MPAGS SM2 Lectures 9 & 10 - Warwick
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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)
Transcript of MPAGS SM2 Lectures 9 & 10 - Warwick
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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)
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Quantum statistical mechanics
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Quantum Ising model
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Quantum paramagnet
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Ferromagnetic phase
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Quantum phase transition
continuous (second-order) phase transition:
paramagnetferromagnet
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Path integral for partition function
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Quantum–classical mapping
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QC mapping: General case
quantum classical
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QC mapping: Ising model
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QC mapping: Ising model
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Quantum Ising chain
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Jordan–Wigner transformation
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Ising chain: Exact spectrum
(see practice problems)
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Ising chain: Quantum phase transition
Sachdev (1999/2011)