Exact TBA expressions for impurity free energy and entropy in all four phases of the Heisenberg chain explain non-monotonic and negative impurity entropy via a split Hilbert space of excitation towers.
Hulth´ en,¨Uber das Austauschproblem eines Kristalles, Arkiv f¨ or Matematik, Astronomi och Fysik 26A, 1 (1938)
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Thermodynamics in a split Hilbert space: Quantum impurity at the edge of the Heisenberg chain
Exact TBA expressions for impurity free energy and entropy in all four phases of the Heisenberg chain explain non-monotonic and negative impurity entropy via a split Hilbert space of excitation towers.