 Solution

ID: past-exam-of-the-quantum-condensed-matter-field-theory-course-of-the-university-of-cambridge/2012/paper-1/1/d/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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