264 research outputs found
Probing many-body localization with neural networks
We show that a simple artificial neural network trained on entanglement
spectra of individual states of a many-body quantum system can be used to
determine the transition between a many-body localized and a thermalizing
regime. Specifically, we study the Heisenberg spin-1/2 chain in a random
external field. We employ a multilayer perceptron with a single hidden layer,
which is trained on labeled entanglement spectra pertaining to the fully
localized and fully thermal regimes. We then apply this network to classify
spectra belonging to states in the transition region. For training, we use a
cost function that contains, in addition to the usual error and regularization
parts, a term that favors a confident classification of the transition region
states. The resulting phase diagram is in good agreement with the one obtained
by more conventional methods and can be computed for small systems. In
particular, the neural network outperforms conventional methods in classifying
individual eigenstates pertaining to a single disorder realization. It allows
us to map out the structure of these eigenstates across the transition with
spatial resolution. Furthermore, we analyze the network operation using the
dreaming technique to show that the neural network correctly learns by itself
the power-law structure of the entanglement spectra in the many-body localized
regime.Comment: 12 pages, 10 figure
M\"obius molecules and fragile Mott insulators
Motivated by the concept of M\"obius aromatics in organic chemistry, we
extend the recently introduced concept of fragile Mott insulators (FMI) to
ring-shaped molecules with repulsive Hubbard interactions threaded by a
half-quantum of magnetic flux (). In this context, a FMI is the
insulating ground state of a finite-size molecule that cannot be adiabatically
connected to a single Slater determinant, i.e., to a band insulator, provided
that time-reversal and lattice translation symmetries are preserved. Based on
exact numerical diagonalization for finite Hubbard interaction strength and
existing Bethe-ansatz studies of the one-dimensional Hubbard model in the
large- limit, we establish a duality between Hubbard molecules with and
sites, with integer. A molecule with sites is an FMI in the
absence of flux but becomes a band insulator in the presence of a half-quantum
of flux, while a molecule with sites is a band insulator in the absence
of flux but becomes an FMI in the presence of a half-quantum of flux. Including
next-nearest-neighbor-hoppings gives rise to new FMI states that belong to
multidimensional irreducible representations of the molecular point group,
giving rise to a rich phase diagram
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