Flow equations for Hamiltonians.

Ann. Physik, Leipzig 3, 77 (1994)

In general these equations generate many-particle interactions. However, for an n-orbital model the equations for the two-particle interaction are closed in the limit of large n. Solutions of these equations for a one-dimensional model are considered. There appear convergency problems, which are removed, if instead of diagonalization only a block-diagonalization into blocks with the same number of quasiparticles is performed.

Back

Flow equations for the Anderson Hamiltonian.

J. Phys. A - Math. Gen. 27, 4259-4279 (1994); corrigendum 27, 5705 (1994)

Back

Flow equations for the spin-boson problem.

Z. Phys. B 99, 269 (1996)

Back

Theory of the Anderson impurity model: The Schrieffer-Wolff transformation re-examined

Ann. Phys. (NY) 252 (1995) 1

Back

On the spin-boson model with a sub-Ohmic bath.

Phys. Lett. A 219, 313 (1996).

Back

Flow equations for electron-phonon interactions.

Nucl. Phys. B482 [FS] (1996) 693-712 .

Back

Low temperature equilibrium correlation functions in dissipative quantum systems.

Ann. Physik (Leipzig)

Back

Similarity renormalization of the electron-phonon coupling.

Ann. Physik (Leizpzig)

Back

Diagonalization of system plus environment Hamiltonians.

J. Stat. Phys.

Back

Flow equations and the strong-coupling expansion for the Hubbard model.

J. Stat. Phys.

Back

Calculating critical temperatures of superconductivity from a renormalized Hamiltonian.

Europhys. Lett.

Back

Flow Equations for Hamiltonians: Crossover from Luttinger to Landau-Liquid Behaviour in the n-Orbital Model

Z. Phys. B

Back

Flow Equations for Hamiltonians.

Proceedings of the Bar-Ilan 1997 Minerva Workshop on Mesoscopics, Fractals, and Neural Networks, Eilat

Phil. Mag. B

Back

Hamiltonian Flow in Condensed Matter Physics.

in M. Grangé et al (eds.), New Non-Perturbative Methods and Quantization on the Light Cone, Les Houches School 1997, Editions de Physique/Springer Vol. 8 (1998) 33

Back

Flow equations for QED in the light front dynamics

hep-th/9710233

Back

Flow equations for band-matrices

Euro. Phys. J. B 5, 605-611 (1998), quant-ph/9803040

Back

Flow equations and extended Bogoliubov transformation for the Heisenberg antiferromagnet near the classical limit.

Eur. Phys. J. B

Back

Flow Equations for Electron-Phonon Interactions: Phonon Damping.

Eur. Phys. J. B

Back

Flow equations for the Henon-Heiles Hamiltonian.

Physica D 126, 123-135 (1999), quant-ph/9809086

Back

Light-cone Hamiltonian flow for positronium, preprint MPI-H-V33-1998.

Back

Hamiltonian Flow Equations for the Lipkin model.

Phys. Lett. B434, 231 (1998), nucl-th/9804039

Hamiltonian Flow Equations for a Dirac Particle in an external Potential

Phys. Lett. B428, 329 (1998), hep-th/9712203

Flow equations and the Ruderman-Kittel-Kasuya-Yosida interaction.

Eur. Phys. J. B

Back

Flow equations and new weak-coupling solution for the spin-polaron in a quantum antiferromagnet.

Europhys. Lett.

Back

Unitary flow of the bosonized large-

J. Phys. G

Back

Flow Equations for Hamiltonians.

Physics Reports 348 (2001) 77.

Proceedings of the RG 2000 in Taxco, Mexico

Back

Flow Equations for Hamiltonians.

Nucl. Phys. B (Proc. Suppl.) 90 (2000) 141

Back

Flow Equations for Hamiltonians.

Advances in Solid State Physics 40 (2000) 113

(i) In perturbation theory one obtains new results for effective interactions which are less singular than those obtained by conventional perturbation theory, eg. for the effective pair interaction by eliminating the electron-phonon interaction. (P. Lenz and F.W.)

(ii) In systems with impurities as for example in the spin-boson problem large parameter regions can be treated in a consistent way (S. Kehrein and A. Mielke).

Back

Diagonalization of Dissipative Quantum Systems I: Exact Solution of the Spin-Boson Model with an Ohmic bath at alpha=1/2.

preprint (2000).

Back

Stability Analysis of the Hubbard Model.

J. Low Temp. Phys. 126 (2002) 1385.

cond-mat/0106604

Back

Pomeranchuk and other Instabilities in the

Phys. Rev. B66 (2002) 094516.

cond-mat/0205213

Superconductivity and Instabilities in the

Acta Phys. Pol. B 34 (2003) 497, Erratum 34 (2003) 1591

Contributed paper to the International Conference on Strongly Correlated Electron Systems SCES'02 in Cracov.

cond-mat/0205597.

We present a stability analysis of the 2D

Equilibrium Correlation Functions of the Spin-Boson Model with Sub-Ohmic Bath.

cond-mat/0207414.

The spin-boson model is studied by means of flow equations for Hamiltonians. Our truncation scheme includes all coupling terms which are linear in the bosonic operators. Starting with the canonical generator

Possible Phases of the Two-Dimensional

Eur. Phys. Journal B 31 (2003) 497.

cond-mat/0207612.

We present a stability analysis of the 2D

Contrasting Different Flow Equations for a Numerically Solvable Model.

cond-mat/0209643.

To contrast different generators for flow equations and to discuss the dependence of physical quantities on unitarily equivalent, but effectively different initial Hamiltonians, a numerically solvable model is considered which is structurally similar to impurity models. A general truncation scheme is established that produces good results for the Hamiltonian flow as well as for the operator flow. Nevertheless, it is also pointed out that a systematic and feasible scheme for the operator flow on the operator level is missing. More explicitly, truncation of the series of the observable flow after the linear or bilinear terms does not yield satisfactory results for the entire parameter regime as - especially close to resonances - even high orders of the exact series expansion carry considerable weight. Back

Universal Asymptotic Behavior in Flow Equations of Dissipative Systems.

cond-mat/0211596.

Based on two dissipative models, universal asymptotic behavior of flow equations for Hamiltonians is found and discussed. The asymptotic behavior only depends on fundamental bath properties but not on initial system parameters and the integro-differential equations possess an universal attractor. The asymptotic flow of the Hamiltonian is characterized by a non-local differential equation which only depends on one parameter - independent of the dissipative system nor of the truncation scheme. Since the fixed point Hamiltonian is trivial, the physical information is completely transferred to the transformation of the observables. This yields a more stable flow which is crucial for the numerical evaluation of correlation functions. The presented procedure also works if relevant perturbations are present as is demonstrated by evaluating the Shiba relation for sub-Ohmic baths. It can further be generalized to other dissipative systems. Back

Tomonaga-Luttinger model with impurity at weak two-body interaction.

cond-mat/0211598.

The Tomonaga-Luttinger model with impurity is studied by means of flow equations for Hamiltonians. The system is formulated within collective density fluctuations but no use of the bosonization formula is made. The truncation scheme includes operators consisting of up to four fermionic operators and is valid for small electron-electron interactions. In this regime, the algebraic behavior of correlation functions close to the Fermi point is recovered involving the

One-dimensional conductance through an arbitrary delta impurity cond-mat/0301586.

The finite-size Tomonaga-Luttinger Hamiltonian with an arbitrary delta impurity at weak electron-electron interaction is mapped onto a non-interacting Fermi gas with renormalized impurity potential by means of flow equations for Hamiltonians. The conductance can then be evaluated using the Landauer formula. We obtain similar results for infinite systems at finite temperature by identifying the flow parameter with the inverse squared temperature. This also yields the finite-size scaling relations of a free electron gas. We recover the algebraic behavior of the conductance obtained by Kane and Fisher in the limit of low temperatures but conclude that this limit might be hard to reach for certain impurity strengths. Back

Flow Equations and Normal Ordering

J. Phys. A 39 (2006) 1231-1237 cond-mat/0509801.

Flow Equations and Normal Ordering: A Survey

J. Phys. A 39 (2006) 8221-8230 cond-mat/0511660.

Back to main page Flow equations.

Nov. 2007