Matrix product states and projected entangled pair states: Concepts, symmetries, theorems
The theory of entanglement provides a fundamentally new language for describing
interactions and correlations in many-body systems. Its vocabulary consists of qubits and …
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
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 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 …
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
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 …
dimensional quantum many body states. During the last few years, numerous new methods …
Hilbert space fragmentation and commutant algebras
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 …
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 …
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 …
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 …
nonintegrable models we introduced in Phys. Rev. B 98, 235155 (2018) 10.1103/PhysRevB …
Time-evolving a matrix product state with long-ranged interactions
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 …
under a long-ranged Hamiltonian in moderately entangled systems. In the effectively one …
Efficient simulation of moiré materials using the density matrix renormalization group
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 …
continuum model of twisted bilayer graphene (tBLG) near the magic angle. Because of the …
Variational optimization algorithms for uniform matrix product states
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 …
tangent space concepts to construct a variational algorithm for finding ground states of one …