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 Quantum Interferometry.
The density-matrix renormalization group in the age of matrix product states
9 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
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.
years
2026 9representative citing papers
The claimed intrinsic dipole moment at FQH edges is protected only at filling factor 1/3 and absent in other representative edge systems.
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 composite c=2 critical line.
Peaked quantum circuits claimed to show quantum advantage can be classically simulated in one hour on a GPU via mirrored MPO contraction and unswapping.
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 phase with fourfold degeneracy described by an Ising CFT.
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.
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.
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.
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.
citing papers explorer
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A Factorization Identity for Twisted Multinomial Coefficients with Application to Pilot States in Hamiltonian Decoded Quantum Interferometry
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 Quantum Interferometry.
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Does a Fractional Quantum Hall Edge Have a Protected Intrinsic Dipole Moment?
The claimed intrinsic dipole moment at FQH edges is protected only at filling factor 1/3 and absent in other representative edge systems.
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Non-magnetic floating phases in frustrated Haldane chains with a single-ion anisotropy
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 composite c=2 critical line.
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Efficient Classical Simulation of Heuristic Peaked Quantum Circuits
Peaked quantum circuits claimed to show quantum advantage can be classically simulated in one hour on a GPU via mirrored MPO contraction and unswapping.
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Symmetry breaking phases and transitions in an Ising fusion category lattice model
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 phase with fourfold degeneracy described by an Ising CFT.
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High-Precision Variational Quantum SVD via Classical Orthogonality Correction
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.
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Preparing High-Fidelity Thermofield Double States
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.
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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
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.
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Entanglement is Half the Story: Post-Selection vs. Partial Traces
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.