Orbital effect of a magnetic field on two-leg Hubbard ladder

By setting up the relevant recursion relations and by doing exact and approximate calculations, we show that there is no critical dimension in a self-avoiding random walk on a simplex fractal. Received: 6 April 1998 / Revised: 4 August 1998 / Accepted: 26 August 1998     

The density-matrix renormalization group in the age of matrix product states

The density-matrix renormalization group method (DMRG) has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems. In the further development of the method, the realization that DMRG operates on a highly interesting class of quantum states, so-called matrix product states (MPS), has allowed a much deeper understanding of the inner structure of the DMRG method, its further potential and its limitations. In this paper, I want to give a detailed exposition of current DMRG thinking in the MPS language in order to make the advisable implementation of the family of DMRG algorithms in exclusively MPS terms transparent. I then move on to discuss some directions of potentially fruitful further algorithmic development: while DMRG is a very mature method by now, I still see potential for further improvements, as exemplified by a number of recently introduced algorithms.     

Effect of relevant umklapp process on the two-leg Hubbard ladder with a half-filled band under pressure

By means of perturbative renormalization approach we study the effect of relevant umklapp process on dimensional crossover caused by interladder one particle hopping in weakly coupled two-leg Hubbard ladders with a half filled-band. We found that a crossover takes place at a finite value which increases as the amplitude of umklapp process increases. For the system undergoes a phase transition to the spin density wave phase (SDW) via the two particle hopping process, while for the system undergoes a crossover to the two dimensional Fermi liquid phase via one particle hopping process. Received 25 December 1998     

A generation-based particle–hole density-matrix renormalization group study of interacting quantum dots

The particle–hole version of the density-matrix renormalization-group method (PH-DMRG) is utilized to calculate the ground-state energy of an interacting two-dimensional quantum dot. We show that a modification of the method, termed generation-based PH-DMRG, leads to significant improvement of the results, and discuss its feasibility for the treatment of large systems. As another application we calculate the addition spectrum.     

The ground state of the neutral Hubbard model

The ground state energy of the neutral Hubbard model is calculated by BCS methods for all values of total spinS _z . Numerical results are given for the simple cubic and for the body centred cubic lattice. Antiferromagnetic ordering and a finite paramagnetic susceptibility is found for all values of the coupling constantV ₀.     

Density-matrix renormalization group study of the spin-Peierls instability in the antiferromagnetic Heisenberg ladder

The columnar dimerized antiferromagnetic S?=?1/2 spin ladder is numerically studied by the density-matrix renormalization-group (DMRG) method. The elastic lattice with spin-phonon coupling ?? and lattice elastic force k is introduced into the system. Thus the S?=?1?/?2 Heisenberg spin chain is unstable towards dimerization (the spin-Peierls transition). However, the dimerization should be suppressed if the rung coupling J _?? is sufficiently large, and a Columnar dimer to Rung singlet phase transition takes place. After a self-consistent calculation of the dimerization, we determine the quantum phase diagram by numerically computing the singlet-triplet gap, the dimerization amplitude, the order parameters, the rung spin correlation and quantum entropies. Our results show that the phase boundary between the Columnar dimer phase and Rung singlet phase is approximately of the form J _?? ~ \hbox{$(\frac{k}{\alpha^{2}})^{-\frac{5}{4}}$} ( k ?? 2 ) ? 5 4.     

Superconducting gap for a two-leg t-J ladder

Single-particle diagonal and off-diagonal Green's functions of a two-leg t-J ladder at 1/8 doping are investigated by exact diagonalizations techniques. A numerically tractable expression for the superconducting gap is proposed and the frequency dependence of the real and imaginary parts of the gap are determined. The role of the low-energy gapped spin modes, whose energies are computed by a (one-step) contractor renormalization procedure, is discussed.     

Perturbative study of thermodynamic properties for the two-leg spin ladder

We apply finite-temperature perturbation theory to study thermodynamic properties of the two-leg antiferromagnetic spin ladder in the strong interchain coupling limit. The internal energy, specific heat and uniform susceptibility are calculated analytically by third-order perturbation expansions. At zero temperature, the present method results in the same ground state energy as that obtained by the strong coupling expansion without temperature. At finite-temperature, we obtain a peak in the specific heat and a broad maximum in the uniform susceptibility. The results agree quite well with experimental data for the material Cu₂(C₅H₁₂N₂)₂Cl₄ and the numerical data of 8-order series expansion theory.     

Topological phases of the two-leg Kitaev ladder

We study the phase diagram of the two-leg Kitaev model. Different topological phases can be characterized by either the number of Majorana modes for a deformed chain of the open ladder, or by a winding number related to the ‘h  -loop’ in the momentum space. By adding a three-spin interaction term to break the time-reversal symmetry, two originally different phases are glued together, so that the number of Majorana modes reduce to 0 or 1, namely, the topological invariant collapses to _Z2$Z_2$ from an integer Z. These observations are consistent with a recent general study [S. Tewari, J.D. Sau, arXiv:1111.6592v2].     

The ground state problem in the infinite-U Hubbard model

The problem of the ground state of the electronic system in the Hubbard model for U=∞ is discussed. The author investigates the normal (singlet or nonmagnetic) N state of the electronic system over the entire range of electron densities n⩽1. It is shown that the energy of the N state ɛ ₀ ⁽¹⁾ (n) in a one-particle approximation, such as (e.g.) the extended Hartree-Fock approximation, is lower than the energy of the saturated ferromagnetic FM state ɛ _FM(n) for all n. The dynamic magnetic susceptibility is calculated in the random phase approximation, and it is shown that the N state is stable over the entire range of electron densities: The static susceptibility (ω=0) does not have a band singularity in the zero-wave vector limit q→0. A formally exact representation is obtained for the mass operator of the one-particle Green’s function, and an approximation of this operator is proposed: M _k(E)⋍λF(E), where λ=n(1−n)/(1−n/2)z is the kinematic interaction parameter, z is the number of nearest neighbors, and F(E) is the total single-site Green’s function. For an elliptical density of states the integral equation for F(E) is solved exactly, ad it is shown that the spectral intensity rigorously satisfies the sum rule. The calculated energy of the strongly correlated N state ɛ ₀(n)<ɛ _FM(n) for all n, and in light of this relationship the author discusses the hypothesis that the ground state of the system is the normal (singlet) state in the thermodynamic limit. The electron distribution function at T=0 differs significantly from the Fermi step; it is “smeared” along the entire energy spectrum, and discontinuities do not occur in the region of the chemical potential m. Fiz. Tverd. Tela (St. Petersburg) 39, 193–203 (February 1997)     

Ground-state phase diagram of 2D electrons in a high Landau level: a density-matrix renormalization group study.

The ground-state phase diagram of 2D electrons in a high Landau level (index N = 2) is studied by the density-matrix renormalization group method. Pair correlation functions are systematically calculated for various filling factors from nu = 1/8 to 1/2. It is shown that the ground-state phase diagram consists of three different charge density wave states called stripe phase, bubble phase, and Wigner crystal. The boundary between the stripe and the bubble phases is determined to be nu(s-b)c approximately 0.38, and that for the bubble phase and Wigner crystal is nu(b-W)c approximately 0.24. Each transition is of first order.     

Correlated ground state of the Hubbard model

The variational many-body approach or, more generally, the method of correlated basis functions initiated for a quantitative analysis of strongly interacting quantum fluids may be adapted with minor modifications for exploring the properties of lattice models. This is demonstrated by performing an explicit analysis of the paramagnetic ground state of the Hubbard model. In a first step of the approximation scheme we represent the correlated state by a spin-dependent wave function of Jastrow-type. We analyze in detail the associated density-matrix elements and set up the corresponding Fermi hypernetted-chain equations which determine the irreducible constituents of these quantities. The solutions are discussed and constructed by iteration in terms of cluster approximants. Specializing the input data and the formal results provides a Fermi hypernetted-chain analysis of the correlations induced by a ground state wave function of the Gutzwiller form.     

Approximate ground state of the Lipkin model hamiltonian in density-matrix formalism

A method for finding the ground state of a many-body system, which is consistent with the truncation scheme used in the time-dependent density-matrix formalism of Wang and Cassing, is presented and applied to the Lipkin model. It is found that the method gives better ground states than the Hartree-Fock approximation. However, they significantly differ from the exact ground states.     

Functional renormalization group analysis of the half-filled one-dimensional extended Hubbard model

We study the phase diagram of the half-filled one-dimensional extended Hubbard model at weak coupling using a novel functional renormalization group (FRG) approach. The FRG method includes in a systematic manner the effects of the scattering processes involving electrons away from the Fermi points. Our results confirm the existence of a finite region of bond charge density wave, also known as a "bond order wave" near U=2V and clarify why earlier g-ology calculations have not found this phase. We argue that this is an example in which formally irrelevant corrections change the topology of the phase diagram. Whenever marginal terms lead to an accidental symmetry, this generalized FRG method may be crucial to characterize the phase diagram accurately.     

On the ground state of the half-filled Hubbard model

We calculate the ground state of the half-filled Hubbard model and its energy by starting from a spindensity wave approximation and improving it by incorporating transverse spin fluctuations. The calculations are done by employing a projection method. The quality of the proposed approximation is particularly high for intermediate and large Coulomb repulsionU, where it exceeds considerably e.g. that of the Gutzwiller projected spin-density wave state. To ordert ²/U (wheret is the hopping matrix element), our approximation is shown to be equivalent to a recent Coupled Cluster calculation for the Heisenberg antiferromagnet. Finally we show how to ordert ²/U the linear spin-wave approximation for the Heisenberg antiferromagnet may be obtained.