Renormalization of Entanglement in quantum spin models

R. Jafari , M. Kargarian , A. Langari

Sharif University of TechnologyDepartment of Physics

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:

• Resorting to the approximate methods are unavoidable.

– QMC

– QRG

Effective Hilbert Space Physically Relevant

Hilbert Space

QRG

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 JJ JJ

J’ J’

J’=R(J)

ITF Model

H=

HBB=

HB=

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