Spin Drude weight of the 1D anisotropic Heisenberg spin-1/2 chain

The 1D anisotropic Heisenberg spin-1/2 chain in the thermodynamic limit is an exactly solvable quantum integrable model. Quantum integrability stems from an infinite number of local conserved charges, resulting in exciting transport properties that are accessible by low-temperature experiments. Our focus is on spin transport, which exhibits a non-zero long-time spin current (the finite spin Drude weight) at critical values of anisotropy with an external magnetic field of zero. This Drude weight exhibits a continuous dependence on the anisotropy at zero temperature, however becomes nowhere continuous at non-zero temperatures. Our goal in this presentation is to convey the current understanding with a focus on the limitations of the thermodynamic Bethe ansatz as applied to the Drude weight calculation.