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Lectures 9 & 10
• Quantum phase transitions
◦ Introduction
◦ Quantum Ising model
• Quantum critical phenomena
◦ Connection to classical criticality
• Exact solution of quantum Ising chain
◦ Critical behaviour
Sachdev (1999/2011)
Quantum statistical mechanics
Quantum Ising model
Quantum paramagnet
Ferromagnetic phase
Quantum phase transition
continuous (second-order) phase transition:
paramagnetferromagnet
Path integral for partition function
Quantum–classical mapping
QC mapping: General case
quantum classical
QC mapping: Ising model
QC mapping: Ising model
Quantum Ising chain
Jordan–Wigner transformation
Ising chain: Exact spectrum
(see practice problems)
Ising chain: Quantum phase transition
Sachdev (1999/2011)