We calculate the finite temperature thermal conductivity of a time-reversal invariant chiral ${\mathbb{Z}}_3$ clock model along an integrable line in the parameter space using the time-dependent density matrix renormalization group. The thermal current itself is not a conserved charge, unlike in the case of XXZ model, but has a finite overlap with a local conserved charge $Q^{\left(2\right)}$ obtained from the transfer matrix. We find that the Drude weight is finite at nonzero temperature, and the Mazur bound from $Q^{\left(2\right)}$ saturates the Drude weight, allowing us to obtain an asymptotic expression for the Drude weight at high temperatures. The numerical estimates of the conductivity are validated using a sum rule for thermal conductivity. On the computational side, we also explore the effectiveness of the ancilla disentangler in the integrable and nonintegrable regimes of the model. We find that at high temperature, the disentangler helps by localizing the entanglement growth around the quench location allowing us to obtain the Drude weight in the integrable model. The improvement is insufficient to extract the asymptotic value of the correlator in the nonintegrable regime. The ancilla disentangler also provides no additional advantage at low temperatures.

• Received 19 May 2023
• Revised 26 July 2023
• Accepted 27 July 2023

DOI:https://doi.org/10.1103/PhysRevB.108.054304