32 research outputs found
Localized spin ordering in Kondo lattice models
Using a non-Abelian density matrix renormalization group method we determine
the phase diagram of the Kondo lattice model in one dimension, by directly
measuring the magnetization of the ground-state. This allowed us to discover a
second ferromagnetic phase missed in previous approaches. The phase transitions
are found to be continuous. The spin-spin correlation function is studied in
detail, and we determine in which regions the large and small Fermi surfaces
dominate. The importance of double-exchange ordering and its competition with
Kondo singlet formation is emphasized in understanding the complexity of the
model.Comment: Revtex, 4 pages, 4 eps figures embedde
Magnetism in the dilute Kondo lattice model
The one dimensional dilute Kondo lattice model is investigated by means of
bosonization for different dilution patterns of the array of impurity spins.
The physical picture is very different if a commensurate or incommensurate
doping of the impurity spins is considered. For the commensurate case, the
obtained phase diagram is verified using a non-Abelian density-matrix
renormalization-group algorithm. The paramagnetic phase widens at the expense
of the ferromagnetic phase as the -spins are diluted. For the incommensurate
case, antiferromagnetism is found at low doping, which distinguishes the dilute
Kondo lattice model from the standard Kondo lattice model.Comment: 11 pages, 2 figure
Density-Matrix Renormalization-Group Analysis of Quantum Critical Points: I. Quantum Spin Chains
We present a simple method, combining the density-matrix
renormalization-group (DMRG) algorithm with finite-size scaling, which permits
the study of critical behavior in quantum spin chains. Spin moments and
dimerization are induced by boundary conditions at the chain ends and these
exhibit power-law decay at critical points. Results are presented for the
spin-1/2 Heisenberg antiferromagnet; an analytic calculation shows that
logarithmic corrections to scaling can sometimes be avoided. We also examine
the spin-1 chain at the critical point separating the Haldane gap and dimerized
phases. Exponents for the dimer-dimer and the spin-spin correlation functions
are consistent with results obtained from bosonization.Comment: 21 pages, 12 figures, new results and added references, to appear in
PR
The density-matrix renormalization group
The density-matrix renormalization group (DMRG) is a numerical algorithm for
the efficient truncation of the Hilbert space of low-dimensional strongly
correlated quantum systems based on a rather general decimation prescription.
This algorithm has achieved unprecedented precision in the description of
one-dimensional quantum systems. It has therefore quickly acquired the status
of method of choice for numerical studies of one-dimensional quantum systems.
Its applications to the calculation of static, dynamic and thermodynamic
quantities in such systems are reviewed. The potential of DMRG applications in
the fields of two-dimensional quantum systems, quantum chemistry,
three-dimensional small grains, nuclear physics, equilibrium and
non-equilibrium statistical physics, and time-dependent phenomena is discussed.
This review also considers the theoretical foundations of the method, examining
its relationship to matrix-product states and the quantum information content
of the density matrices generated by DMRG.Comment: accepted by Rev. Mod. Phys. in July 2004; scheduled to appear in the
January 2005 issu
The one dimensional Kondo lattice model at partial band filling
The Kondo lattice model introduced in 1977 describes a lattice of localized
magnetic moments interacting with a sea of conduction electrons. It is one of
the most important canonical models in the study of a class of rare earth
compounds, called heavy fermion systems, and as such has been studied
intensively by a wide variety of techniques for more than a quarter of a
century. This review focuses on the one dimensional case at partial band
filling, in which the number of conduction electrons is less than the number of
localized moments. The theoretical understanding, based on the bosonized
solution, of the conventional Kondo lattice model is presented in great detail.
This review divides naturally into two parts, the first relating to the
description of the formalism, and the second to its application. After an
all-inclusive description of the bosonization technique, the bosonized form of
the Kondo lattice hamiltonian is constructed in detail. Next the
double-exchange ordering, Kondo singlet formation, the RKKY interaction and
spin polaron formation are described comprehensively. An in-depth analysis of
the phase diagram follows, with special emphasis on the destruction of the
ferromagnetic phase by spin-flip disorder scattering, and of recent numerical
results. The results are shown to hold for both antiferromagnetic and
ferromagnetic Kondo lattice. The general exposition is pedagogic in tone.Comment: Review, 258 pages, 19 figure
Ferromagnetism in Kondo lattice models
We report the discovery of a new ferromagnetic phase in the one-dimensional Kondo lattice model for intermediate values of the coupling constant. This new ferromagnetic phase was observed using a non-Abelian density-matrix renormalization group algorithm, which allowed us to measure directly the magnetization of the ground state with high accuracy
Localized Spin Ordering in Kondo Lattice Models
Using a non-Abelian density matrix renormalization group method we determine the phase diagram of the Kondo lattice model in one dimension, by directly measuring the magnetization of the ground state. This allowed us to discover a second ferromagnetic phase missed in previous approaches. The phase transitions are found to be continuous. The spin-spin correlation function is studied in detail, and we determine in which regions the large and small Fermi surfaces dominate. The importance of double-exchange ordering and its competition with Kondo singlet formation is emphasized in understanding the complexity of the model