obtained for the second central moment (dispersion) of the entropy operator Ŝ = -lnρ with reduced density matrix ρ, which corresponds to a semi-infinite part of the model chain occurring in the ground state. In the vicinity of a critical point λ_c = 1, the entanglement entropy fluctuation ΔS (defined as the square root of dispersion) diverges as ΔS ∼ [ln(1/|1 − λ|)]^1/2. For the known behavior of the entanglement entropy S, this divergence results in that the relative fluctuation δS = ΔS/S vanishes at the critical point, that is, a state with almost nonfluctuating entanglement is attained.     

Random and aperiodic quantum spin chains: A comparative study

According to the Harris-Luck criterion the relevance of a fluctuating interaction at the critical point is connected to the value of the fluctuation exponent . Here we consider different types of relevant fluctuations in the quantum Ising chain and investigate the universality class of random as well as deterministic-aperiodic models. At the critical point the random and aperiodic systems behave similarly, due to the same type of extreme broad distribution of the energy scales at low energies. The critical exponents of some averaged quantities are found to be a universal function of , but some others do depend on other parameters of the distribution of the couplings. In the off-critical region there is an important difference between the two systems: there are no Griffiths singularities in aperiodic models. Received: 18 November 1997 / Received in final form: 24 November 1997 / Accepted: 8 January 1997     

Electronic spectrum and localization of electronic states in aperiodic quantum dot chains

The electronic energy spectra of aperiodic Thue-Morse, Rudin-Shapiro, and double-periodic quantum dot chains are investigated in the tight-binding approximation. The dependence of the spectrum on all parameters of a “mixed” aperiodic chain model is studied: the electronic energy at quantum dots and the hopping integrals. The electronic degree of localization in the chains under consideration is determined by analyzing the inverse participation ratio. Its spectral distribution and the dependence of the band-averaged degree of localization on these model parameters have been calculated. It is shown that a transition of the system’s sites to a resonant state in which the degree of electron localization decreases, while an overlap between the subbands occurs in the spectrum is possible when the parameters are varied.     

Dynamics in quantum Ising chain driven by inhomogeneous transverse magnetization

We study the dynamics caused by transport of transverse magnetization in one dimensional transverse Ising chain at zero temperature. We observe that a class of initial states having product structure in fermionic momentum-space and satisfying certain criteria, produce spatial variation in transverse magnetization. Starting from such a state, we obtain the transverse magnetization analytically and then observe its dynamics in presence of a homogeneous constant field Γ. In contradiction with general expectation, whatever be the strength of the field, the magnetization of the system does not become homogeneous even after infinite time. At each site, the dynamics is associated with oscillations having two different timescales. The envelope of the larger timescale oscillation decays algebraically with an exponent which is invariant for all such special initial states. The frequency of this oscillation varies differently with external field in ordered and disordered phases. The local magnetization after infinite time also characterizes the quantum phase transition.     

Order parameter statistics in the critical quantum Ising chain

The probability distribution of the order parameter is expected to take a universal scaling form at a phase transition. In a spin system at a quantum critical point, this corresponds to universal statistics in the distribution of the total magnetization in the low-lying states. We obtain this scaling function exactly for the ground state and first excited state of the critical quantum Ising spin chain. This is achieved through a remarkable relation to the partition function of the anisotropic Kondo problem, which can be computed by exploiting the integrability of the system.     

ac-Conductivity of aperiodic chains re-examined

ac-Conductivity of infinite quasiperiodic chanins have been calculated using the Miller-Abrahams equations and a real space decimation technique. Our approach deals with the infinite lattice directly, instead of calculating the conductivity for periodic repetitions of long quasiperiodic segments, as has been done recently. We point out an interesting observation that, some aperiodic chains show the same analytical behaviour in the low frequency ac-conductivity as an ordered chain, whereas, some others behave in a totally different way. We explain this observation from a renormalization group point of view.     

Comparative study of the critical behavior in one-dimensional random and aperiodic environments

We consider cooperative processes (quantum spin chains and random walks) in one-dimensional fluctuating random and aperiodic environments characterized by fluctuating exponents . At the critical point the random and aperiodic systems scale essentially anisotropically in a similar fashion: length (L) and time (t) scales are related as . Also some critical exponents, characterizing the singularities of average quantities, are found to be universal functions of , whereas some others do depend on details of the distribution of the disorder. In the off-critical region there is an important difference between the two types of environments: in aperiodic systems there are no extra (Griffiths)-singularities. Received: 5 February 1998 / Accepted: 17 April 1998     

Junction of three off-critical quantum Ising chains and two-channel Kondo effect in a superconductor

We show that a junction of three off-critical quantum Ising chains can be regarded as a quantum spin chain realization of the two-channel spin-1/2 overscreened Kondo effect with two superconducting leads. We prove that, as long as the Kondo temperature is larger than the superconducting gap, the equivalent Kondo model flows towards the two channel Kondo fixed point. We argue that our system provides the first controlled realization of two channel Kondo effect with superconducting leads. Besides its theoretical interest, this result is of importance for potential applications to a number of contexts, including the analysis of the quantum entanglement properties of a Kondo system.     

Quantum critical behavior of the Kondo necklace model with aperiodic exchange modulation

The low energy behavior of the Kondo necklace model with an aperiodic exchange modulation is studied using a representation for the localized and conduction electron spins, in terms of local Kondo singlet and triplet operators at zero and finite temperature for arbitrary d dimensions. A decoupling scheme on the double time Green's functions is used to find the dispersion relation for the excitations of the system. We determined the dependence between the chemical aperiodic exchange modulation and the spin gap in 1d, 2d and 3d, at zero temperature and in the paramagnetic side of the phase diagram. On the other hand, at low but finite temperatures, the line of Néel transitions in the antiferromagnetic phase is calculated in function of the aperiodic exchange modulation.