46,240 research outputs found
Efficient representation of fully many-body localized systems using tensor networks
We propose a tensor network encoding the set of all eigenstates of a fully
many-body localized system in one dimension. Our construction, conceptually
based on the ansatz introduced in Phys. Rev. B 94, 041116(R) (2016), is built
from two layers of unitary matrices which act on blocks of contiguous
sites.
We argue this yields an exponential reduction in computational time and
memory requirement as compared to all previous approaches for finding a
representation of the complete eigenspectrum of large many-body localized
systems with a given accuracy. Concretely, we optimize the unitaries by
minimizing the magnitude of the commutator of the approximate integrals of
motion and the Hamiltonian, which can be done in a local fashion. This further
reduces the computational complexity of the tensor networks arising in the
minimization process compared to previous work. We test the accuracy of our
method by comparing the approximate energy spectrum to exact diagonalization
results for the random field Heisenberg model on 16 sites. We find that the
technique is highly accurate deep in the localized regime and maintains a
surprising degree of accuracy in predicting certain local quantities even in
the vicinity of the predicted dynamical phase transition. To demonstrate the
power of our technique, we study a system of 72 sites and we are able to see
clear signatures of the phase transition. Our work opens a new avenue to study
properties of the many-body localization transition in large systems.Comment: Version 2, 16 pages, 16 figures. Larger systems and greater
efficienc
Designing colloidal ground state patterns using short-range isotropic interactions
DNA-coated colloids are a popular model system for self-assembly through
tunable interactions. The DNA-encoded linkages between particles theoretically
allow for very high specificity, but generally no directionality or long-range
interactions. We introduce a two-dimensional lattice model for particles of
many different types with short-range isotropic interactions that are pairwise
specific. For this class of models, we address the fundamental question whether
it is possible to reliably design the interactions so that the ground state is
unique and corresponds to a given crystal structure. First, we determine lower
limits for the interaction range between particles, depending on the complexity
of the desired pattern and the underlying lattice. Then, we introduce a
`recipe' for determining the pairwise interactions that exactly satisfies this
minimum criterion, and we show that it is sufficient to uniquely determine the
ground state for a large class of crystal structures. Finally, we verify these
results using Monte Carlo simulations.Comment: 19 pages, 7 figure
Pauli-Fierz model with Kato-class potentials and exponential decays
Generalized Pauli-Fierz Hamiltonian with Kato-class potential \KPF in
nonrelativistic quantum electrodynamics is defined and studied by a path
measure. \KPF is defined as the self-adjoint generator of a strongly
continuous one-parameter symmetric semigroup and it is shown that its bound
states spatially exponentially decay pointwise and the ground state is unique.Comment: We deleted Lemma 3.1 in vol.
S3 Quantum Hall Wavefunctions
We construct a family of quantum Hall Hamiltonians whose ground states, at
least for small system sizes, give correlators of the S3 conformal field
theories. The ground states are considered as trial wavefunctions for quantum
Hall effect of bosons at filling fraction nu=3/4 interacting either via delta
function interaction or delta function plus dipole interaction. While the S3
theories can be either unitary or nonunitary, we find high overlaps with exact
diagonalizations only for the nonunitary case, suggesting that these
wavefunctions may correspond to critical points, possibly analogous to the
previously studied Gaffnian wavefunction. These wavefunctions give an explicit
example which cannot be fully characterized by their thin-torus limit or by
their pattern of zeros.Comment: 4+epsilon pages. 1 figure. Revised version includes: 1 additional
author; additional numerical work; several minor corrections. Our main
results are unchange
Singular Continuous Spectrum for the Laplacian on Certain Sparse Trees
We present examples of rooted tree graphs for which the Laplacian has
singular continuous spectral measures. For some of these examples we further
establish fractional Hausdorff dimensions. The singular continuous components,
in these models, have an interesting multiplicity structure. The results are
obtained via a decomposition of the Laplacian into a direct sum of Jacobi
matrices
Witten index, axial anomaly, and Krein's spectral shift function in supersymmetric quantum mechanics
A new method is presented to study supersymmetric quantum mechanics. Using relative scattering techniques, basic relations are derived between Kreinâs spectral shift function, the Witten index, and the anomaly. The topological invariance of the spectral shift function is discussed. The power of this method is illustrated by treating various models and calculating explicitly the spectral shift function, the Witten index, and the anomaly. In particular, a complete treatment of the twoâdimensional magnetic field problem is given, without assuming that the magnetic flux is quantized
Bulk-edge coupling in the non-abelian quantum Hall interferometer
Recent schemes for experimentally probing non-abelian statistics in the
quantum Hall effect are based on geometries where current-carrying
quasiparticles flow along edges that encircle bulk quasiparticles, which are
localized. Here we consider one such scheme, the Fabry-Perot interferometer,
and analyze how its interference patterns are affected by a coupling that
allows tunneling of neutral Majorana fermions between the bulk and edge. While
at weak coupling this tunneling degrades the interference signal, we find that
at strong coupling, the bulk quasiparticle becomes essentially absorbed by the
edge and the intereference signal is fully restored.Comment: 5 pages, 1 figur
Microtubule length distributions in the presence of protein-induced severing
Microtubules are highly regulated dynamic elements of the cytoskeleton of
eukaryotic cells. One of the regulation mechanisms observed in living cells is
the severing by the proteins katanin and spastin. We introduce a model for the
dynamics of microtubules in the presence of randomly occurring severing events.
Under the biologically motivated assumption that the newly created plus end
undergoes a catastrophe, we investigate the steady state length distribution.
We show that the presence of severing does not affect the number of
microtubules, regardless of the distribution of severing events. In the special
case in which the microtubules cannot recover from the depolymerizing state (no
rescue events) we derive an analytical expression for the length distribution.
In the general case we transform the problem into a single ODE that is solved
numerically.Comment: 9 pages, 4 figure
Singular components of spectral measures for ergodic Jacobi matrices
For ergodic 1d Jacobi operators we prove that the random singular components
of any spectral measure are almost surely mutually disjoint as long as one
restricts to the set of positive Lyapunov exponent. In the context of extended
Harper's equation this yields the first rigorous proof of the Thouless' formula
for the Lyapunov exponent in the dual regions.Comment: to appear in the Journal of Mathematical Physics, vol 52 (2011
- âŠ