Effect of the Dzyaloshinskii-Moriya interaction on heat conductivity in one-dimensional quantum Ising chains

Abstract

The effect of the Dzyaloshinskii-Moriya (DM) interaction on the heat conduction in the quantum Ising chain has been studied by solving the Lindblad master equation. The chain is subject to a uniform transverse field h, while the exchange couplings {Jm} between the nearest-neighbor spins are either uniform, random or quasi-periodic. The average energy-density profile and the average energy current in the non-equilibrium steady state have been numerically calculated. The ballistic transport is observed in the uniform Ising chain with DM interaction. For the random Ising chain with DM interaction, the energy gradient is observed in the bulk of the spin chain whose energy current appears to scale as the system size ⟨Q⟩ ∼ exp(βN) with β < 0. For the quasi-periodic Ising chain with DM interaction, the Jm takes the two values JA and JB arranged in the Fibonacci sequence. The energy gradient also exists in the spin chain and the energy current behaves as ⟨Q⟩ ∼ Nα with α < 0. By increasing the strength of the DM interaction D, a non-trivial transition from the thermal insulator heat transport to anomalous heat conduction is found in the Fibonacci Ising chain with large ratio of couplings λ = JA/JB. A rough phase diagram of λ vs. D is given in this paper as well.