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 …

Diagonalizing transfer matrices and matrix product operators: A medley of exact and computational methods

J Haegeman, F Verstraete - Annual Review of Condensed …, 2017 - annualreviews.org
Transfer matrices and matrix product operators play a ubiquitous role in the field of many-
body physics. This review gives an idiosyncratic overview of applications, exact results, and …

Unconventional topological mixed-state transition and critical phase induced by self-dual coherent errors

YH Chen, T Grover - Physical Review B, 2024 - APS
A topological phase can undergo a phase transition driven by anyon condensation. A
potential obstruction to such a mechanism could arise if there exists a symmetry between …

Signatures of Dirac cones in a DMRG study of the kagome Heisenberg model

YC He, MP Zaletel, M Oshikawa, F Pollmann - Physical Review X, 2017 - APS
The antiferromagnetic spin-1/2 Heisenberg model on a kagome lattice is one of the most
paradigmatic models in the context of spin liquids, yet the precise nature of its ground state …

Robust teleportation of a surface code and cascade of topological quantum phase transitions

F Eckstein, B Han, S Trebst, GY Zhu - PRX Quantum, 2024 - APS
Teleportation is a facet where quantum measurements can act as a powerful resource in
quantum physics, as local measurements allow us to steer quantum information in a …

Tangent-space methods for uniform matrix product states

L Vanderstraeten, J Haegeman… - SciPost Physics Lecture …, 2019 - scipost.org
In these lecture notes we give a technical overview of tangent-space methods for matrix
product states in the thermodynamic limit. We introduce the manifold of uniform matrix …

Gapped spin liquid with topological order for the kagome Heisenberg model

JW Mei, JY Chen, H He, XG Wen - Physical Review B, 2017 - APS
We apply the symmetric tensor network state (TNS) to study the nearest-neighbor spin-1/2
antiferromagnetic Heisenberg model on the kagome lattice. Our method keeps track of the …

Anyons and matrix product operator algebras

N Bultinck, M Mariën, DJ Williamson, MB Şahinoğlu… - Annals of physics, 2017 - Elsevier
Quantum tensor network states and more particularly projected entangled-pair states
provide a natural framework for representing ground states of gapped, topologically ordered …

Matrix product operator symmetries and intertwiners in string-nets with domain walls

L Lootens, J Fuchs, J Haegeman, C Schweigert… - SciPost Physics, 2021 - scipost.org
We provide a description of virtual non-local matrix product operator (MPO) symmetries in
projected entangled pair state (PEPS) representations of string-net models. Given such a …

Simulating excitation spectra with projected entangled-pair states

L Vanderstraeten, J Haegeman, F Verstraete - Physical Review B, 2019 - APS
We develop and benchmark a technique for simulating excitation spectra of generic two-
dimensional quantum lattice systems using the framework of projected entangled-pair states …