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We have found that for a wide range of two-qubit Hamiltonians thecanonical-ensemble thermal state is entangled in two distinct temperatureregions. In most cases the ground state is entangled; however we have alsofound an example where the ground state is separable and there are still tworegions. This demonstrates that the qualitative behavior of entanglement withtemperature can be much more complicated than might otherwise have beenexpected; it is not simply determined by the entanglement of the ground state,even for the simple case of two qubits. Furthermore, we prove a finite bound onthe number of possible entangled regions for two qubits, thus showing thatarbitrarily many transitions from entanglement to separability are notpossible. We also provide an elementary proof that the spectrum of the thermalstate at a lower temperature majorizes that at a higher temperature, for anyHamiltonian, and use this result to show that only one entangled region ispossible for the special case of Hamiltonians without magnetic fields.Comment: 6 pages, 4 figures, many new result

Two qubits can be entangled in two distinct temperature regions