Integrability of one-dimensional Lindbladians from operator-space fragmentation

Abstract

We introduce families of one-dimensional Lindblad equations describing open many-particle quantum systems that are exactly solvable in the following sense: (i) the space of operators splits into exponentially many (in system size) subspaces that are left invariant under the dissipative evolution; (ii) the time evolution of the density matrix on each invariant subspace is described by an integrable Hamiltonian. The prototypical example is the quantum version of the asymmetric simple exclusion process (ASEP) which we analyze in some detail. We show that in each invariant subspace the dynamics is described in terms of an integrable spin-1/2 XXZ Heisenberg chain with either open or twisted boundary conditions. We further demonstrate that Lindbladians featuring integrable operator-space fragmentation can be found in spin chains with arbitrary local physical dimension.

Unbounded entanglement production via a dissipative impurity

“…Within the so-called Markovian approximation, the Lindblad equation provides a powerful framework to address open quantum systems [5]. Interestingly, for some models it is possible to obtain exact solutions of the Lindblad equation [6][7][8][9][10][11][12][13][14][15][16], for instance, in noninteracting systems with linear dissipators [6]. Perturbative field-theoretical approaches are also available [17].…”

Diffusion and thermalization in a boundary-driven dephasing model

“…The spectral properties of the model in terms of the Liouvillian spectrum have been extensively discussed [6] as well as its transport properties [7][8][9][10][11][12] when the model is supplemented by a boundary Markovian driving. The pure dephasing model is furthermore exactly solvable [13,14], its Lindbladian spectrum being obtainable through Bethe Ansatz techniques [14][15][16]. Recent works have discussed various extensions of this model [17].…”

Out-of-Time-Ordered Crystals and Fragmentation

“…Finally, similarity between fragmentation and strictly local weak symmetries [56] has also been noted for open quantum systems [57].…”