1,101 research outputs found
Quantum oscillations in electron doped high temperature superconductors
Quantum oscillations in hole doped high temperature superconductors are
difficult to understand within the prevailing views. An emerging idea is that
of a putative normal ground state, which appears to be a Fermi liquid with a
reconstructed Fermi surface. The oscillations are due to formation of Landau
levels. Recently the same oscillations were found in the electron doped
cuprate, , in the optimal to overdoped regime.
Although these electron doped non-stoichiometric materials are naturally more
disordered, they strikingly complement the hole doped cuprates. Here we provide
an explanation of these observations from the perspective of density waves
using a powerful transfer matrix method to compute the conductance as a
function of the magnetic field.Comment: An expanded version, accepted in Phys. Rev. B
Resolution of two apparent paradoxes concerning quantum oscillations in underdoped high- superconductors
Recent quantum oscillation experiments in underdoped high temperature
superconductors seem to imply two paradoxes. The first paradox concerns the
apparent non-existence of the signature of the electron pockets in angle
resolved photoemission spectroscopy (ARPES). The second paradox is a clear
signature of a small electron pocket in quantum oscillation experiments, but no
evidence as yet of the corresponding hole pockets of approximately double the
frequency of the electron pocket. This hole pockets should be present if the
Fermi surface reconstruction is due to a commensurate density wave, assuming
that Luttinger sum rule relating the area of the pockets and the total number
of charge carriers holds. Here we provide possible resolutions of these
apparent paradoxes from the commensurate -density wave theory. To address
the first paradox we have computed the ARPES spectral function subject to
correlated disorder, natural to a class of experiments relevant to the
materials studied in quantum oscillations. The intensity of the spectral
function is significantly reduced for the electron pockets for an intermediate
range of disorder correlation length, and typically less than half the hole
pocket is visible, mimicking Fermi arcs. Next we show from an exact transfer
matrix calculation of the Shubnikov-de Haas oscillation that the usual disorder
affects the electron pocket more significantly than the hole pocket. However,
when, in addition, the scattering from vortices in the mixed state is included,
it wipes out the frequency corresponding to the hole pocket. Thus, if we are
correct, it will be necessary to do measurements at higher magnetic fields and
even higher quality samples to recover the hole pocket frequency.Comment: Accepted version, Phys. Rev. B, brief clarifying comments and updated
reference
Dissipation and criticality in the lowest Landau level of graphene
The lowest Landau level of graphene is studied numerically by considering a
tight-binding Hamiltonian with disorder. The Hall conductance
and the longitudinal conductance are
computed. We demonstrate that bond disorder can produce a plateau-like feature
centered at , while the longitudinal conductance is nonzero in the same
region, reflecting a band of extended states between , whose
magnitude depends on the disorder strength. The critical exponent corresponding
to the localization length at the edges of this band is found to be . When both bond disorder and a finite mass term exist the localization
length exponent varies continuously between and .Comment: 4 pages, 5 figure
Quantum dynamics of an Ising spin-chain in a random transverse field
We consider an Ising spin-chain in a random transverse magnetic field and
compute the zero temperature wave vector and frequency dependent dynamic
structure factor numerically by using Jordan-Wigner transformation. Two types
of distributions of magnetic fields are introduced. For a rectangular
distribution, a dispersing branch is observed, and disorder tends to broaden
the dispersion peak and close the excitation gap. For a binary distribution, a
non-dispersing branch at almost zero energy is recovered. We discuss the
relationship of our work to the neutron scattering measurement in
.Comment: 4 pages and 6 eps figures; minor clarifications were made; the text
was shortened to add an additional figur
q-Learning in Continuous Time
We study the continuous-time counterpart of Q-learning for reinforcement
learning (RL) under the entropy-regularized, exploratory diffusion process
formulation introduced by Wang et al. (2020). As the conventional (big)
Q-function collapses in continuous time, we consider its first-order
approximation and coin the term ``(little) q-function". This function is
related to the instantaneous advantage rate function as well as the
Hamiltonian. We develop a ``q-learning" theory around the q-function that is
independent of time discretization. Given a stochastic policy, we jointly
characterize the associated q-function and value function by martingale
conditions of certain stochastic processes, in both on-policy and off-policy
settings. We then apply the theory to devise different actor-critic algorithms
for solving underlying RL problems, depending on whether or not the density
function of the Gibbs measure generated from the q-function can be computed
explicitly. One of our algorithms interprets the well-known Q-learning
algorithm SARSA, and another recovers a policy gradient (PG) based
continuous-time algorithm proposed in Jia and Zhou (2022b). Finally, we conduct
simulation experiments to compare the performance of our algorithms with those
of PG-based algorithms in Jia and Zhou (2022b) and time-discretized
conventional Q-learning algorithms.Comment: 64 pages, 4 figure
Policy Gradient and Actor-Critic Learning in Continuous Time and Space: Theory and Algorithms
We study policy gradient (PG) for reinforcement learning in continuous time
and space under the regularized exploratory formulation developed by Wang et
al. (2020). We represent the gradient of the value function with respect to a
given parameterized stochastic policy as the expected integration of an
auxiliary running reward function that can be evaluated using samples and the
current value function. This effectively turns PG into a policy evaluation (PE)
problem, enabling us to apply the martingale approach recently developed by Jia
and Zhou (2021) for PE to solve our PG problem. Based on this analysis, we
propose two types of the actor-critic algorithms for RL, where we learn and
update value functions and policies simultaneously and alternatingly. The first
type is based directly on the aforementioned representation which involves
future trajectories and hence is offline. The second type, designed for online
learning, employs the first-order condition of the policy gradient and turns it
into martingale orthogonality conditions. These conditions are then
incorporated using stochastic approximation when updating policies. Finally, we
demonstrate the algorithms by simulations in two concrete examples.Comment: 52 pages, 1 figur
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