Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0103301 · Physical review. B, Condensed matter

Density-matrix spectra of solvable fermionic systems

Ming-Chiang Chung, Ingo Peschel

Published Jul 23, 2001• 281 citations
arXivHTMLPDF

Abstract

We consider noninteracting fermions on a lattice and give a general result for the reduced density matrices corresponding to parts of the system. This allows to calculate their spectra, which are essential in the density-matrix renormalization group method, by diagonalizing small matrices. We discuss these spectra and their typical features for various fermionic quantum chains and for the two-dimensional tight-binding model.

DOI
10.1103/physrevb.64.064412

Related papers

Calculation of reduced density matrices from correlation functions

Ingo Peschel

It is shown that for solvable fermionic and bosonic lattice systems, the reduced density matrices can be determined from the properties of the correlation functions. This provides the simplest way to these quantities which are used in the density-matrix renormalization group method.

arXiv:cond-mat/0212631•Journal of Physics A Mathematical and General•Mar 27, 2003•1,095 citations

Density-matrix spectra for two-dimensional quantum systems

Ming-Chiang Chung, Ingo Peschel

For a two-dimensional system of coupled oscillators, the spectra of reduced density matrices can be obtained analytically. This provides an example where the features of these quantities, which are of central importance in numerical studies using the density-matrix renormalization-group method, can be seen

arXiv:cond-mat/0004222•Physical review. B, Condensed matter•Aug 15, 2000•93 citations

Density matrices for a chain of oscillators

Ingo Peschel, Ming-Chiang Chung

We consider chains with an optical phonon spectrum and study the reduced density matrices which occur in density-matrix renormalization group calculations. Both for one site and for half of the chain, these are found to be exponentials of bosonic operators. Their spectra, which are correspondingly exponential, are determined and discussed. The results for large systems are obtained from the relation to a two-dimensional Gaussian model.

arXiv:cond-mat/9906224•Journal of Physics A Mathematical and General•Nov 17, 1999•85 citations

Block-Lanczos Density-Matrix Renormalization-Group Approach to Spin Transport in Heisenberg Chains Coupled to Leads

Florian Lange, Satoshi Ejima, Tomonori Shirakawa +2 more

We adapt the block-Lanczos density-matrix renormalization-group technique to study the spin transport in a spin chain coupled to two non-interacting fermionic leads. As an example, we consider leads described by two-dimensional tight-binding models on a square lattice. Although the simulations are carried out using a chain representation of the leads, observables in the original two-dimensional lattice can be calculated by reversing the block-Lanczos transformation. This is demonstrated for leads with Rashba spin-orbit coupling.

arXiv:2001.02926•Journal of the Physical Society of Japan•Mar 6, 2020•3 citations

Density Matrices for a Chain of Oscillators

Ingo Peschel, Ming-Chiang Chung, Fachbereich Physik Freie Universität

We consider chains with an optical phonon spectrum and study the reduced density matrices which occur in density-matrix renormalization group (DMRG) calculations. Both for one site and for half of the chain, these are found to be exponentials of bosonic operators. Their spectra, which are correspondingly exponential, are determined and discussed. The results for large systems are obtained from the relation to a two-dimensional Gaussian model. 1

•Jan 1, 2008•41 citations

Density-matrix spectra for integrable models

Ingo Peschel, Matthias Kaulke, Örs Legeza

The spectra which occur in numerical density-matrix renormalization group (DMRG) calculations for quantum chains can be obtained analytically for integrable models via corner transfer matrices. This is shown in detail for the transverse Ising chain and the uniaxial XXZ Heisenberg model and explains in particular their exponential character in these cases.

arXiv:cond-mat/9810174•Annalen der Physik•Feb 1, 1999•151 citations
We consider noninteracting fermions on a lattice and give a general result for the reduced density matrices corresponding to parts of the system. This allows to calculate their spectra, which are essential in the density-matrix renormalization group method, by diagonalizing small matrices. We discuss these spectra and their typical features for various fermionic quantum chains and for the two-dimensional tight-binding model.
We adapt the block-Lanczos density-matrix renormalization-group technique to study the spin transport in a spin chain coupled to two non-interacting fermionic leads. As an example, we consider leads described by two-dimensional tight-binding models on a square lattice. Although the simulations are carried out using a chain representation of the leads, observables in the original two-dimensional lattice can be calculated by reversing the block-Lanczos transformation. This is demonstrated for leads with Rashba spin-orbit coupling.