Dissipative dynamics in open XXZ Richardson-Gaudin models05 August 2021
New work with Austen Lamacraft on Dissipative dynamics in open XXZ Richardson-Gaudin models now on arXiv! Extending on previous work by Austen and Daniel Rowlands, we consider open systems with collective dissipation that can be mapped to Richardson-Gaudin models. While this mapping was previously known, the exact solution remained surprisingly unexplored, and we here investigate the physics of such collective models.
Moving from closed systems to open systems, the usual description in terms of a Hermitian Hamiltonian no longer applies and we rather need to consider a non-Hermitian Liouvillian. While we lose most of the salient properties of Hermiticity, the Liouvillian that we obtain turns out to be pseudo-Hermitian. This can be interpreted as an additional symmetry of the system, and as we change the coupling to the environment the dynamics of the system qualitatively changes if this symmetry is broken. At weak coupling the system essentially behaves as a closed system with weak dissipation, but as the coupling to the environment is increased at some point the system becomes overdamped, and all correlations exhibit purely exponential decay. Mathematically, the Liouvillian passes through exceptional points and PT-symmetry/pseudo-Hermiticity is spontaneously broken. We also uncover some additional structure in the spectrum, showing how at large coupling to the environment the spectrum exhibits features of the homogeneous model — where we can exactly solve the system using collective spins.
In specific open systems with collective dissipation the Liouvillian can be mapped to a non-Hermitian Hamiltonian. We here consider such a system where the Liouvillian is mapped to an XXZ Richardson-Gaudin integrable model and detail its exact Bethe ansatz solution. While no longer Hermitian, the Hamiltonian is pseudo-Hermitian/PT-symmetric, and as the strength of the coupling to the environment is increased the spectrum in a fixed symmetry sector changes from a broken pseudo-Hermitian phase with complex conjugate eigenvalues to a pseudo-Hermitian phase with real eigenvalues, passing through a series of exceptional points and associated dissipative quantum phase transitions. The homogeneous limit supports a nontrivial steady state, and away from this limit this state gives rise to a slow logarithmic growth of the decay rate (spectral gap) with system size. Using the exact solution, it is furthermore shown how at large coupling strengths the ratio of the imaginary to the real part of the eigenvalues becomes approximately quantized in the remaining symmetry sectors.
Seminar at BAQIS25 June 2021
On Thursday July 1st I'll be giving a seminar on Thermalization and scrambling in dual-unitary circuit models at the Beijing Academy of Quantum Information Sciences (BAQIS). Feel free to join, all information can be found below!
Interacting Topological Matter: Atomic, Molecular and Optical Systems05 June 2021
On Monday June 7th I'll be presenting various results on Floquet-engineering counterdiabatic protocols at the KITP program on Interacting Topological Matter: Atomic, Molecular and Optical Systems. I'll be in good company — check out the full program, focusing on Floquet systems, here. A recording of the talk will also appear online afterwards.