Publications of Jan T. Schneider

The study of many-body quantum systems out of equilibrium remains a significant challenge with complexity barriers arising in both state and operator-based representations. In this work, we review recent approaches based on finding better contraction strategies for the full spatio-temporal tensor networks that encode the path integral of the dynamics, as well as the conceptual integration of influence functionals, process tensors, and transfer matrices within the tensor network formalism. We discuss recent algorithmic developments, highlight the complexity of influence functionals in various dynamical regimes and present consistent results of different communities, showing how ergodic dynamics render these functionals exponentially difficult to compress. Finally, we provide an outlook on strategies to encode complementary influence functional overlaps, paving the way for accurate descriptions of open and closed quantum systems with tensor networks.

We set up an effective field theory formulation for the renormalization flow of matrix product states (MPS) with finite bond dimension, focusing on systems exhibiting finite-entanglement scaling close to a conformally invariant critical fixed point. We show that the finite MPS bond dimension $\chi$ is equivalent to introducing a perturbation by a relevant operator to the fixed-point Hamiltonian. The fingerprint of this mechanism is encoded in the $\chi$-independent universal transfer matrix’s gap ratios, which are distinct from those predicted by the unperturbed Conformal Field Theory. This phenomenon defines a renormalization group self-congruent point, where the relevant coupling constant ceases to flow due to a balance of two effects; When increasing $\chi$, the infrared scale, set by the correlation length $\xi(\chi)$, increases, while the strength of the perturbation at the lattice scale decreases. The presence of a self-congruent point does not alter the validity of the finite-entanglement scaling hypothesis, since the self-congruent point is located at a finite distance from the critical fixed point, well inside the scaling regime of the CFT. We corroborate this framework with numerical evidences from the exact solution of the Ising model and density matrix renormalization group (DMRG) simulations of an effective lattice model.

We introduce a novel experimental approach to probe many-body quantum systems by developing a protocol to measure generalized temporal entropies. We demonstrate that the recently proposed generalized temporal entropies [Phys. Rev. Research 6, 033021] are equivalent to observing the out-of-equilibrium dynamics of a replicated system induced by a double quench protocol using local operators as probes. This equivalence, confirmed through state-of-the-art tensor network simulations for one-dimensional systems, validates the feasibility of measuring generalized temporal entropies experimentally. Our results reveal that the dynamics governed by the transverse field Ising model integrable Hamiltonian differ qualitatively from those driven by the same model with an additional parallel field, breaking integrability. They thus suggest that generalized temporal entropies can serve as a tool for identifying different dynamical classes. This work represents the first practical application of generalized temporal entropy characterization in one-dimensional many-body quantum systems and offers a new pathway for experimentally detecting integrability. We conclude by outlining the experimental requirements for implementing this protocol with state of the art quantum simulators.

Photonic quantum metrology harnesses quantum states of light, such as NOON or Twin-Fock states, to measure unknown parameters beyond classical precision limits. Current protocols suffer from two severe limitations that preclude their scalability: the exponential decrease in fidelities (or probabilities) when generating states with large photon numbers due to gate errors, and the increased sensitivity of such states to noise. Here, we develop a deterministic protocol combining quantum optical non-linearities and variational quantum algorithms that provides a substantial improvement on both fronts. First, we show how the variational protocol can generate metrologically-relevant states with a small number of operations which does not significantly depend on photon-number, resulting in exponential improvements in fidelities when gate errors are considered. Second, we show that such states offer a better robustness to noise compared to other states in the literature. Since our protocol harnesses interactions already appearing in state-of-the-art setups, such as cavity QED, we expect that it will lead to more scalable photonic quantum metrology in the near future.

Entanglement is a central feature of many-body quantum systems and plays a unique role in quantum phase transitions. In many cases, the entanglement spectrum, which represents the spectrum of the density matrix of a bipartite system, contains valuable information beyond the sole entanglement entropy. Here we investigate the entanglement spectrum of the long-range XXZ model. We show that within the critical phase it exhibits a remarkable self-similarity. The breakdown of self-similarity and the transition away from a Luttinger liquid is consistent with renormalization group theory. Combining the two, we are able to determine the quantum phase diagram of the model and locate the corresponding phase transitions. Our results are confirmed by numerically-exact calculations using tensor-network techniques. Moreover, we show that the self-similar rescaling extends to the geometrical entanglement as well as the Luttinger parameter in the critical phase. Our results pave the way to further studies of entanglement properties in long-range quantum models.

Whether long-range interactions allow for a form of causality in non-relativistic quantum models remains an open question with far-reaching implications for the propagation of information and thermalization processes. Here, we study the out-of-equilibrium dynamics of the one-dimensional transverse Ising model with algebraic long-range exchange coupling. Using a state of the art tensor-network approach, complemented by analytic calculations and considering various observables, we show that a weak form of causality emerges, characterized by non-universal dynamical exponents. While the local spin and spin correlation causal edges are sub-ballistic, the causal region has a rich internal structure, which, depending on the observable, displays ballistic or super-ballistic features. In contrast, the causal region of entanglement entropy is featureless and its edge is always ballistic, irrespective of the interaction range. Our results shed light on the propagation of information in long-range interacting lattice models and pave the way to future experiments, which are discussed.