Entanglement at the interplay between single- and many-bodyness

Abstract

The tensor network representation of the ground state of a Bethe chain is analytically obtained and studied in relation to its entanglement distribution. Block entanglement displays a maximum at the interplay between single- and many-bodyness. In systems of two fermions, tensor networks describing ground states of interacting Hamiltonians cannot be written as a sequence of next-neighbor unitaries applied on an uncorrelated state, but need four-next-neighbor unitaries in addition. This differs from the idea that the ground state can be obtained as a sequence of next-neighbor operations applied on a tensor network. The work uncovers the transcendence of the notion of many-bodyness in the implementation of protocols based on matrix product states.

arXiv comment6 pages + appendix, 3 figures. Comments are always welcome

References in corpus (29)

• The density-matrix renormalization group in the age of matrix product states
• Concentrating Partial Entanglement by Local Operations
• Area laws for the entanglement entropy - a review
• Nonequilibrium dynamics of closed interacting quantum systems
• Entanglement in quantum critical phenomena
• Efficient classical simulation of slightly entangled quantum computations
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Efficient simulation of one-dimensional quantum many-body systems
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• The iTEBD algorithm beyond unitary evolution
• Bridging entanglement dynamics and chaos in semiclassical systems
• Higher order Schmidt decompositions
• Operationally accessible entanglement of one dimensional spinless fermions
• Exact solutions of exactly integrable quantum chains by a matrix product ansatz
• The Algebraic Bethe Ansatz and Tensor Networks
• Numerical Contraction of the Tensor Network generated by the Algebraic Bethe Ansatz
• Tensor network representations of parton wave functions
• Algebraic Bethe Circuits
• Preparing Bethe Ansatz Eigenstates on a Quantum Computer
• Derivation of Matrix Product Ansatz for the Heisenberg Chain from Algebraic Bethe Ansatz
• Efficient tensor network representation for Gutzwiller projected states of paired fermions
• Classical Dynamics of Quantum Entanglement
• The nested Algebraic Bethe Ansatz for the supersymmetric t-J and Tensor Networks
• Particle partition entanglement of one dimensional spinless fermions
• Derivation of matrix product states for the Heisenberg spin chain with open boundary conditions
• End-to-end correlations in the Kitaev chain
• Uncoupled Majorana fermions in open quantum systems: On the efficient simulation of non-equilibrium stationary states of quadratic Fermi models
• Operator folding and matrix product states in linearly-coupled bosonic arrays
• Mode folding in systems with local interaction: unitary and non-unitary transformations using tensor states