554 research outputs found
Exact results for fidelity susceptibility of the quantum Ising model: The interplay between parity, system size, and magnetic field
We derive an exact closed-form expression for fidelity susceptibility of
even- and odd-sized quantum Ising chains in the transverse field. To this aim,
we diagonalize the Ising Hamiltonian and study the gap between its positive and
negative parity subspaces. We derive an exact closed-form expression for the
gap and use it to identify the parity of the ground state. We point out
misunderstanding in some of the former studies of fidelity susceptibility and
discuss its consequences. Last but not least, we rigorously analyze the
properties of the gap. For example, we derive analytical expressions showing
its exponential dependence on the ratio between the system size and the
correlation length.Comment: 11 pages, updated references, version accepted in JP
Breaking the entanglement barrier: Tensor network simulation of quantum transport
The recognition that large classes of quantum many-body systems have limited
entanglement in the ground and low-lying excited states led to dramatic
advances in their numerical simulation via so-called tensor networks. However,
global dynamics elevates many particles into excited states, and can lead to
macroscopic entanglement and the failure of tensor networks. Here, we show that
for quantum transport -- one of the most important cases of this failure -- the
fundamental issue is the canonical basis in which the scenario is cast: When
particles flow through an interface, they scatter, generating a "bit" of
entanglement between spatial regions with each event. The frequency basis
naturally captures that -- in the long-time limit and in the absence of
inelastic scattering -- particles tend to flow from a state with one frequency
to a state of identical frequency. Recognizing this natural structure yields a
striking -- potentially exponential in some cases -- increase in simulation
efficiency, greatly extending the attainable spatial- and time-scales, and
broadening the scope of tensor network simulation to hitherto inaccessible
classes of non-equilibrium many-body problems.Comment: Published version; 6+9 pages; 4+4 figures; Added: an example of
interacting reservoirs, further evidence on performance scaling, and extended
discussion of the numerical detail
Multi-scale Entanglement Renormalization Ansatz in Two Dimensions: Quantum Ising Model
We propose a symmetric version of the multi-scale entanglement
renormalization Ansatz (MERA) in two spatial dimensions (2D) and use this
Ansatz to find an unknown ground state of a 2D quantum system. Results in the
simple 2D quantum Ising model on the square lattice are found to be
very accurate even with the smallest non-trivial truncation parameter.Comment: version to appear in Phys. Rev. Letter
Nonhyperbolic step skew-products: Ergodic approximation
We study transitive step skew-product maps modeled over a complete shift of
, , symbols whose fiber maps are defined on the circle and have
intermingled contracting and expanding regions. These dynamics are genuinely
nonhyperbolic and exhibit simultaneously ergodic measures with positive,
negative, and zero exponents.
We introduce a set of axioms for the fiber maps and study the dynamics of the
resulting skew-product. These axioms turn out to capture the key mechanisms of
the dynamics of nonhyperbolic robustly transitive maps with compact central
leaves.
Focusing on the nonhyperbolic ergodic measures (with zero fiber exponent) of
these systems, we prove that such measures are approximated in the weak
topology and in entropy by hyperbolic ones. We also prove that they are in the
intersection of the convex hulls of the measures with positive fiber exponent
and with negative fiber exponent. Our methods also allow us to perturb
hyperbolic measures. We can perturb a measure with negative exponent directly
to a measure with positive exponent (and vice-versa), however we lose some
amount of entropy in this process. The loss of entropy is determined by the
difference between the Lyapunov exponents of the measures.Comment: 43 pages, 5 figure
Visible parts of fractal percolation
We study dimensional properties of visible parts of fractal percolation in
the plane. Provided that the dimension of the fractal percolation is at least
1, we show that, conditioned on non-extinction, almost surely all visible parts
from lines are 1-dimensional. Furthermore, almost all of them have positive and
finite Hausdorff measure. We also verify analogous results for visible parts
from points. These results are motivated by an open problem on the dimensions
of visible parts.Comment: 22 pages, 3 figure
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