Dissipative spin chain as a non-Hermitian Kitaev ladder
- URL: http://arxiv.org/abs/1812.10373v4
- Date: Sat, 15 Apr 2023 08:31:11 GMT
- Title: Dissipative spin chain as a non-Hermitian Kitaev ladder
- Authors: Naoyuki Shibata and Hosho Katsura
- Abstract summary: We derive exact results for the Lindblad equation for a quantum spin chain with dephasing noise.
We show that the system can be mapped to a non-Hermitian Kitaev model on a two-leg ladder.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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 $ \gamma $ is small, while it
decreases monotonically for large $ \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.
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