Renormalization group transformations on quantum states

Abstract

We construct a general renormalization group transformation on quantum states, independent of any Hamiltonian dynamics of the system. We illustrate this procedure for translational invariant matrix product states in one dimension and show that product, GHZ, W and domain wall states are special cases of an emerging classification of the fixed points of this coarse--graining transformation.

5 pages, 2 figure

References in corpus (6)

• Three qubits can be entangled in two inequivalent ways
• Entanglement in quantum critical phenomena
• Persistent entanglement in arrays of interacting particles
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• DMRG and periodic boundary conditions: a quantum information perspective
• Fine-grained entanglement loss along renormalization group flows

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