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Purity and Continuous Quantum Phase Transition in XX spin chain

Purity and Continuous Quantum Phase Transition in XX spin chain. Wonmin Son. CQT, NUS, Singapore. In collaboration with ; Luigi Amico (Madrid), Francesco Plastina (Italy), Vlatko Vedral (Leeds, Singapore);. First question and motivation.

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Purity and Continuous Quantum Phase Transition in XX spin chain

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  1. Purity and Continuous Quantum Phase Transition in XX spin chain Wonmin Son CQT, NUS, Singapore In collaboration with; Luigi Amico (Madrid), Francesco Plastina (Italy), Vlatko Vedral (Leeds, Singapore);

  2. First question and motivation • What is quantum phase (transition) in many-body system? • Zero temperature quantum state with specified external parameter. • Energy level crossing • Non-analycity of Free energy. (and entanglement) • Finite Temperature?? • Can the quantum phase transition be detected always by singularity? • Meaning of higher order singularity? To see the recent progress on the topic, refer: “Quantum magnetism and criticality”, Subir Sachdev, Nature physics, (2008). “Many-body entanglement”, Amico, Fazio, Osterloh and Vedral, Rev. Mod. Phys. (2007).

  3. Hamiltonian • Ground state and energy XX model and Ground state

  4. Lowest energy • Ground state XX model and Ground state

  5. Single spin state and state for any two spins • Correlation functions Ground state and Correlation function

  6. Single site entanglement (Single spin and the rest of chain) • Concurrence (Entanglement between any two spins) Correlation function and Entanglement

  7. Ground state energy in the thermodynamic limit Thermodynamic Limit(Ground state energy) -> Continuous QPT

  8. Correlation functions in the limit Correlation and Entanglement in the Limit • Entanglement of any two spins 1 1 2 3 2 3

  9. Discussions • Kosterlitz-Touless type transition in spin chain. • Continuous energy level crossing so thus continuous (smooth) quantum phase transition. • Quantum phase -> quantum state -> Pure (Finite size, T=0), Mixed (infinite, T=0) state. The formalism can be applied for T >0 • Entanglement change is the way of detecting quantum phase up to local invariance. • Future direction: Relation between continuous QT and information processing. • “Quantum instability in a quasi-long range order” W.Son, L. Amico, F. Plastina and V. Vedral. ArXiv:0807.2529

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