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

2. What is quantum phase (transition) in many-body system? 1.Zero temperature quantum state with specified external parameter. 2.Energy level crossing 3.Non-analycity of Free energy. (and entanglement) Finite Temperature?? Can the quantum phase transition be detected always by singularity? Meaning of higher order singularity? First question and motivation 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. a. Single site entanglement ( Single spin and the rest of chain ) b.Concurrence ( Entanglement between any two spins ) Correlation function and Entanglement

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

8. Entanglement of any two spins Correlation and Entanglement in the Limit Correlation functions in the limit 1 1 2 23 3

9. 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 Discussions