Research highlights obtained in the project include:
(i) The establishment of a new universality class for bosons, in which quantum coherent effects are crucial even at criticality, in this way realizing an analogue of a quantum critical point. At the same time, detailed balance is manifestly absent, highlighting the importance of non-equilibrium conditions.
(ii) The identification of a new first order phase transition which occurs as function of the strength of the violation of detailed balance. This phase transition could be a representative of a new class of phase transitions between and dissipative fixed point and a non-equilibrium chaotic phase.
(iii) We discover that – contrary to common wisdom – topological order persists in mixed many-body quantum states of fermions in one dimension, provided suitable many-body correlators are considered. We establish the mechanism behind this scenario and provide a prescription how to measure these correlators using many-body interferometry.
(iv) We unravel the nature of phase transitions in rapidly driven, open Floquet systems: Naïve reasoning suggests that the fast scale induced by the drive cannot affect the critical behavior. In contrast, we discover a mechanism according to which even the very nature of the phase transition is changed from second to first order. This fast-drive scenario is dual to the slow-drive Kibble-Zurek paradigm.
(v) We identify a fluctuation induced quantum Zeno effect: We address the physics of dissipative impurities in a Hamiltonian quantum systems in its ground state. This comprises the case of loss impurity, where we find a fluctuation induced Quantum Zeno effect as anticipated in the proposal, but also addresses an analog of the orthogonality catastrophe by a dephasing impurity.
(vi) We establish self-organized criticality in a driven open Rydberg gas: In collaboration with the group of Prof. Whitlock (Strasbourg), experimental observations could be successfully theoretically explained as manifestations of a self-organized variant of absorbing state phase transitions. It represents the first observation of self-organized criticality with ultracold atoms and sparks the hope for establishing them as a new quantitative platform.
(vii) We show that the topological gauge theory principle universally extends beyond thermal equilibrium, qualifying the precise conditions under which this holds true. As a corollary, in a concrete driven-open analog of a quantum Hall insulator, we predict undamped chiral edge modes stabilized by a purely dissipative bulk.
(viii) We present a full symmetry classification of dissipatively evolving fermion matter. We demonstrate that there are no more than 10 symmetry classes available in stationary state. A further key insight lies in the different representations of the linear and anti-linear Fock-space symmetries depending on whether the generator of dynamics is of equilibrium or non-equilibrium type. This enables a grand total of 17 dynamical universality classes.
(ix) We point out a route to engineer highly entangle states of matter - quantum spin liquids - by immersion of quantum materials into optical cavities. Frustration is the key mechanism to enable spin liquids. Here we propose to engineer frustration by exploiting the coupling of quantum magnets to the quantized light of an optical cavity, resulting in a tunable long-range interaction between spins. This cavity-induced frustration robustly stabilizes spin liquid states. Remarkably, this occurs even in originally unfrustrated systems, as we showcase for the Heisenberg model on the square lattice. This project was not foreseen in the original project plan.
(x) We establish a novel kind of phase transition in the quantum trajectory dynamics of free fermions subject to non-unitary density monitoring processes. We find a sharp transition as a function of increasing monitoring strength from a robust critical state with logarithmically growing entanglement entropy to one with an area law growth. This research has developed dynamically within the runtime of the project.
(xi) We develop the first analytical theory for measurement induced phase transitions in fermion systems. It builds on a replicated version of the Keldysh functional integral, and a bosonization of the fermionic degrees of freedom. We identify the relevant degrees of freedom driving the transition, which are associated to the inter-replica fluctuations. It predicts the pahse transition to be of the Kosterlitz-Thouless type, in accord with numerics.
All the work discussed here has been disseminated in high-impact journals (PRL, PRX, Nature Communications, Nature, see publication summary) and was presented in various conferences and colloquia by the PI and the members of the DOQS team.
