352 research outputs found
Error estimates for extrapolations with matrix-product states
We introduce a new error measure for matrix-product states without requiring
the relatively costly two-site density matrix renormalization group (2DMRG).
This error measure is based on an approximation of the full variance . When applied to a series of
matrix-product states at different bond dimensions obtained from a single-site
density matrix renormalization group (1DMRG) calculation, it allows for the
extrapolation of observables towards the zero-error case representing the exact
ground state of the system. The calculation of the error measure is split into
a sequential part of cost equivalent to two calculations of and a trivially parallelized part scaling like a single
operator application in 2DMRG. The reliability of the new error measure is
demonstrated at four examples: the Heisenberg chain, the
Hubbard chain, an electronic model with long-range Coulomb-like
interactions and the Hubbard model on a cylinder of size .
Extrapolation in the new error measure is shown to be on-par with extrapolation
in the 2DMRG truncation error or the full variance at a fraction of the computational effort.Comment: 10 pages, 11 figure
Interaction quench and thermalization in a one-dimensional topological Kondo insulator
We study the nonequilibrium dynamics of a one-dimensional topological Kondo
insulator, modelled by a -wave Anderson lattice model, following a quantum
quench of the on-site interaction strength. Our goal is to examine how the
quench influences the topological properties of the system, therefore our main
focus is the time evolution of the string order parameter, entanglement
spectrum and the topologically-protected edge states. We point out that
postquench local observables can be well captured by a thermal ensemble up to a
certain interaction strength. Our results demonstrate that the topological
properties after the interaction quench are preserved. Though the absolute
value of the string order parameter decays in time, the analysis of the
entanglement spectrum, Loschmidt echo and the edge states indicates the
robustness of the topological properties in the time-evolved state. These
predictions could be directly tested in state-of-the-art cold-atom experiments.Comment: 8.5 pages, 11 figure
Generic Construction of Efficient Matrix Product Operators
Matrix Product Operators (MPOs) are at the heart of the second-generation
Density Matrix Renormalisation Group (DMRG) algorithm formulated in Matrix
Product State language. We first summarise the widely known facts on MPO
arithmetic and representations of single-site operators. Second, we introduce
three compression methods (Rescaled SVD, Deparallelisation and Delinearisation)
for MPOs and show that it is possible to construct efficient representations of
arbitrary operators using MPO arithmetic and compression. As examples, we
construct powers of a short-ranged spin-chain Hamiltonian, a complicated
Hamiltonian of a two-dimensional system and, as proof of principle, the
long-range four-body Hamiltonian from quantum chemistry.Comment: 13 pages, 10 figure
Spin-charge separation in cold Fermi-gases: a real time analysis
Using the adaptive time-dependent density-matrix renormalization group method
for the 1D Hubbard model, the splitting of local perturbations into separate
wave packets carrying charge and spin is observed in real-time. We show the
robustness of this separation beyond the low-energy Luttinger liquid theory by
studying the time-evolution of single particle excitations and density wave
packets. A striking signature of spin-charge separation is found in 1D cold
Fermi gases in a harmonic trap at the boundary between liquid and
Mott-insulating phases. We give quantitative estimates for an experimental
observation of spin-charge separation in an array of atomic wires
Dynamical topological quantum phase transitions in nonintegrable models
We consider sudden quenches across quantum phase transitions in the XXZ
model starting from the Haldane phase. We demonstrate that dynamical phase
transitions may occur during these quenches that are identified by
nonanalyticities in the rate function for the return probability. In addition,
we show that the temporal behavior of the string order parameter is intimately
related to the subsequent dynamical phase transitions. We furthermore find that
the dynamical quantum phase transitions can be accompanied by enhanced two-site
entanglement.Comment: 5+1 pages, 4+1 figure
Entanglement scaling in critical two-dimensional fermionic and bosonic systems
We relate the reduced density matrices of quadratic bosonic and fermionic
models to their Green's function matrices in a unified way and calculate the
scaling of bipartite entanglement of finite systems in an infinite universe
exactly. For critical fermionic 2D systems at T=0, two regimes of scaling are
identified: generically, we find a logarithmic correction to the area law with
a prefactor dependence on the chemical potential that confirms earlier
predictions based on the Widom conjecture. If, however, the Fermi surface of
the critical system is zero-dimensional, we find an area law with a
sublogarithmic correction. For a critical bosonic 2D array of coupled
oscillators at T=0, our results show that entanglement follows the area law
without corrections.Comment: 4 pages, 4 figure
Haldane Gap and Hidden Order in the S=2 Antiferromagnetic Quantum Spin Chain
We have investigated Haldane's conjecture for the S=2 isotropic
antiferromagnetic quantum spin chain with nearest-neighbor exchange J. Using a
density matrix renormalization group algorithm for chains up to L=350 spins, we
find in the thermodynamic limit a finite spin gap of Delta = 0.085(5)J and a
finite spin-spin correlation length xi = 49(1) lattice spacings. We establish
the ground state energy per bond to be E_0=-4.761248(1)J. We show that the
ground state has a hidden topological order that is revealed in a nonlocal
string correlation function. This means that the physics of the S=2 chain can
be captured by a valence-bond solid description. We also observe effective free
spin-1 states at the ends of an open S=2 chain.Comment: 6 pages, LaTeX 2.09, 3 PostScript figure
Comprehensive quantum Monte Carlo study of the quantum critical points in planar dimerized/quadrumerized Heisenberg models
We study two planar square lattice Heisenberg models with explicit
dimerization or quadrumerization of the couplings in the form of ladder and
plaquette arrangements. We investigate the quantum critical points of those
models by means of (stochastic series expansion) quantum Monte Carlo
simulations as a function of the coupling ratio . The
critical point of the order-disorder quantum phase transition in the ladder
model is determined as improving on previous
studies. For the plaquette model we obtain
establishing a first benchmark for this model from quantum Monte Carlo
simulations. Based on those values we give further convincing evidence that the
models are in the three-dimensional (3D) classical Heisenberg universality
class. The results of this contribution shall be useful as references for
future investigations on planar Heisenberg models such as concerning the
influence of non-magnetic impurities at the quantum critical point.Comment: 10+ pages, 7 figures, 4 table
The Haldane gap for the S=2 antiferromagnetic Heisenberg chain revisited
Using the density matrix renormalization group (DMRG) technique, we carry out
a large scale numerical calculation for the S=2 antiferromagnetic Heisenberg
chain. Performing systematic scaling analysis for both the chain length and
the number of optimal states kept in the iterations , the Haldane gap
is estimated accurately as . Our systematic
analysis for the S=2 chains not only ends the controversies arising from
various DMRG calculations and Monte Carlo simulations, but also sheds light on
how to obtain reliable results from the DMRG calculations for other complicated
systems.Comment: 4 pages and 1 figur
Spatial correlations of trapped 1d bosons in an optical lattice
We investigate a quasi-one dimensional system of trapped cold bosonic atoms
in an optical lattice by using the density matrix renormalization group to
study the Bose-Hubbard model at T=0 for experimentally realistic numbers of
lattice sites. It is shown that a properly rescaled one-particle density matrix
characterizes superfluid versus insulating states just as in the homogeneous
system. For typical parabolic traps we also confirm the widely used local
density approach for describing correlations in the limit of weak interaction.
Finally, we note that the superfluid to Mott-insulating transition is seen most
directly in the half width of the interference peak
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