1,464 research outputs found
Discretized Thermal Green's Functions
We present a spectral weight conserving formalism for Fermionic thermal
Green's functions that are discretized in imaginary time and thus periodic in
imaginary ("Matsubara") frequency. The formalism requires a generalization of
the Dyson equation and the Baym-Kadanoff-Luttinger-Ward functional for the free
energy. A conformal transformation is used to analytically continue the
periodized Matsubara Green's function to the continuous real axis in a way that
conserves the discontinuity at t=0 of the corresponding real-time Green's
function. For given discretization the method allows numerical Green's function
calculations of very high precision and it appears to give a well controlled
convergent approximation as we decrease the discretization interval. The ideas
are tested on Dynamical Mean Field Theory calculations of the paramagnetic
Hubbard model
Do Finite-Size Lyapunov Exponents Detect Coherent Structures?
Ridges of the Finite-Size Lyapunov Exponent (FSLE) field have been used as
indicators of hyperbolic Lagrangian Coherent Structures (LCSs). A rigorous
mathematical link between the FSLE and LCSs, however, has been missing. Here we
prove that an FSLE ridge satisfying certain conditions does signal a nearby
ridge of some Finite-Time Lyapunov Exponent (FTLE) field, which in turn
indicates a hyperbolic LCS under further conditions. Other FSLE ridges
violating our conditions, however, are seen to be false positives for LCSs. We
also find further limitations of the FSLE in Lagrangian coherence detection,
including ill-posedness, artificial jump-discontinuities, and sensitivity with
respect to the computational time step.Comment: 22 pages, 7 figures, v3: corrects the z-axis labels of Fig. 2 (left)
that appears in the version published in Chao
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
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
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
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
- …