Real-space scaling methods applied to an interacting fermion Hamiltonian

Spronken, G.; Jullien, R.; Avignon, M.

doi:10.1103/physrevb.24.5356

Cited by 49 publications

(18 citation statements)

References 16 publications

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“…The idea is that a system of N sites, which is essentially singular (v = co) at the Heisenberg point (c = 1), the RSRG result was incorrect [45] in that v | 2 as b -4 oo.…”

Section: Coupling Constant Transformations From the Dmrgmentioning

confidence: 99%

Applications of Density Matrix Renormalization Group to Problems in Magnetism

1997

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The application of real space renormalization group methods to quantum lattice models has become a topic of great interest following the development of the density matrix renormalization group by White. This method has been used to find the ground and low-lying excited state energies and wave functions of quantum spin models in which the form of the ground state is not clear, for instance because the interactions are frustrated. It has also been applied to fermion problems where the tendency for localization due to the strong Coulomb repulsion is opposed by the lowering of the kinetic energy which occurs as a result of electron transfer. The approach is particularly suitable for one-, or quasi-one-dimensional problems. The method involves truncating the Hilbert space in a systematic and optimised manner. Results for the ground state energy are thus variational bounds. The results for low-lying energies and correlation functions for one-dimensional systems have unprecedented accuracy and the method has become the method of choice for solving one-dimensional quantum spin problems. We review the method and results obtained for the spin-1 chain with biquadratic exchange as well as the spin-1/2 model with competing nearest and next nearest neighbour exchange will be described. More recently, the density matrix renormalization group has been applied to reformulate the coupling constant renormalization group approach which is appropriate for the study of critical properties. This approach has been applied to the anisotropic spin-1/2 Heisenberg chain. Finally, we discuss recent work which has borne promising applications in two dimensions -the Ising model and the two-dimensional Hubbard model.

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“…The idea is that a system of N sites, which is essentially singular (v = co) at the Heisenberg point (c = 1), the RSRG result was incorrect [45] in that v | 2 as b -4 oo.…”

Section: Coupling Constant Transformations From the Dmrgmentioning

confidence: 99%

Applications of Density Matrix Renormalization Group to Problems in Magnetism

1997

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“…., N -1 is an integer defined mod N ; in one electron space, it is the quantum number of the operator c", defined by N-1 c^N = c C+',,. (5)…”

Section: N-1mentioning

confidence: 99%

The PPP model of alternant cyclic polyenes with modified boundary conditions

Bendazzoli¹,

Evangelisti²

1995

Int J of Quantum Chemistry

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rnThe extension of the PPP Hamiltonian for altemant cyclic polyenes to noninteger values of the pseudomomentum by imposing modified boundary conditions is discussed in detail.It is shown that a computer program for periodic boundary conditions can be easily adapted to the new boundary conditions. Full CI computations are carried out for some low-lying states of the PPP model of altemant cyclic polyenes (CH), (N men) at half-filling. The energy values obtained by using periodic (Bloch) and antiperiodic (Mobius) orbitals are used to perform energy extrapolations for N -+ m. 0

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“…First, we average over the D 0 -fold degenerate ground-state manifold. Our first motivation for doing so is as follows: if G is the point symmetry group of the square lattice, and its subgroup G is the point symmetry group of the R 1 ×R 2 system, then we will find that the cluster density matrices 12) one for each wave function Ψ i within the D 0 -fold degenerate ground-state manifold, are not invariant under G, much less G . We remove this artificial symmetry breaking by calculating the degeneracy-averaged cluster DM (2.13) over the cluster density matrices ρ C,i within the ground-state manifold.…”

Section: Degeneracy Averagingmentioning

confidence: 99%

“…We eliminate these as much as we can 11 with the third averaging device, twist boundary conditions averaging. 12 The usual way to implement twist boundary conditions is to work in the boundary gauge, keeping the Hamiltonian unchanged, and demanding that 16) where R 1 and R 2 are the lattice vectors defining our finite system, R = (R x , R y ) is a site within the system, and φ = (φ x , φ y ) is the twist vector parametrizing the twist boundary conditions. In choice of gauge (2.16), the Hamiltonian (1.1) is not manifestly invariant under translations.…”

Section: Twist Boundary Conditions Averagingmentioning

confidence: 99%

Many-body density matrices on a two-dimensional square lattice: Noninteracting and strongly interacting spinless fermions

Cheong

Henley

2006

Phys. Rev. B

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The reduced density matrix of an interacting system can be used as the basis for a truncation scheme, or in an unbiased method to discover the strongest kind of correlation in the ground state. In this paper, we investigate the structure of the many-body fermion density matrix of a small cluster in a square lattice. The cluster density matrix is evaluated numerically over a set of finite systems, subject to non-square periodic boundary conditions given by the lattice vectors R 1 ≡ (R 1x , R 1y ) and R 2 ≡ (R 2x , R 2y ). We then approximate the infinite-system cluster density-matrix spectrum, by averaging the finite-system cluster density matrix (i) over degeneracies in the ground state, and orientations of the system relative to the cluster, to ensure it has the proper point-group symmetry; and (ii) over various twist boundary conditions to reduce finite size effects. We then compare the eigenvalue structure of the averaged cluster density matrix for noninteracting and strongly-interacting spinless fermions, as a function of the filling fractionn, and discuss whether it can be approximated as being built up from a truncated set of single-particle operators.

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Real-space scaling methods applied to an interacting fermion Hamiltonian

Cited by 49 publications

References 16 publications

Applications of Density Matrix Renormalization Group to Problems in Magnetism

Applications of Density Matrix Renormalization Group to Problems in Magnetism

The PPP model of alternant cyclic polyenes with modified boundary conditions

Many-body density matrices on a two-dimensional square lattice: Noninteracting and strongly interacting spinless fermions

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