Linear and Non-Linear Response of Quadratic Lindbladians
- URL: http://arxiv.org/abs/2402.06593v2
- Date: Fri, 1 Mar 2024 15:54:05 GMT
- Title: Linear and Non-Linear Response of Quadratic Lindbladians
- Authors: Spenser Talkington, Martin Claassen
- Abstract summary: Quadratic Lindbladians encompass a rich class of dissipative electronic and bosonic quantum systems.
We develop a Lindblad-Keldysh response formalism for open quantum systems that elucidates their steady-state response properties.
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- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Quadratic Lindbladians encompass a rich class of dissipative electronic and
bosonic quantum systems, which have been predicted to host new and exotic
physics. In this study, we develop a Lindblad-Keldysh spectroscopic response
formalism for open quantum systems that elucidates their steady-state response
properties and dissipative phase transitions via finite-frequency linear and
non-linear probes. As illustrative examples, we utilize this formalism to
calculate the (1) density and dynamic spin susceptibilities of a boundary
driven XY model at and near criticality, (2) linear and non-linear optical
responses in Bernal bilayer graphene coupled to dissipative leads, and (3)
steady state susceptibilities in a bosonic optical lattice. We find that the XY
model spin density wavelength diverges with critical exponent 1/2, and there
are gapless dispersive modes in the dynamic spin response that originate from
the underlying spin density wave order; additionally the dispersing modes of
the weak and ultra-strong dissipation limits exhibit a striking correspondence
since the boundary dissipators couple only weakly to the bulk in both cases. In
the optical response of the Bernal bilayer, we find that the diamagnetic
response can decrease with increasing occupation, as opposed to in closed
systems where the response increases monotonically with occupation; we study
the effect of second harmonic generation and shift current and find that these
responses, forbidden in centrosymmetric closed systems, can manifest in these
open systems as a result of dissipation. We compare this formalism to its
equilibrium counterpart and draw analogies between these non-interacting open
systems and strongly interacting closed systems.
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