22 research outputs found
Discriminative Cooperative Networks for Detecting Phase Transitions
The classification of states of matter and their corresponding phase
transitions is a special kind of machine-learning task, where physical data
allow for the analysis of new algorithms, which have not been considered in the
general computer-science setting so far. Here we introduce an unsupervised
machine-learning scheme for detecting phase transitions with a pair of
discriminative cooperative networks (DCN). In this scheme, a guesser network
and a learner network cooperate to detect phase transitions from fully
unlabeled data. The new scheme is efficient enough for dealing with phase
diagrams in two-dimensional parameter spaces, where we can utilize an active
contour model -- the snake -- from computer vision to host the two networks.
The snake, with a DCN "brain", moves and learns actively in the parameter
space, and locates phase boundaries automatically
Renormalization group approach to symmetry protected topological phases
A defining feature of a symmetry protected topological phase (SPT) in
one-dimension is the degeneracy of the Schmidt values for any given
bipartition. For the system to go through a topological phase transition
separating two SPTs, the Schmidt values must either split or cross at the
critical point in order to change their degeneracies. A renormalization group
(RG) approach based on this splitting or crossing is proposed, through which we
obtain an RG flow that identifies the topological phase transitions in the
parameter space. Our approach can be implemented numerically in an efficient
manner, for example, using the matrix product state formalism, since only the
largest first few Schmidt values need to be calculated with sufficient
accuracy. Using several concrete models, we demonstrate that the critical
points and fixed points of the RG flow coincide with the maxima and minima of
the entanglement entropy, respectively, and the method can serve as a
numerically efficient tool to analyze interacting SPTs in the parameter space.Comment: 5 pages, 3 figure
Single spin probe of Many-Body Localization
We use an external spin as a dynamical probe of many body localization. The
probe spin is coupled to an interacting and disordered environment described by
a Heisenberg spin chain in a random field. The spin-chain environment can be
tuned between a thermalizing delocalized phase and non-thermalizing localized
phase, both in its ground- and high-energy states. We study the decoherence of
the probe spin when it couples to the environment prepared in three states: the
ground state, the infinite temperature state and a high energy N\'eel state. In
the non-thermalizing many body localized regime, the coherence shows scaling
behaviour in the disorder strength. The long-time dynamics of the probe spin
shows a logarithmic dephasing in analogy with the logarithmic growth of
entanglement entropy for a bi-partition of a many-body localized system. In
summary, we show that decoherence of the probe spin provides clear signatures
of many-body localization.Comment: 5 pages, 4 figure
From Dynamical Localization to Bunching in interacting Floquet Systems
We show that a quantum many-body system may be controlled by means of Floquet
engineering, i.e., their properties may be controlled and manipulated by
employing periodic driving. We present a concrete driving scheme that allows
control over the nature of mobile units and the amount of diffusion in generic
many-body systems. We demonstrate these ideas for the Fermi-Hubbard model,
where the drive renders doubly occupied sites (doublons) the mobile excitations
in the system. In particular, we show that the amount of diffusion in the
system and the level of fermion-pairing may be controlled and understood solely
in terms of the doublon dynamics. We find that under certain circumstances the
diffusion in the system may be eliminated completely. We conclude our work by
generalizing these ideas to generic many-body systems.Comment: 10 pages, 5 figure