Fixed-Point Few-Body Hamiltonians

Raffaele Carlone

Lauro Tomio, T. Frederico, V. S. Timóteo +1 more

We revisited how Weinberg's ideas in Nuclear Physics influenced our own work and lead to a renormalization group invariant framework within the quantum mechanical few-body problem, and we also update the discussion on the relevant scales in the limit of short-range interactions. In this context, it is revised the formulation of the subtracted scattering equations and fixed-point Hamiltonians applied to few-body systems, in which the original interaction contains point-like singularities, such as Dirac-delta and/or its derivatives. The approach is being illustrated by considering two-nucleons described by singular interactions. This revision also includes an extension of the renormalization formalism to three-body systems, which is followed by an updated discussion on the applications to four particles.

W. Glöckle

Ian J. van Beek, Bernd Braunecker

We carry out a theoretical analysis of a prototypical Majorana system, which demonstrates the existence of a Majorana-mediated many-body state and an associated intermediate low-energy fixed point. Starting from two Majorana bound states, hosted by a Coulomb-blockaded topological superconductor and each coupled to a separate lead, we derive an effective low-energy Hamiltonian, which displays a Kondo-like character. However, in contrast to the Kondo model which tends to a strong- or weak-coupling limit under renormalization, we show that this effective Hamiltonian scales to an intermediate fixed point, whose existence is contingent upon teleportation via the Majorana modes. We conclude by determining experimental signatures of this fixed point, as well as the exotic many-body state associated with it.

Renzo Alzetta, Giorgio Parisi A, Teresa Semeraro

María Laura Olivera-Atencio, Jesús Casado-Pascual, Denis Lacroix

We introduce a reinforcement learning algorithm designed to identify the fixed points of a given quantum operation. The method iteratively constructs the unitary transformation that maps the computational basis onto the basis of fixed points through a reward-penalty scheme based on quantum measurements. In cases where the operation corresponds to a Hamiltonian evolution, this task reduces to determining the Hamiltonian eigenstates. The algorithm is first benchmarked on random Hamiltonians acting on two and three qubits and then applied to many-body systems of up to six qubits, including the transverse-field Ising model and the all-to-all pairing Hamiltonian. In both cases, the algorithm is demonstrated to perform successfully; in the pairing model, it can also reveal hidden symmetries, which can be exploited to restrict learning to specific symmetry sectors. Finally, we discuss the possibility of post-selecting high-fidelity states even when full convergence has not been reached.