pith. machine review for the scientific record. sign in

arxiv: 1008.3477 · v2 · submitted 2010-08-20 · ❄️ cond-mat.str-el

Recognition: unknown

The density-matrix renormalization group in the age of matrix product states

Authors on Pith no claims yet
classification ❄️ cond-mat.str-el
keywords dmrgmethodfurtherstatesalgorithmsdensity-matrixdevelopmentgroup
0
0 comments X
read the original abstract

The density-matrix renormalization group method (DMRG) has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems. In the further development of the method, the realization that DMRG operates on a highly interesting class of quantum states, so-called matrix product states (MPS), has allowed a much deeper understanding of the inner structure of the DMRG method, its further potential and its limitations. In this paper, I want to give a detailed exposition of current DMRG thinking in the MPS language in order to make the advisable implementation of the family of DMRG algorithms in exclusively MPS terms transparent. I then move on to discuss some directions of potentially fruitful further algorithmic development: while DMRG is a very mature method by now, I still see potential for further improvements, as exemplified by a number of recently introduced algorithms.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 9 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Does a Fractional Quantum Hall Edge Have a Protected Intrinsic Dipole Moment?

    cond-mat.str-el 2026-05 unverdicted novelty 7.0

    The claimed intrinsic dipole moment at FQH edges is protected only at filling factor 1/3 and absent in other representative edge systems.

  2. Non-magnetic floating phases in frustrated Haldane chains with a single-ion anisotropy

    cond-mat.str-el 2026-04 unverdicted novelty 7.0

    Numerical DMRG study of the anisotropic J1-J2 spin-1 chain uncovers two non-magnetic incommensurate floating Luttinger liquid phases emerging from the trimerized background, separated from the Haldane phase by a compo...

  3. Efficient Classical Simulation of Heuristic Peaked Quantum Circuits

    quant-ph 2026-04 conditional novelty 7.0

    Peaked quantum circuits claimed to show quantum advantage can be classically simulated in one hour on a GPU via mirrored MPO contraction and unswapping.

  4. Symmetry breaking phases and transitions in an Ising fusion category lattice model

    cond-mat.str-el 2026-04 unverdicted novelty 7.0

    The Ising fusion category lattice model features a symmetric critical phase equivalent to the Ising model, a categorical ferromagnetic phase with threefold degeneracy, and a critical categorical antiferromagnetic phas...

  5. A Factorization Identity for Twisted Multinomial Coefficients with Application to Pilot States in Hamiltonian Decoded Quantum Interferometry

    quant-ph 2026-04 unverdicted novelty 7.0

    Twisted multinomial coefficients factorize into a product of site-dependent q-binomials when inversion weights satisfy predecessor-uniformity, yielding exact MPS representations for pilot states in Hamiltonian Decoded...

  6. High-Precision Variational Quantum SVD via Classical Orthogonality Correction

    quant-ph 2026-05 unverdicted novelty 6.0

    A variational quantum SVD framework with classical orthogonality correction enables high-precision extraction of Schmidt components from bipartite states using shallow circuits and classical tensor-network post-processing.

  7. Preparing High-Fidelity Thermofield Double States

    quant-ph 2026-05 unverdicted novelty 6.0

    A gapped parent Hamiltonian built from two copies of a target Hamiltonian plus ultra-local inter-copy couplings allows adiabatic preparation of high-fidelity thermofield double states for ETH-obeying systems.

  8. Conformal Data for the $O(2)$ Wilson-Fisher CFT in $(2+1)$-Dimensional Spacetime from Exact Diagonalization and Matrix Product States on the Fuzzy Sphere

    cond-mat.str-el 2026-04 unverdicted novelty 6.0

    Numerical extraction of scaling dimensions and OPE coefficients for 32 primary operators in the O(2) Wilson-Fisher CFT via fuzzy-sphere regularization shows agreement with bootstrap predictions.

  9. Entanglement is Half the Story: Post-Selection vs. Partial Traces

    quant-ph 2026-05 unverdicted novelty 4.0

    A hybrid tensor network framework interpolates between classical and quantum models via controllable post-selection, with a trainable hyperparameter that complements bond dimension to enhance quantum machine learning.