Dissipative spin chain as a non-Hermitian Kitaev ladder
Dissipative spin chain as a non-Hermitian Kitaev ladder
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DOI：
10.1103/physrevb.99.174303
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发表时间：
2018-12
影响因子：
3.7
通讯作者：
Naoyuki Shibata;H. Katsura
中科院分区：
文献类型：
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作者：
Naoyuki Shibata;H. Katsura
我们得到了具有退相噪声的量子自旋链(一维量子罗盘模型)的Lindblad方程的精确结果。由于存在与哈密顿算符和Lindblad算符交换的守恒电荷，系统具有双重简并的非平衡定态。我们证明了系统可以映射到两腿阶梯上的非厄米特Kitaev模型，这可以通过用Majorana费米子来表示自旋来求解。这使我们能够详细地研究与弛豫时间相反的柳维利亚间隙。我们发现，当耗散强度较小时，Liouvillian带隙单调增加，而当耗散强度较大时，Liouvillian带隙单调减小，这意味着在第一衰变模式下存在一种相变。在自旋链为临界点的情况下，Liouvillian带隙和相变点以封闭形式得到。我们还得到了边缘自旋的自相关器的显式表达式。结果表明，当自旋链处于拓扑区时，退相干受到了抑制。
We derive exact results for the Lindblad equation for a quantum spin chain (one-dimensional quantum compass model) with dephasing noise. The system possesses doubly degenerate nonequilibrium steady states due to the presence of a conserved charge commuting with the Hamiltonian and Lindblad operators. We show that the system can be mapped to a non-Hermitian Kitaev model on a two-leg ladder, which is solvable by representing the spins in terms of Majorana fermions. This allows us to study the Liouvillian gap, the inverse of relaxation time, in detail. We find that the Liouvillian gap increases monotonically when the dissipation strength $\ensuremath{\gamma}$ is small, while it decreases monotonically for large $\ensuremath{\gamma}$, implying a kind of phase transition in the first decay mode. The Liouvillian gap and the transition point are obtained in closed form in the case where the spin chain is critical. We also obtain the explicit expression for the autocorrelator of the edge spin. The result implies the suppression of decoherence when the spin chain is in the topological regime.