Boundary-driven steady states of the Hubbard model

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Stationary states of low-dimensional open many-body quantum systems exhibit intriguing prop-erties such as long-range correlations even at non-zero temperature, anomalous transport andintriguing entanglement properties. A paradigmatic model of correlated electrons where thephysics behind these unusual non-equilibrium phenomena can be studied is one-dimensional Hub-bard model. With this model far-from-equilibrium behaviour can be studied by introducing dis-sipative Lindblad boundary terms which drive the system into a steady state far from thermalequilibrium. Such a state is inaccessible to approaches based on linear response theory or meanfield methods, but can be analysed even for large system sizes with a recently developed matrixproduct technique for the exact computation of the density matrix for the boundary-driven sys-tem.This is especially interesting for applications since under certain circumstances the steadystates are stable against decoherence.Our goal is to push further the development of exact tools for the construction of non-equilibriumsteady states in the boundary-driven one-dimensional Hubbard model and the study of anoma-lous transport, non-equilibrium quantum phase transitions and the quantum Zeno effect undernon-projective measurements. Computation of the density profiles will reveal the phase diagramas a function of the boundary coupling and open up the possibility to engineer steady stateswhere one passes from a pure, fully coherent state to a maximally mixed state. An intriguingnon-commutativity of limits was observed which leads to abrupt changes of transport propertiesrelated to the quantum Zeno and inverse Zeno effect. Studying the non-equilibrium entanglementspectrum and time-dependent dynamical properties of the XXZ Heisenberg chain and the Hub-bard model in the gapless regime will provide further insight into unusual quantum effects. Byinvestigating which boundary terms preserve the exact solvability of the density matrix we expectimpact of our exact results on the development of a theory of integrability of open one-dimensionalquantum systems.Given the paradigmatic nature and wide applicability of the Hubbard model, these studies provideinsight into generic non-equilibrium behaviour of low-dimensional dissipative quantum systemsfar from thermal equilibrium that are difficult to treat with traditional statistical or numericalapproaches.