Dissipation-driven integrable fermionic systems: from graded Yangians to exact nonequilibrium steady states

Abstract

Using the Lindblad master equation approach, we investigate the structure of steadystate solutions of open integrable quantum lattice models, driven far from equilibrium by incoherent particle reservoirs attached at the boundaries. We identify a class of boundary dissipation processes which permits to derive exact steady-state density matrices in the form of graded matrix-product operators. All the solutions factorize in terms of vacuum analogues of Baxter's Q-operators which are realized in terms of non-unitary representations of certain finite dimensional subalgebras of graded Yangians. We present a unifying framework which allows to solve fermionic models and naturally incorporates higher-rank symmetries. This enables to explain underlying algebraic content behind most of the previously-found solutions.

Superuniversality of superdiffusion

“…We thus wish to stress that the list of models discussed in this study is unlikely to be exhaustive and other classes of integrable models not included in our study are likewise expected to host a superdiffusive charge transport with characteristic exponent z = 3/2: we anticipate that the phenomenon extends beyond Yangians associated with simple Lie algebras to other classes of models based on rational solutions to the Yang-Baxter equations which includes (but is necessarily limited to) the Fermi-Hubbard model [36] and to other supersymmetric su(n|m) (or orthosymplectic osp(n|2m)) integrable spin chains that realize Yangian symmetries associated with Lie superalgebras (see e.g. [99,165,166]) whose bosonic Noether charges are known to display divergent diffusion constants [44], or integrable models based on infinite-dimensional affine symmetry algebras [167] (such as the Izergin-Korepin model [168]).…”

Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos

“…Understanding decoherence and dissipation effects arising in open quantum mechanical systems requires dealing with nonunitary dynamics generated by nonhermitian operators. Nonhermitian physics has attracted much attention recently, for instance, in the study of Lindbladian dynamics of integrable [1][2][3][4][5][6][7][8][9][10][11] and chaotic [12][13][14][15] open quantum systems, topological phases of open systems [16][17][18][19][20][21][22][23][24][25][26][27], PT -symmetric and general nonhermitian optics [28][29][30][31][32][33][34][35], nonhermitian many-body localization [36], nonhermitian quantum critical phenomena [37][38][39][40], or quantum chaotic scattering [41,42]. However, a methodology to classify all of these nonhermitian systems into different classes or phases, in terms of their universal spectral correlations, is still lacking.…”

Quantum contact process

“…From the experimental side, recent technological developments and increased capabilities in the realisation and control of quantum systems offer promising platforms for the investigation of quantum phenomena far from equilibrium [1][2][3][4][5][6][7][8][9][10][11][12]. However, from a theoretical perspective, non-equilibrium quantum systems are typically much more complex than classical ones and their characterization is still an open problem, especially when going beyond the realm of exactly solvable models or the application of semi-classical approaches [13][14][15][16][17][18][19][20]. Even numerical studies, which in the classical case allow for the accurate investigation of nonintegrable systems, in quantum settings are often severely limited due to computational constraints.…”