Matrix product states and projected entangled pair states: Concepts, symmetries, theorems

JI Cirac, D Perez-Garcia, N Schuch, F Verstraete - Reviews of Modern Physics, 2021 - APS
The theory of entanglement provides a fundamentally new language for describing
interactions and correlations in many-body systems. Its vocabulary consists of qubits and …

Quantum many-body scars and Hilbert space fragmentation: a review of exact results

S Moudgalya, BA Bernevig… - Reports on Progress in …, 2022 - iopscience.iop.org
The discovery of quantum many-body scars (QMBS) both in Rydberg atom simulators and in
the Affleck–Kennedy–Lieb–Tasaki spin-1 chain model, have shown that a weak violation of …

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

U Schollwöck - Annals of physics, 2011 - Elsevier
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 …

[HTML][HTML] Time-evolution methods for matrix-product states

S Paeckel, T Köhler, A Swoboda, SR Manmana… - Annals of Physics, 2019 - Elsevier
Matrix-product states have become the de facto standard for the representation of one-
dimensional quantum many body states. During the last few years, numerous new methods …

Hilbert space fragmentation and commutant algebras

S Moudgalya, OI Motrunich - Physical Review X, 2022 - APS
We study the phenomenon of Hilbert space fragmentation in isolated Hamiltonian and
Floquet quantum systems using the language of commutant algebras, the algebra of all …

Efficient numerical simulations with tensor networks: Tensor Network Python (TeNPy)

J Hauschild, F Pollmann - SciPost Physics Lecture Notes, 2018 - scipost.org
Tensor product state (TPS) based methods are powerful tools to efficiently simulate quantum
many-body systems in and out of equilibrium. In particular, the one-dimensional matrix …

Entanglement of exact excited states of Affleck-Kennedy-Lieb-Tasaki models: Exact results, many-body scars, and violation of the strong eigenstate thermalization …

S Moudgalya, N Regnault, BA Bernevig - Physical Review B, 2018 - APS
We obtain multiple exact results on the entanglement of the exact excited states of
nonintegrable models we introduced in Phys. Rev. B 98, 235155 (2018) 10.1103/PhysRevB …

Time-evolving a matrix product state with long-ranged interactions

MP Zaletel, RSK Mong, C Karrasch, JE Moore… - Physical Review B, 2015 - APS
We introduce a numerical algorithm to simulate the time evolution of a matrix product state
under a long-ranged Hamiltonian in moderately entangled systems. In the effectively one …

Efficient simulation of moiré materials using the density matrix renormalization group

T Soejima, DE Parker, N Bultinck, J Hauschild… - Physical Review B, 2020 - APS
We present an infinite density-matrix renormalization group (DMRG) study of an interacting
continuum model of twisted bilayer graphene (tBLG) near the magic angle. Because of the …

Variational optimization algorithms for uniform matrix product states

V Zauner-Stauber, L Vanderstraeten, MT Fishman… - Physical Review B, 2018 - APS
We combine the density matrix renormalization group (DMRG) with matrix product state
tangent space concepts to construct a variational algorithm for finding ground states of one …