Density Matrix Renormalization Group Study of One-Dimensional Acoustic Phonons

Abstract

We study the application of the density matrix renormalization group (DMRG) to systems with one-dimensional acoustic phonons. We show how the use of a local oscillator basis circumvents the difficulties with the long-range interactions generated in real space using the normal phonon basis. When applied to a harmonic atomic chain, we find excellent agreement with the exact solution even when using a modest number of oscillator and block states (a few times ten). We discuss the use of this algorithm in more complex cases and point out its value when other techniques are deficient.

12 pages. To be published in PRB rapid com

Cited by in corpus (19)

• The density-matrix renormalization group
• New Trends in Density Matrix Renormalization
• Density matrix renormalization group study of the polaron problem in the Holstein model
• Phase diagram of the one-dimensional Holstein model of spinless fermions
• Phase diagram of a Heisenberg spin-Peierls model with quantum phonons
• Density Matrices for a Chain of Oscillators
• Matrix Product States Algorithms and Continuous Systems
• A density matrix renormalisation group algorithm for quantum lattice systems with a large number of states per site
• Density matrix renormalization group study of dimerization of the Pariser-Parr-Pople model of polyacetilene
• Comparative Study of State-of-the-Art Matrix-Product-State Methods for Lattice Models with Large Local Hilbert Spaces
• Angular quantization and the density matrix renormalization group
• Peierls transition in the quantum spin-Peierls model
• Can Quantum Lattice Fluctuations Destroy the Peierls Broken Symmetry Ground State?
• Quantum-fluctuation-induced repelling interaction of quantum string between walls
• Density Matrix Renormalization Group study on incommensurate quantum Frenkel-Kontorova model
• Lattice vibration as a knob for novel quantum criticality: Emergence of supersymmetry from spin-lattice coupling
• Density-matrix renormalization using three classes of block states
• Quantum phase transition in one-dimensional commensurate Frenkel-Kontorova model
• Error analysis of the density-matrix renormalization group algorithm for a chain of harmonic oscillators