Boundary-driven steady states of the Hubbard model

低维开放多体量子系统的定态具有许多有趣的性质，如在非零温度下的长程关联、反常输运和有趣的纠缠特性。一维Hub-bard模型是研究这些不寻常的非平衡现象背后的物理机制的一个范例。在这个模型中，通过引入耗散的Lindblad边界项，可以研究远离平衡态的行为，这些边界项使系统进入远离热平衡态的稳态。这种状态是基于线性响应理论或平均场方法的方法无法达到的，但是，即使对于大的系统尺寸，也可以用最近开发的矩阵乘积技术进行分析，用于边界驱动系统的密度矩阵的精确计算。这对应用特别有意义，因为在某些情况下，稳态是稳定的，不受退相干的影响。我们的目标是进一步推动精确工具的发展在边界驱动的一维Hubbard模型中构造非平衡-定态，研究非投影测量下的反常输运、非平衡量子相变和量子Zeno效应。密度分布的计算将揭示的相位的边界耦合的函数，并开辟了可能性，工程师的稳态，其中一个从一个纯粹的，完全相干的状态，以最大的混合状态。发现了一种有趣的极限非对易性，它导致了与量子Zeno效应和逆Zeno效应有关的输运性质的突变。研究XXZ Heisenberg链和Hub-bard模型在无隙区的非平衡纠缠谱和含时动力学性质，将有助于进一步了解不寻常的量子效应。通过研究哪些边界项保持密度矩阵的精确可解性，我们期望我们的精确结果对发展开放一维量子系统的可积性理论有一定的影响。这些研究提供了对一般非平衡行为的深入了解，维耗散量子系统远离热平衡，难以处理与传统的统计或数值方法。

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.