Violation of the area law and long range correlations in infinite matrix product states

Abstract

We propose to construct a family of states of one-dimensional spin chains by replacing the finite dimensional matrices in matrix product states by infinite dimensional operators constructed from bosonic annihilation and creation operators. The resulting states are demonstrated to violate the area law and to exhibit long range correlations. In addition, we propose an efficient way to prepare the states experimentally, in which the spins interact sequentially with an ancilla system.

9+4 pages, 13+0 figures

References in corpus (6)

• Matrix product states represent ground states faithfully
• Progressive field-state collapse and quantum non-demolition photon counting
• Entanglement renormalization, scale invariance, and quantum criticality
• Sequential Generation of Matrix-Product States in Cavity QED
• Deterministic loading of individual atoms to a high-finesse optical cavity
• Holographic quantum states

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• Interaction-induced phase transitions at topological quantum criticality of an extended Su-Schrieffer-Heeger model
• Recognizing critical lines via entanglement in non-Hermitian systems
• Quantum impurity models from conformal field theory
• Topological phases protected by projective space-time inversion symmetry in alkaline-earth-metal-like atoms
• Symmetries and field tensor network states