1,459 research outputs found
Classical correlations of defects in lattices with geometrical frustration in the motion of a particle
We map certain highly correlated electron systems on lattices with
geometrical frustration in the motion of added particles or holes to the
spatial defect-defect correlations of dimer models in different geometries.
These models are studied analytically and numerically. We consider different
coverings for four different lattices: square, honeycomb, triangular, and
diamond. In the case of hard-core dimer covering, we verify the existed results
for the square and triangular lattice and obtain new ones for the honeycomb and
the diamond lattices while in the case of loop covering we obtain new numerical
results for all the lattices and use the existing analytical Liouville field
theory for the case of square lattice.The results show power-law correlations
for the square and honeycomb lattice, while exponential decay with distance is
found for the triangular and exponential decay with the inverse distance on the
diamond lattice. We relate this fact with the lack of bipartiteness of the
triangular lattice and in the latter case with the three-dimensionality of the
diamond. The connection of our findings to the problem of fractionalized charge
in such lattices is pointed out.Comment: 6 pages, 6 figures, 1 tabl
Entanglement scaling and spatial correlations of the transverse field Ising model with perturbations
We study numerically the entanglement entropy and spatial correlations of the
one dimensional transverse field Ising model with three different
perturbations. First, we focus on the out of equilibrium, steady state with an
energy current passing through the system. By employing a variety of
matrix-product state based methods, we confirm the phase diagram and compute
the entanglement entropy. Second, we consider a small perturbation that takes
the system away from integrability and calculate the correlations, the central
charge and the entanglement entropy. Third, we consider periodically weakened
bonds, exploring the phase diagram and entanglement properties first in the
situation when the weak and strong bonds alternate (period two-bonds) and then
the general situation of a period of n bonds. In the latter case we find a
critical weak bond that scales with the transverse field as =
, where is the strength of the strong bond, of the weak bond
and the transverse field. We explicitly show that the energy current is not
a conserved quantity in this case.Comment: 9 pages, 12 figures, version accepted in PR
Correlated Fermions on a Checkerboard Lattice
A model of strongly correlated spinless fermions hopping on a checkerboard
lattice is mapped onto a quantum fully-packed loop model. We identify a large
number of fluctuationless states specific to the fermionic case. We also show
that for a class of fluctuating states, the fermionic sign problem can be
gauged away. This claim is supported by numerically evaluating the energies of
the low-lying states. Furthermore, we analyze in detail the excitations at the
Rokhsar-Kivelson point of this model thereby using the relation to the height
model and the single-mode approximation.Comment: 4 Pages, 3 Figures; v4: updated version published in Phys. Rev.
Lett.; one reference adde
Characterizing time-irreversibility in disordered fermionic systems by the effect of local perturbations
We study the effects of local perturbations on the dynamics of disordered
fermionic systems in order to characterize time-irreversibility. We focus on
three different systems, the non-interacting Anderson and Aubry-Andr\'e-Harper
(AAH-) models, and the interacting spinless disordered t-V chain. First, we
consider the effect on the full many-body wave-functions by measuring the
Loschmidt echo (LE). We show that in the extended/ergodic phase the LE decays
exponentially fast with time, while in the localized phase the decay is
algebraic. We demonstrate that the exponent of the decay of the LE in the
localized phase diverges proportionally to the single-particle localization
length as we approach the metal-insulator transition in the AAH model. Second,
we probe different phases of disordered systems by studying the time
expectation value of local observables evolved with two Hamiltonians that
differ by a spatially local perturbation. Remarkably, we find that many-body
localized systems could lose memory of the initial state in the long-time
limit, in contrast to the non-interacting localized phase where some memory is
always preserved
Fermionic quantum dimer and fully-packed loop models on the square lattice
We consider fermionic fully-packed loop and quantum dimer models which serve
as effective low-energy models for strongly correlated fermions on a
checkerboard lattice at half and quarter filling, respectively. We identify a
large number of fluctuationless states specific to each case, due to the
fermionic statistics. We discuss the symmetries and conserved quantities of the
system and show that for a class of fluctuating states in the half-filling
case, the fermionic sign problem can be gauged away. This claim is supported by
numerical evaluation of the low-lying states and can be understood by means of
an algebraic construction. The elimination of the sign problem then allows us
to analyze excitations at the Rokhsar-Kivelson point of the models using the
relation to the height model and its excitations, within the single-mode
approximation. We then discuss a mapping to a U(1) lattice gauge theory which
relates the considered low-energy model to the compact quantum electrodynamics
in 2+1 dimensions. Furthermore, we point out consequences and open questions in
the light of these results.Comment: 12 pages, 9 figure
On confined fractional charges: a simple model
We address the question whether features known from quantum chromodynamics
(QCD) can possibly also show up in solid-state physics. It is shown that
spinless fermions of charge on a checkerboard lattice with nearest-neighbor
repulsion provide for a simple model of confined fractional charges. After
defining a proper vacuum the system supports excitations with charges
attached to the ends of strings. There is a constant confining force acting
between the fractional charges. It results from a reduction of vacuum
fluctuations and a polarization of the vacuum in the vicinity of the connecting
strings.Comment: 5 pages, 3 figure
Matrix product states approaches to operator spreading in ergodic quantum systems
We review different tensor network approaches to study the spreading of
operators in generic nonintegrable quantum systems. As a common ground to all
methods, we quantify this spreading by means of the Frobenius norm of the
commutator of a spreading operator with a local operator, which is usually
referred to as the out of time order correlation (OTOC) function. We compare
two approaches based on matrix-product states in the Schr\"odinger picture: the
time dependent block decimation (TEBD) and the time dependent variational
principle (TDVP), as well as TEBD based on matrix-product operators directly in
the Heisenberg picture. The results of all methods are compared to numerically
exact results using Krylov space exact time evolution. We find that for the
Schr\"odinger picture the TDVP algorithm performs better than the TEBD
algorithm. Moreover the tails of the OTOC are accurately obtained both by TDVP
MPS and TEBD MPO. They are in very good agreement with exact results at short
times, and appear to be converged in bond dimension even at longer times.
However the growth and saturation regimes are not well captured by both
methods.Comment: 11 pages, 10 figure
Inflationary dynamics for matrix eigenvalue problems
Many fields of science and engineering require finding eigenvalues and
eigenvectors of large matrices. The solutions can represent oscillatory modes
of a bridge, a violin, the disposition of electrons around an atom or molecule,
the acoustic modes of a concert hall, or hundreds of other physical quantities.
Often only the few eigenpairs with the lowest or highest frequency (extremal
solutions) are needed. Methods that have been developed over the past 60 years
to solve such problems include the Lanczos [1,2] algorithm, Jacobi-Davidson
techniques [3], and the conjugate gradient method [4]. Here we present a way to
solve the extremal eigenvalue/eigenvector problem, turning it into a nonlinear
classical mechanical system with a modified Lagrangian constraint. The
constraint induces exponential inflationary growth of the desired extremal
solutions.Comment: 6 pages, 3 figure
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