463 research outputs found
Dynamical phase transitions after quenches in non-integrable models
We investigate the dynamics following sudden quenches across quantum critical
points belonging to different universality classes. Specifically, we use matrix
product state methods to study the quantum Ising chain in the presence of two
additional terms which break integrability. We find that in all models the rate
function for the return probability to the initial state becomes a non-analytic
function of time in the thermodynamic limit. This so-called `dynamical phase
transition' was first observed in a recent work by Heyl, Polkovnikov, and
Kehrein [Phys. Rev. Lett. 110, 135704 (2013)] for the exactly-solvable quantum
Ising chain, which can be mapped to free fermions. Our results for `interacting
theories' indicate that non-analytic dynamics is a generic feature of sudden
quenches across quantum critical points. We discuss potential connections to
the dynamics of the order parameter
Luttinger liquid physics from infinite-system DMRG
We study one-dimensional spinless fermions at zero and finite temperature T
using the density matrix renormalization group. We consider nearest as well as
next-nearest neighbor interactions; the latter render the system inaccessible
by a Bethe ansatz treatment. Using an infinite-system alogrithm we demonstrate
the emergence of Luttinger liquid physics at low energies for a variety of
static correlation functions as well as for thermodynamic properties. The
characteristic power law suppression of the momentum distribution n(k) function
at T=0 can be directly observed over several orders of magnitude. At finite
temperature, we show that n(k) obeys a scaling relation. The Luttinger liquid
parameter and the renormalized Fermi velocity can be extracted from the density
response function, the specific heat, and/or the susceptibility without the
need to carry out any finite-size analysis. We illustrate that the energy scale
below which Luttinger liquid power laws manifest vanishes as the half-filled
system is driven into a gapped phase by large interactions
Entanglement scaling of excited states in large one-dimensional many-body localized systems
We study the properties of excited states in one-dimensional many-body
localized (MBL) systems using a matrix product state algorithm. First, the
method is tested for a large disordered non-interacting system, where for
comparison we compute a quasi-exact reference solution via a Monte Carlo
sampling of the single-particle levels. Thereafter, we present extensive data
obtained for large interacting systems of L~100 sites and large bond dimensions
chi~1700, which allows us to quantitatively analyze the scaling behavior of the
entanglement S in the system. The MBL phase is characterized by a logarithmic
growth (L)~log(L) over a large scale separating the regimes where volume and
area laws hold. We check the validity of the eigenstate thermalization
hypothesis. Our results are consistent with the existence of a mobility edge
Approaching Many-Body Localization from Disordered Luttinger Liquids via the Functional Renormalization Group
We study the interplay of interactions and disorder in a one-dimensional
fermion lattice coupled adiabatically to infinite reservoirs. We employ both
the functional renormalization group (FRG) as well as matrix product state
techniques, which serve as an accurate benchmark for small systems. Using the
FRG, we compute the length- and temperature-dependence of the conductance
averaged over samples for lattices as large as sites. We
identify regimes in which non-ohmic power law behavior can be observed and
demonstrate that the corresponding exponents can be understood by adapting
earlier predictions obtained perturbatively for disordered Luttinger liquids.
In presence of both disorder and isolated impurities, the conductance has a
universal single-parameter scaling form. This lays the groundwork for an
application of the functional renormalization group to the realm of many-body
localization
Loschmidt-amplitude wave function spectroscopy and the physics of dynamically driven phase transitions
We introduce the Loschmidt amplitude as a powerful tool to perform spectroscopy of generic many-body wave functions and use it to interrogate the wave function obtained after ramping the transverse field quantum Ising model through its quantum critical point. Previous results are confirmed and a more complete understanding of the population of defects and of the effects of magnon-magnon interaction or finite-size corrections is obtained. The influence of quantum coherence is clarified
Finite-temperature linear conductance from the Matsubara Green function without analytic continuation to the real axis
We illustrate how to calculate the finite-temperature linear-response
conductance of quantum impurity models from the Matsubara Green function. A
continued fraction expansion of the Fermi distribution is employed which was
recently introduced by Ozaki [Phys. Rev. B 75, 035123 (2007)] and converges
much faster than the usual Matsubara representation. We give a simplified
derivation of Ozaki's idea using concepts from many-body condensed matter
theory and present results for the rate of convergence. In case that the Green
function of some model of interest is only known numerically, interpolating
between Matsubara frequencies is much more stable than carrying out an analytic
continuation to the real axis. We demonstrate this explicitly by considering an
infinite tight-binding chain with a single site impurity as an exactly-solvable
test system, showing that it is advantageous to calculate transport properties
directly on the imaginary axis. The formalism is applied to the single impurity
Anderson model, and the linear conductance at finite temperatures is calculated
reliably at small to intermediate Coulomb interactions by virtue of the
Matsubara functional renormalization group. Thus, this quantum many-body method
combined with the continued fraction expansion of the Fermi function
constitutes a promising tool to address more complex quantum dot geometries at
finite temperatures.Comment: version accepted by Phys. Rev.
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