Condensed Matter Applications of Entanglement Theory
arXiv:1306.5551
Abstract
These are lecture notes from the 44th IFF Spring School "Quantum Information Processing" in Juelich, discussing applications of entanglement theory in condensed matter. The focus of the notes is on tensor network states, in particular Matrix Product States (MPS) and Projected Entangled Pair States (PEPS), which provide an efficient description of many-body states based on their entanglement structure; both numerical and analytical aspects of tensor networks are being covered. The notes close with a brief introduction to quantum complexity, which allows to assess the limitations to our ability to simulate quantum many-body systems.
Lecture notes for the 44th IFF Spring School "Quantum Information Processing" in Juelich, 2013. 29 pages
References in corpus (15)
- Accurate determination of tensor network state of quantum lattice models in two dimensions
- Entropy scaling and simulability by Matrix Product States
- Tensor-entanglement renormalization group approach to 2D quantum systems
- String order and symmetries in quantum spin lattices
- The power of quantum systems on a line
- Matrix Product States for dynamical simulation of infinite chains
- Variational quantum Monte Carlo simulations with tensor-network states
- Resonating valence bond states in the PEPS formalism
- Explicit tensor network representation for the ground states of string-net models
- Strings, Projected Entangled Pair States, and variational Monte Carlo methods
- On entropy growth and the hardness of simulating time evolution
- Matrix Product States: Symmetries and Two-Body Hamiltonians
- Monte Carlo simulation with Tensor Network States
- The computational difficulty of finding MPS ground states
- Tensor-product representations for string-net condensed states
Cited by in corpus (11)
- Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study
- Quantum critical phase with infinite projected entangled paired states
- Systematic construction of spin liquids on the square lattice from tensor networks with SU(2) symmetry
- Entanglement and tensor network states
- Investigation of the chiral antiferromagnetic Heisenberg model using PEPS
- Lattice model constructions for gapless domain walls between topological phases
- Finite-temperature symmetric tensor network for spin-1/2 Heisenberg antiferromagnets on the square lattice
- Critical colored-RVB states in the frustrated quantum Heisenberg model on the square lattice
- Construction of Non-Hermitian Parent Hamiltonian from Matrix Product States
- Discrete lattice symmetry breaking in a two-dimensional frustrated spin-1 Heisenberg model
- Entanglement properties of the two-dimensional SU(3) AKLT state