Many body physics from a quantum information perspective

Abstract

The quantum information approach to many body physics has been very successful in giving new insight and novel numerical methods. In these lecture notes we take a vertical view of the subject, starting from general concepts and at each step delving into applications or consequences of a particular topic. We first review some general quantum information concepts like entanglement and entanglement measures, which leads us to entanglement area laws. We then continue with one of the most famous examples of area-law abiding states: matrix product states, and tensor product states in general. Of these, we choose one example (classical superposition states) to introduce recent developments on a novel quantum many body approach: quantum kinetic Ising models. We conclude with a brief outlook of the field.

Lectures from the Les Houches School on "Modern theories of correlated electron systems". Improved version new references added

References in corpus (82)

• Quantum entanglement
• Entanglement of Formation of an Arbitrary State of Two Qubits
• Mixed State Entanglement and Quantum Error Correction
• Separability Criterion for Density Matrices
• A computable measure of entanglement
• Separability of Mixed States: Necessary and Sufficient Conditions
• Concentrating Partial Entanglement by Local Operations
• Area laws for the entanglement entropy - a review
• Entanglement of a Pair of Quantum Bits
• Entanglement in quantum critical phenomena
• Entanglement detection
• Efficient classical simulation of slightly entangled quantum computations
• Quantifying Entanglement
• Scaling of Entanglement close to a Quantum Phase Transitions
• Entropy and Area
• Entanglement entropy and conformal field theory
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• The holographic principle
• Average Entropy of a Subsystem
• The logarithmic negativity: A full entanglement monotone that is not convex
• Entanglement in a simple quantum phase transition
• On the volume of the set of mixed entangled states
• Separability criterion and inseparable mixed states with positive partial transposition
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Entanglement renormalization
• An Area Law for One Dimensional Quantum Systems
• Conditions for a class of entanglement transformations
• Universal state inversion and concurrence in arbitrary dimensions
• Ground state overlap and quantum phase transitions
• Entanglement of atoms via cold controlled collisions
• Bell Inequalities and the Separability Criterion
• Preparation of Entangled States by Quantum Markov Processes
• Entanglement monotones
• Area laws in quantum systems: mutual information and correlations
• Optimization of entanglement witnesses
• Decay of Loschmidt Echo Enhanced by Quantum Criticality
• On the quantum, classical and total amount of correlations in a quantum state
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Entanglement Measures under Symmetry
• Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture
• Violation of the entropic area law for Fermions
• Entanglement versus Correlations in Spin Systems
• Entanglement spectrum in one-dimensional systems
• $p_x+i{p}_y$ superfluid from s-wave interactions of fermionic cold atoms
• Distinguishing separable and entangled states
• Simulation of strongly correlated fermions in two spatial dimensions with fermionic Projected Entangled-Pair States
• The computational complexity of PEPS
• Entanglement in XY Spin Chain
• The Entanglement of Formation for Isotropic States
• Fermionic Projected Entangled Pair States
• Quantum inseparability as local pseudomixture
• Evidence for Bound Entangled States with Negative Partial Transpose
• Distillability and partial transposition in bipartite systems
• Minimal conditions for local pure-state entanglement manipulation
• Average Entropy of a Subsystem
• I-concurrence and tangle for isotropic states
• General entanglement scaling laws from time evolution
• Separability of n-particle mixed states: necessary and sufficient conditions in terms of linear maps
• Optimal entanglement criterion for mixed quantum states
• Locality in Quantum and Markov Dynamics on Lattices and Networks
• A short review on entanglement in quantum spin systems
• Fermionic multi-scale entanglement renormalization ansatz
• Quantitative Determination of Temperature in the Approach to Magnetic Order of Ultracold Fermions in an Optical Lattice
• Contraction of fermionic operator circuits and the simulation of strongly correlated fermions
• Simulation of interacting fermions with entanglement renormalization
• Entanglement in spin chains and lattices with long-range Ising-type interactions
• Entanglement in Quantum Spin Chains, Symmetry Classes of Random Matrices, and Conformal Field Theory
• An area law for the entropy of low-energy states
• Black holes and information theory
• Single-copy entanglement in critical spin chains
• Measuring Multipartite Concurrence with a Single Factorizable Observable
• Unitary circuits for strongly correlated fermions
• Direct observation of quantum criticality in Ising spin chains
• Entanglement, quantum phase transitions, and density matrix renormalization
• Dynamics of the superfluid to Mott insulator transition in one dimension
• A two-way algorithm for the entanglement problem
• The von Neumann entropy asymptotics in multidimensional fermionic systems
• Separability, entanglement and full families of commuting normal matrices
• Dual entanglement measures based on no local cloning and no local deleting
• Quantum kinetic Ising models

Cited by in corpus (8)

• Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
• Quantum Simulating Nature's Fundamental Fields
• Entanglement entropies of minimal models from null-vectors
• Mixed s-sourcery: Building many-body states using bubbles of Nothing
• Group Field theory and Tensor Networks: towards a Ryu-Takayanagi formula in full quantum gravity
• Topological Minimally Entangled States via Geometric Measure
• Symmetry-protected intermediate trivial phases in quantum spin chains
• Open system approach to Neutrino oscillations in a quantum walk framework