Past exam of the quantum Condensed Matter Field Theory course of the University of Cambridge / 2012 / Paper 1 / 1 / d / ii

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- Solution ii

Solution

At large positive g,

ϵ_{k} = 2 J g - 2 J cos k + O (J / g)

. The gap grows as

2 J (g - 1)

while the leading bandwidth remains 4J. The field-polarized vacuum is unique.

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