206 research outputs found
Tunable Quantum Chaos in the Sachdev-Ye-Kitaev Model Coupled to a Thermal Bath
The Sachdev-Ye-Kitaev (SYK) model describes Majorana fermions with random
interaction, which displays many interesting properties such as non-Fermi
liquid behavior, quantum chaos, emergent conformal symmetry and holographic
duality. Here we consider a SYK model or a chain of SYK models with
Majorana fermion modes coupled to another SYK model with Majorana fermion
modes, in which the latter has many more degrees of freedom and plays the role
as a thermal bath. For a single SYK model coupled to the thermal bath, we show
that although the Lyapunov exponent is still proportional to temperature, it
monotonically decreases from (, is
temperature) to zero as the coupling strength to the thermal bath increases.
For a chain of SYK models, when they are uniformly coupled to the thermal bath,
we show that the butterfly velocity displays a crossover from a
-dependence at relatively high temperature to a linear -dependence
at low temperature, with the crossover temperature also controlled by the
coupling strength to the thermal bath. If only the end of the SYK chain is
coupled to the thermal bath, the model can introduce a spatial dependence of
both the Lyapunov exponent and the butterfly velocity. Our models provide
canonical examples for the study of thermalization within chaotic models.Comment: 28 pages, 9 figures. References adde
Machine Learning Topological Invariants with Neural Networks
In this Letter we supervisedly train neural networks to distinguish different
topological phases in the context of topological band insulators. After
training with Hamiltonians of one-dimensional insulators with chiral symmetry,
the neural network can predict their topological winding numbers with nearly
100% accuracy, even for Hamiltonians with larger winding numbers that are not
included in the training data. These results show a remarkable success that the
neural network can capture the global and nonlinear topological features of
quantum phases from local inputs. By opening up the neural network, we confirm
that the network does learn the discrete version of the winding number formula.
We also make a couple of remarks regarding the role of the symmetry and the
opposite effect of regularization techniques when applying machine learning to
physical systems.Comment: 6 pages, 4 figures and 1 table + 2 pages of supplemental materia
Out-of-Time-Order Correlation at a Quantum Phase Transition
In this paper we numerically calculate the out-of-time-order correlation
functions in the one-dimensional Bose-Hubbard model. Our study is motivated by
the conjecture that a system with Lyapunov exponent saturating the upper bound
will have a holographic dual to a black hole at finite
temperature. We further conjecture that for a many-body quantum system with a
quantum phase transition, the Lyapunov exponent will have a peak in the quantum
critical region where there exists an emergent conformal symmetry and is absent
of well-defined quasi-particles. With the help of a relation between the
R\'enyi entropy and the out-of-time-order correlation function, we argue that
the out-of-time-order correlation function of the Bose-Hubbard model will also
exhibit an exponential behavior at the scrambling time. By fitting the
numerical results with an exponential function, we extract the Lyapunov
exponents in the one-dimensional Bose-Hubbard model across the quantum critical
regime at finite temperature. Our results on the Bose-Hubbard model support the
conjecture. We also compute the butterfly velocity and propose how the echo
type measurement of this correlator in the cold atom realizations of the
Bose-Hubbard model without inverting the Hamiltonian.Comment: 7 pages, 6 figures, published versio
Out-of-Time-Order Correlation for Many-Body Localization
In this paper we first compute the out-of-time-order correlators (OTOC) for
both a phenomenological model and a random-field XXZ model in the many-body
localized phase. We show that the OTOC decreases in power law in a many-body
localized system at the scrambling time. We also find that the OTOC can also be
used to distinguish a many-body localized phase from an Anderson localized
phase, while a normal correlator cannot. Furthermore, we prove an exact theorem
that relates the growth of the second R\'enyi entropy in the quench dynamics to
the decay of the OTOC in equilibrium. This theorem works for a generic quantum
system. We discuss various implications of this theorem.Comment: 6 pages, 3 figures, published versio
Information Scrambling in Quantum Neural Networks
The quantum neural network is one of the promising applications for near-term noisy intermediate-scale quantum computers. A quantum neural network distills the information from the input wave function into the output qubits. In this Letter, we show that this process can also be viewed from the opposite direction: the quantum information in the output qubits is scrambled into the input. This observation motivates us to use the tripartite information—a quantity recently developed to characterize information scrambling—to diagnose the training dynamics of quantum neural networks. We empirically find strong correlation between the dynamical behavior of the tripartite information and the loss function in the training process, from which we identify that the training process has two stages for randomly initialized networks. In the early stage, the network performance improves rapidly and the tripartite information increases linearly with a universal slope, meaning that the neural network becomes less scrambled than the random unitary. In the latter stage, the network performance improves slowly while the tripartite information decreases. We present evidences that the network constructs local correlations in the early stage and learns large-scale structures in the latter stage. We believe this two-stage training dynamics is universal and is applicable to a wide range of problems. Our work builds bridges between two research subjects of quantum neural networks and information scrambling, which opens up a new perspective to understand quantum neural networks
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