Download Renormalization of Entanglement

Sharif University of Technology
Department of Physics
Renormalization of Entanglement
in quantum spin models
R. Jafari , M. Kargarian , A. Langari
Outlines:
• Motivations
• Quantum Renormalization Group
• RG of Entanglement
• conclusions
Motivations
 entanglement is the essential resource for quantum
information processing and quantum communication.
Protocols based on entangled states can offer an
exponential speedup with respect to classical
computation.
 entanglement measures quantum correlations for pure
states, it is natural to think of a close connection
between entanglement and the correlation functions of
highly correlated states in condensed matter systems.
QRG
• In condensed matter physics, we are faced with huge number of
particles.
• Diagonalizing the Hamailtonian of the quantum many body system:
• Dimensionality of the Hilbert space:
QRG
• Resorting to the approximate methods are unavoidable.
– QMC
– QRG
Hilbert Space
Effective Hilbert Space
Physically Relevant
Mathematical Framework
• A prescription is that Block Real Space RG
Real Space RG
• So an implementation of RG:
– Reduction the size of the lattice
– How many sates to be retained in the
truncation procedure
Real Space RG
• Block RG or coarse graining
J
J
J
J
J’
J’
J’=R(J)
J
ITF Model
H=
H B=
HBB=
ITF Model
ITF Model
XXZ Model
Entanglement and QPT
ITF Model
A. Osterloh, et al. Nature, 416 (2002) 608
Renormalization of Entanglement in ITF
Renormalization of Entanglement in ITF
Renormalization of Entanglement in ITF
XXZ Model
XXZ Model
summary
• Tackling the quantum many body systems in condensed
matter physics from the quantum information perspective
deepen our understanding of exotic states of matter.
• We combine the quantum renormalization group notion
with the entanglement in order to study the entanglement
in some quantum spin models.
• Evolution of entanglement through the renormalization
procedure truly captures the critical behavior of the
lattice models.
Thanks for your attention
Mathematical Framework
ITF Model