Entanglement and quantum phase transitions in matrix product spin one chains

Abstract

We consider a one-parameter family of matrix product states of spin one particles on a periodic chain and study in detail the entanglement properties of such a state. In particular we calculate exactly the entanglement of one site with the rest of the chain, and the entanglement of two distant sites with each other and show that the derivative of both these properties diverge when the parameter $g$ of the states passes through a critical point. Such a point can be called a point of quantum phase transition, since at this point, the character of the matrix product state which is the ground state of a Hamiltonian, changes discontinuously. We also study the finite size effects and show how the entanglement depends on the size of the chain. This later part is relevant to the field of quantum computation where the problem of initial state preparation in finite arrays of qubits or qutrits is important. It is also shown that entanglement of two sites have scaling behavior near the critical point.

References in corpus (17)

• Separability Criterion for Density Matrices
• A computable measure of entanglement
• Scaling of Entanglement close to a Quantum Phase Transitions
• Entanglement in a simple quantum phase transition
• Natural Thermal and Magnetic Entanglement in 1D Heisenberg Model
• Entangled Rings
• Matrix-product-groundstates for one-dimensional spin-1 quantum antiferromagnets
• Quantum fidelity and quantum phase transitions in matrix product states
• Quantum phase transitions in matrix product systems
• Entanglement in a Valence-Bond-Solid State
• Quantum phase transition in spin-3/2 systems on the hexagonal lattice - optimum ground state approach
• Entropy and Exact Matrix Product Representation of the Laughlin Wave Function
• Simulation of many-qubit quantum computation with matrix product states
• Thermal entanglement of spins in the Heisenberg model at low temperatures
• Quantum Phase Transitions and Matrix Product States in Spin Ladders
• Exact ground states of quantum spin-2 models on the hexagonal lattice
• Quantum Critical Point and Entanglement in a Matrix Product Ground State

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• A complete characterization of the spectrum of the Kitaev model on spin ladders
• Scaling of macroscopic superpositions close to a quantum phase transition
• Entanglement and level crossings in frustrated ferromagnetic rings
• An effective spin-1 Heisenberg chain in coupled cavities
• Characterizing coherence with quantum observables
• Impurity Entanglement in the $J-J_2-\delta$ Quantum Spin Chain
• Exact Results for the Bipartite Entanglement Entropy of the AKLT spin-1 chain
• Exact symmetry breaking ground states for quantum spin chains
• Exact ground states for two new spin-1 quantum chains, new features of matrix product states
• Unfolding system-environment correlation in open quantum systems: Revisiting master equations and the Born approximation
• A classification of spin 1/2 matrix product states with two dimensional auxiliary matrices
• A new family of matrix product states with Dzyaloshinski-Moriya interactions