Flow Equations and Normal Ordering. A Survey

Abstract

First we give an introduction to the method of diagonalizing or block-diagonalizing continuously a Hamiltonian and explain how this procedure can be used to analyze the two-dimensional Hubbard model. Then we give a short survey on applications of this flow equation on other models. Finally we outline, how symmetry breaking can be introduced by means of a symmetry breaking of the normal ordering, not of the Hamiltonian.

11 pages, contribution to the workshop on the Renormalization Group, Helsinki 2005

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• Systematic Mapping of the Hubbard Model to the Generalized t-J Model
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• Rung-singlet phase of the S=1/2 two-leg spin-ladder with four-spin cyclic exchange
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• Special relativity constraints on the effective constituent theory of hybrids
• Flow Equations for the Henon-Heiles Hamiltonian
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Cited by in corpus (31)

• On Many-Body Localization for Quantum Spin Chains
• Quench Dynamics in a Model with Tuneable Integrability Breaking
• A driven similarity renormalization group approach to quantum many-body problems
• Real-time evolution for weak interaction quenches in quantum systems
• New applications of renormalization group methods in nuclear physics
• Accurate effective Hamiltonians via unitary flow in Floquet space
• Analytic approaches to periodically driven closed quantum systems: Methods and Applications
• Flow towards diagonalization for Many-Body-Localization models : adaptation of the Toda matrix differential flow to random quantum spin chains
• The Renormalization Group in Nuclear Physics
• Exact resummation of the Holstein-Primakoff expansion and differential equation approach to operator square-roots
• Quasi-Many-Body Localization of Interacting Fermions with Long-Range Couplings
• Local Integrals of Motion in Quasiperiodic Many-Body Localized Systems
• Multi-Scale Jacobi Method for Anderson Localization
• Dynamics of Disordered Quantum Systems Using Flow Equations
• Renormalization group procedure for effective particles: elementary example of exact solution with finite mass corrections and no involvement of vacuum
• Double-bracket quantum algorithms for diagonalization
• Limit cycles of effective theories
• Flow Equations for Disordered Floquet Systems
• Non-equilibrium dynamics of a system with Quantum Frustration
• Fermion mass mixing and vacuum triviality in the renormalization group procedure for effective particles
• Truncation errors in self-similar continuous unitary transformations
• Effective Models for the Anderson Impurity and the Kondo Model from Continuous Unitary Transformations
• Flow Equations for the Ionic Hubbard Model
• Local integrals of motion and the stability of many-body localisation in Wannier-Stark potentials
• Double-bracket quantum algorithms for quantum imaginary-time evolution
• Disorder-induced spin-charge separation in the 1-D Hubbard model
• Hamiltonian statistical mechanics
• The exact solution of the Wegner flow equation with the Mielke generator for $3\times 3$ Hermitian matrices
• On the Geodesic Nature of Wegner's Flow
• The flow equation approach to the pairing instability problem
• Double-bracket quantum algorithms for high-fidelity ground state preparation