Locality of the field operators of many-body theory

Dieter Schütte

Sara Murciano, Vittorio Vitale, Marcello Dalmonte +1 more

In the context of ground states of quantum many-body systems, the locality of entanglement between connected regions of space is directly tied to the locality of the corresponding entanglement Hamiltonian: the latter is dominated by local, few-body terms. In this work, we introduce the negativity Hamiltonian as the (non-Hermitian) effective Hamiltonian operator describing the logarithm of the partial transpose of a many-body system. This allows us to address the connection between entanglement and operator locality beyond the paradigm of bipartite pure systems. As a first step in this direction, we study the structure of the negativity Hamiltonian for fermionic conformal field theories and a free-fermion chain: in both cases, we show that the negativity Hamiltonian assumes a quasilocal functional form, that is captured by simple functional relations.

Philippe A. Martin, FRANÇOIS ROTHEN

Adrian Hutter, Fabio L. Pedrocchi, James R. Wootton +1 more

In Phys. Rev. A 88, 062313 (2013) we proposed and studied a model for a self-correcting quantum memory in which the energetic cost for introducing a defect in the memory grows without bounds as a function of system size. This positive behavior is due to attractive long-range interactions mediated by a bosonic field to which the memory is coupled. The crucial ingredients for the implementation of such a memory are the physical realization of the bosonic field as well as local five-body interactions between the stabilizer operators of the memory and the bosonic field. Here, we show that both of these ingredients appear in a low-energy effective theory of a Hamiltonian that involves only two-body interactions between neighboring spins. In particular, we consider the low-energy, long-wavelength excitations of an ordered Heisenberg ferromagnet (magnons) as a realization of the bosonic field. Furthermore, we present perturbative gadgets for generating the required five-spin operators. Our Hamiltonian involving only local two-body interactions is thus expected to exhibit self-correcting properties as long as the noise affecting it is in the regime where the effective low-energy description remains valid.

Eric Aboagye Amankwah

DLWPT: Many-Body Coherence, Bell Correlations, and No-Signaling extends the Dynamical Localized Wave Packet Theory (DLWPT) to many-body quantum systems and investigates its implications for Bell correlations, quantum nonlocality, contextuality, and the measurement problem. The paper develops a deterministic, collapse-free framework in which the fundamental ontic entity is a conserved coherence field defined on configuration space rather than a probabilistic wavefunction interpretation. The work demonstrates how local detector interactions arise through marginal coupling to the coherence density while the global non-separable structure of the many-body field naturally generates Bell-inequality violations. Operational no-signaling is preserved despite ontic nonlocality, thereby providing a deterministic account of quantum correlations without invoking wavefunction collapse, hidden particle trajectories, superdeterminism, or retrocausality. A concrete Stern–Gerlach detector model is developed to show how discrete measurement outcomes emerge through spatial sorting and temporal coarse-graining of the coherence density. The paper further establishes the contextual nature of DLWPT in accordance with the Kochen–Specker theorem and proposes experimentally testable deviations from standard quantum mechanics in ultrafast and high-energy Bell experiments. Overall, this work positions DLWPT as a coherence-based reconstruction of quantum foundations in which the Born rule, Bell correlations, and operational no-signaling emerge from a unified dynamical principle based on the conservation and evolution of coherence density.

Philippe A. Martin, FRANÇOIS ROTHEN