Abstract
Although originally thought to show great promise in solving quantum many-body problems on a lattice, numerical real-space renormalization-group techniques have had little success for such problems. We explore the nature of the difficulties involved by studying the applicaton of the method to the simple tight-binding model in one dimension. The standard approach fails dramatically for this model. We show that the key to successfully applying the renormalization-group technique lies in applying a variety of boundary conditions to a block in order to simulate the effect of neighboring blocks.
Keywords
Renormalization groupRenormalizationLattice (music)Density matrix renormalization groupQuantumTheoretical physicsStatistical physicsVariety (cybernetics)Space (punctuation)PhysicsSimple (philosophy)Critical dimensionSpacetimeComputer scienceQuantum mechanicsEpistemologyArtificial intelligence
Related Publications
Density matrix formulation for quantum renormalization groups
A generalization of the numerical renormalization-group procedure used first by Wilson for the Kondo problem is presented. It is shown that this formulation is optimal in a cert...
Theory of dynamic critical phenomena
An introductory review of the central ideas in the modern theory of dynamic critical phenomena is followed by a more detailed account of recent developments in the field. The co...
<i>Ab initio</i>multicenter tight-binding model for molecular-dynamics simulations and other applications in covalent systems
A new, approximate method has been developed for computing total energies and forces for a variety of applications including molecular-dynamics simulations of covalent materials...
Zoo of Quantum Phases and Excitations of Cold Bosonic Atoms in Optical Lattices
Quantum phases and phase transitions of weakly to strongly interacting bosonic atoms in deep to shallow optical lattices are described by a single multiorbital mean-field approa...
Lattice Green's Functions for the Cubic Lattices in Terms of the Complete Elliptic Integral
The real and imaginary parts of the lattice Green's functions for the simple cubic (actually the tetragonal), body-centered cubic, and face-centered cubic lattices, at the varia...
Publication Info
- Year
- 1992
- Type
- article
- Volume
- 68
- Issue
- 24
- Pages
- 3487-3490
- Citations
- 287
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
287
OpenAlex
Cite This
Steven R. White,
R. M. Noack
(1992).
Real-space quantum renormalization groups.
Physical Review Letters
, 68
(24)
, 3487-3490.
https://doi.org/10.1103/physrevlett.68.3487
Identifiers
- DOI
- 10.1103/physrevlett.68.3487