Thermodynamics of the anisotropic Heisenberg chain calculated by the density matrix renormalization group method

The density matrix renormalization group (DMRG) method is applied to the anisotropic Heisenberg chain at finite temperatures. The free energy of the system is obtained using the quantum transfer matrix which is iteratively enlarged in the imaginary time direction. The magnetic susceptibility and the specific heat are calculated down to T=0.01J and compared with the Bethe ansatz results. The agreement including the logarithmic correction in the magnetic susceptibility at the isotropic point is fairly good.Comment: 4 pages, 3 Postscript figures, REVTeX, to appear in J. Phys. Soc. Jpn. Vol.66 No.8 (1997

Efficiency of symmetric targeting for finite-T DMRG

Two targeting schemes have been known for the density matrix renormalization group (DMRG) applied to non-Hermitian problems; one uses an asymmetric density matrix and the other uses symmetric density matrix. We compare the numerical efficiency of these two targeting schemes when they are used for the finite temperature DMRG.Comment: 4 pages, 3 Postscript figures, REVTe

Finite-temperature phase transitions in quasi-one-dimensional molecular conductors

Phase transitions in 1/4-filled quasi-one-dimensional molecular conductors are studied theoretically on the basis of extended Hubbard chains including electron-lattice interactions coupled by interchain Coulomb repulsion. We apply the numerical quantum transfer-matrix method to an effective one-dimensional model, treating the interchain term within mean-field approximation. Finite-temperature properties are investigated for the charge ordering, the "dimer Mott" transition (bond dimerization), and the spin-Peierls transition (bond tetramerization). A coexistent state of charge order and bond dimerization exhibiting dielectricity is predicted in a certain parameter range, even when intrinsic dimerization is absent.Comment: to be published in J. Phys. Soc. Jpn., Vol. 76 (2007) No. 1 (5 pages, 4 figures); typo correcte

The Free Energy and the Scaling Function of the Ferromagnetic Heisenberg Chain in a Magnetic Field

A nonlinear susceptibilities (the third derivative of a magnetization $m_S$ by a magnetic field $h$ ) of the $S$=1/2 ferromagnetic Heisenberg chain and the classical Heisenberg chain are calculated at low temperatures $T.$ In both chains the nonlinear susceptibilities diverge as $T^{-6}$ and a linear susceptibilities diverge as $T^{-2}.$ The arbitrary spin $S$ Heisenberg ferromagnet $[$ ${\cal H} = \sum_{i=1}^{N} \{ - J{\bf S}_{i} {\bf S}_{i+1} - (h/S) S_{i}^{z} \}$ $(J>0),$ $]$ has a scaling relation between $m_S,$ $h$ and $T:$ $m_S(T,h) = F( S^2 Jh/T^2).$ The scaling function $F(x)$=(2$x$/3)-(44$x^{3}$/135) + O($x^{5}$) is common to all values of spin $S.$Comment: 16 pages (revtex 2.0) + 6 PS figures upon reques

Combination of Ferromagnetic and Antiferromagnetic Features in Heisenberg Ferrimagnets

We investigate the thermodynamic properties of Heisenberg ferrimagnetic mixed-spin chains both numerically and analytically with particular emphasis on the combination of ferromagnetic and antiferromagnetic features. Employing a new density-matrix renormalization-group technique as well as a quantum Monte Carlo method, we reveal the overall thermal behavior: At very low temperatures, the specific heat and the magnetic susceptibility times temperature behave like $T^{1/2}$ and $T^{-1}$, respectively, whereas at intermediate temperatures, they exhibit a Schottky-like peak and a minimum, respectively. Developing the modified spin-wave theory, we complement the numerical findings and give a precise estimate of the low-temperature behavior.Comment: 9 pages, 9 postscript figures, RevTe

Thermodynamics of doped Kondo insulator in one dimension: Finite Temperature DMRG Study

The finite-temperature density-matrix renormalization-group method is applied to the one-dimensional Kondo lattice model near half filling to study its thermodynamics. The spin and charge susceptibilities and entropy are calculated down to T=0.03t. We find two crossover temperatures near half filling. The higher crossover temperature continuously connects to the spin gap at half filling, and the susceptibilities are suppressed around this temperature. At low temperatures, the susceptibilities increase again with decreasing temperature when doping is finite. We confirm that they finally approach to the values obtained in the Tomonaga-Luttinger (TL) liquid ground state for several parameters. The crossover temperature to the TL liquid is a new energy scale determined by gapless excitations of the TL liquid. The transition from the metallic phase to the insulating phase is accompanied by the vanishing of the lower crossover temperature.Comment: 4 pages, 7 Postscript figures, REVTe

Doped two orbital chains with strong Hund's rule couplings - ferromagnetism, spin gap, singlet and triplet pairings

Different models for doping of two-orbital chains with mobile $S=1/2$ fermions and strong, ferromagnetic (FM) Hund's rule couplings stabilizing the S=1 spins are investigated by density matrix renormalization group (DMRG) methods. The competition between antiferromagnetic (AF) and FM order leads to a rich phase diagram with a narrow FM region for weak AF couplings and strongly enhanced triplet pairing correlations. Without a level difference between the orbitals, the spin gap persists upon doping, whereas gapless spin excitations are generated by interactions among itinerant polarons in the presence of a level difference. In the charge sector we find dominant singlet pairing correlations without a level difference, whereas upon the inclusion of a Coulomb repulsion between the orbitals or with a level difference, charge density wave (CDW) correlations decay slowest. The string correlation functions remain finite upon doping for all models.Comment: 9pages, 9figure

Finite Temperature DMRG Investigation of the Spin-Peierls Transition in CuGeO3_3

We present a numerical study of thermodynamical properties of dimerized frustrated Heisenberg chains down to extremely low temperatures with applications to CuGeO$_3$. A variant of the finite temperature density matrix renormalization group (DMRG) allows the study of the dimerized phase previously unaccessible to ab initio calculations. We investigate static dimerized systems as well as the instability of the quantum chain towards lattice dimerization. The crossover from a quadratic response in the free energy to the distortion field at finite temperature to nonanalytic behavior at zero temperature is studied quantitatively. Various physical quantities are derived and compared with experimental data for CuGeO$_3$ such as magnetic dimerization, critical temperature, susceptibility and entropy.Comment: LaTeX, 5 pages, 5 eps figures include

Thermodynamics of quantum Heisenberg spin chains

Thermodynamic properties of the quantum Heisenberg spin chains with S = 1/2, 1, and 3/2 are investigated using the transfer-matrix renormalization-group method. The temperature dependence of the magnetization, susceptibility, specific heat, spin-spin correlation length, and several other physical quantities in a zero or finite applied field are calculated and compared. Our data agree well with the Bethe ansatz, exact diagonalization, and quantum Monte Carlo results and provide further insight into the quantum effects in the antiferromagnetic Heisenberg spin chains.Comment: 9 pages, 10 figure

Application of the density matrix renormalization group method to finite temperatures and two-dimensional systems

The density matrix renormalization group (DMRG) method and its applications to finite temperatures and two-dimensional systems are reviewed. The basic idea of the original DMRG method, which allows precise study of the ground state properties and low-energy excitations, is presented for models which include long-range interactions. The DMRG scheme is then applied to the diagonalization of the quantum transfer matrix for one-dimensional systems, and a reliable algorithm at finite temperatures is formulated. Dynamic correlation functions at finite temperatures are calculated from the eigenvectors of the quantum transfer matrix with analytical continuation to the real frequency axis. An application of the DMRG method to two-dimensional quantum systems in a magnetic field is demonstrated and reliable results for quantum Hall systems are presented.Comment: 33 pages, 18 figures; corrected Eq.(117