Real-space renormalization group for gases of topological excitations

David A. Lavis

Gerardo Aldazabal, Néstor Parga

The authors' present a real space renormalisation group technique able to deal explicitly with gases of topological excitations. As examples they consider the two-dimensional XY model and the three-dimensional compact electrodynamics.

Gilad Margalit, Omri Lesser, T. Pereg-Barnea +1 more

We show that artificial neural networks (ANNs) can, to high accuracy, determine the topological invariant of a disordered system given its two-dimensional real-space Hamiltonian. Furthermore, we describe a ``renormalization-group'' (RG) network, an ANN which converts a Hamiltonian on a large lattice to another on a small lattice while preserving the invariant. By iteratively applying the RG network to a ``base'' network that computes the Chern number of a small lattice of set size, we are able to process larger lattices without retraining the system. We therefore show that it is possible to compute real-space topological invariants for systems larger than those on which the network was trained. This opens the door for computation times significantly faster and more scalable than previous methods.

David A. Lavis, G. M. Bell

M. A. Contínentino

Yi‐Zhuang You, Xiao-Liang Qi, Cenke Xu

We introduce the spectrum bifurcation renormalization group (SBRG) as an improved application of the excited-state real-space renormalization group (RSRG-X) for a class of qubit models. Starting from a disordered many-body Hamiltonian in the full many-body localized (MBL) phase, SBRG flows to the MBL fixed-point Hamiltonian, and generates the local integrals of motion and the matrix product state representations for all eigenstates. The method is applicable to many interacting spin and fermion models in the full MBL phase. As a Hilbert-space preserving RG, SBRG also generates an entanglement holographic mapping, which duals the MBL state to a fragmented holographic space.