DMRG. Density matrix renormalization group theory

Click For Summary

Discussion Overview

The discussion centers around the density matrix renormalization group (DMRG) theory, specifically its applicability to one-dimensional systems and potential generalizations to higher dimensions. Participants explore the theoretical foundations and applications of DMRG in the context of quantum systems, including the Heisenberg Hamiltonian.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions why DMRG theory is primarily effective for one-dimensional systems.
  • Another participant mentions that there are generalizations to higher dimensions using matrix product states and other tensor networks, such as the MERA.
  • A participant expresses interest in applying DMRG to the Heisenberg Hamiltonian, implying a potential exploration of its applicability in this context.
  • Another participant references a specific paper discussing the Heisenberg model, suggesting that there may be relevant insights or findings related to DMRG.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the limitations of DMRG to one-dimensional systems, as some suggest generalizations exist while others focus on the original context. The applicability of DMRG to the Heisenberg Hamiltonian remains an open question.

Contextual Notes

There are references to specific papers that may contain additional insights, but the discussion does not resolve the limitations or assumptions regarding the application of DMRG in higher dimensions or specific models.

LagrangeEuler
Messages
711
Reaction score
22
Why density matrix renormalization group theory works only for 1D systems?
 
Physics news on Phys.org

Similar threads

Undergrad Scaling and the renormalization (sub)group
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Renormalized vertex functions in terms of bare ones
  • · Replies 0 ·
Replies
0
Views
1K
Graduate Main Theorem of Renormalization, but in physicist-speak
  • · Replies 10 ·
Replies
10
Views
2K
Graduate Looking for study group to hack on basic theory in condensed matter
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Selection rules using Group Theory: many body
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Create Hamiltonians in condensed matter with group theory
  • · Replies 6 ·
Replies
6
Views
4K
Graduate Symmetry of hamiltonian under renormalization
  • · Replies 4 ·
Replies
4
Views
2K
Graduate How does DFT handle degenerate eigenvectors?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate What is best way to start learning DMRG for Fermions?
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Density matrix representation of a density operator
  • · Replies 8 ·
Replies
8
Views
2K