Dynamic Response of Dissipative Spin Chains

One-dimensional spin chains are paradigmatic platforms to realize unusual phases and phase transitions in and out of equilibrium. Over the past ten years, boundary driven chains have emerged as a class of models exhibiting out-of-equilibrium quantum criticality. We develop a linear and non-linear response formalism for free fermionic and bosonic Lindbladian systems, which we use to study magnetic excitations, quantum criticality and dynamical responses in spin chains with boundary dissipation. In quantum Ising and XY spin chains, we find paramagnetic and spin-density wave (SDW) phases where the SDW wavelength diverges at a critical transverse field. In contrast to closed systems, the dynamic spin susceptibility hosts signatures of new non-equilibrium collective states evidenced by gapless modes. We then discuss dynamic response properties of finite-size spin chains with strong non-linearities such as the XXZ spin chain, and comment on possible implementations on NISQ quantum computing hardware