116 research outputs found
Comment on "Phase separation in a two-species Bose mixture"
In an article in 2007, Mishra, Pai, and Das [Phys. Rev. A 76, 013604 (2007)]
investigated the two-component Bose-Hubbard model using the numerical DMRG
procedure. In the regime of inter-species repulsion larger than the
intra-species repulsion , they found a transition from a uniform miscible
phase to phase-separation occurring at a finite value of , e.g., at around
for and . In
this comment, we show that this result is not correct and in fact the
two-component Bose-Hubbard model is unstable to phase-separation for any
.Comment: 2 pages, 3 figures, submitted to Phys. Rev.
Chebyshev matrix product state approach for time evolution
We present and test a new algorithm for time-evolving quantum many-body
systems initially proposed by Holzner et al. [Phys. Rev. B 83, 195115 (2011)].
The approach is based on merging the matrix product state (MPS) formalism with
the method of expanding the time-evolution operator in Chebyshev polynomials.
We calculate time-dependent observables of a system of hardcore bosons quenched
under the Bose-Hubbard Hamiltonian on a one-dimensional lattice. We compare the
new algorithm to more standard methods using the MPS architecture. We find that
the Chebyshev method gives numerically exact results for small times. However,
the reachable times are smaller than the ones obtained with the other
state-of-the-art methods. We further extend the new method using a
spectral-decomposition-based projective scheme that utilizes an effective
bandwidth significantly smaller than the full bandwidth, leading to longer
evolution times than the non-projective method and more efficient information
storage, data compression, and less computational effort.Comment: 14 pages, 8 figure
Fast convergence of imaginary time evolution tensor network algorithms by recycling the environment
We propose an environment recycling scheme to speed up a class of tensor
network algorithms that produce an approximation to the ground state of a local
Hamiltonian by simulating an evolution in imaginary time. Specifically, we
consider the time-evolving block decimation (TEBD) algorithm applied to
infinite systems in 1D and 2D, where the ground state is encoded, respectively,
in a matrix product state (MPS) and in a projected entangled-pair state (PEPS).
An important ingredient of the TEBD algorithm (and a main computational
bottleneck, especially with PEPS in 2D) is the computation of the so-called
environment, which is used to determine how to optimally truncate the bond
indices of the tensor network so that their dimension is kept constant. In
current algorithms, the environment is computed at each step of the imaginary
time evolution, to account for the changes that the time evolution introduces
in the many-body state represented by the tensor network. Our key insight is
that close to convergence, most of the changes in the environment are due to a
change in the choice of gauge in the bond indices of the tensor network, and
not in the many-body state. Indeed, a consistent choice of gauge in the bond
indices confirms that the environment is essentially the same over many time
steps and can thus be re-used, leading to very substantial computational
savings. We demonstrate the resulting approach in 1D and 2D by computing the
ground state of the quantum Ising model in a transverse magnetic field.Comment: 17 pages, 28 figure
Valence bond entanglement entropy of frustrated spin chains
We extend the definition of the recently introduced valence bond entanglement
entropy to arbitrary SU(2) wave functions of S=1/2 spin systems. Thanks to a
reformulation of this entanglement measure in terms of a projection, we are
able to compute it with various numerical techniques for frustrated spin
models. We provide extensive numerical data for the one-dimensional J1-J2 spin
chain where we are able to locate the quantum phase transition by using the
scaling of this entropy with the block size. We also systematically compare
with the scaling of the von Neumann entanglement entropy. We finally underline
that the valence-bond entropy definition does depend on the choice of
bipartition so that, for frustrated models, a "good" bipartition should be
chosen, for instance according to the Marshall sign.Comment: 10 pages, 6 figures; v2: published versio
Symmetry between repulsive and attractive interactions in driven-dissipative Bose-Hubbard systems
The driven-dissipative Bose-Hubbard model can be experimentally realized with
either negative or positive onsite detunings, inter-site hopping energies, and
onsite interaction energies. Here we use one-dimensional matrix product density
operators to perform a fully quantum investigation of the dependence of the
non-equilibrium steady states of this model on the signs of these parameters.
Due to a symmetry in the Lindblad master equation, we find that simultaneously
changing the sign of the interaction energies, hopping energies, and chemical
potentials leaves the local boson number distribution and inter-site number
correlations invariant, and the steady-state complex conjugated. This shows
that all driven-dissipative phenomena of interacting bosons described by the
Lindblad master equation, such as "fermionization" and "superbunching", can
equivalently occur with attractive or repulsive interactions.Comment: single column 12 pages, 4 figures, 1 tabl
The Miscible-Immiscible Quantum Phase Transition in Coupled Two-Component Bose-Einstein Condensates in 1D Optical Lattices
Using numerical techniques, we study the miscible-immiscible quantum phase
transition in a linearly coupled binary Bose-Hubbard model Hamiltonian that can
describe low-energy properties of a two-component Bose-Einstein condensate in
optical lattices. With the quantum many-body ground state obtained from density
matrix renormalization group algorithm, we calculate the characteristic
physical quantities of the phase transition controlled by the linear coupling
between two components. Furthermore we calculate the Binder cumulant to
determine the critical point and draw the phase diagram. The strong-coupling
expansion shows that in the Mott insulator regime the model Hamiltonian can be
mapped to a spin 1/2 XXZ model with a transverse magnetic field.Comment: 10 pages, 10 figures, submitted to Phys. Rev.
A Strictly Single-Site DMRG Algorithm with Subspace Expansion
We introduce a strictly single-site DMRG algorithm based on the subspace
expansion of the Alternating Minimal Energy (AMEn) method. The proposed new MPS
basis enrichment method is sufficient to avoid local minima during the
optimisation, similarly to the density matrix perturbation method, but
computationally cheaper. Each application of to in the
central eigensolver is reduced in cost for a speed-up of ,
with the physical site dimension. Further speed-ups result from cheaper
auxiliary calculations and an often greatly improved convergence behaviour.
Runtime to convergence improves by up to a factor of 2.5 on the Fermi-Hubbard
model compared to the previous single-site method and by up to a factor of 3.9
compared to two-site DMRG. The method is compatible with real-space
parallelisation and non-abelian symmetries.Comment: 9 pages, 6 figures; added comparison with two-site DMR
Quasiparticles in the Kondo lattice model at partial fillings of the conduction band
We study the spectral properties of the one-dimensional Kondo lattice model
as function of the exchange coupling, the band filling, and the quasimomentum
in the ferromagnetic and paramagnetic phase. Using the density-matrix
renormalization group method, we compute the dispersion relation of the
quasiparticles, their lifetimes, and the Z-factor. As a main result, we provide
evidence for the existence of the spinpolaron at partial band fillings. We find
that the quasiparticle lifetime differs by orders of magnitude between the
ferromagnetic and paramagnetic phase and depends strongly on the quasimomentum.Comment: 9 pages, 9 figure
Spectral functions and time evolution from the Chebyshev recursion
We link linear prediction of Chebyshev and Fourier expansions to analytic
continuation. We push the resolution in the Chebyshev-based computation of
many-body spectral functions to a much higher precision by deriving a
modified Chebyshev series expansion that allows to reduce the expansion order
by a factor . We show that in a certain limit the Chebyshev
technique becomes equivalent to computing spectral functions via time evolution
and subsequent Fourier transform. This introduces a novel recursive time
evolution algorithm that instead of the group operator only involves
the action of the generator . For quantum impurity problems, we introduce an
adapted discretization scheme for the bath spectral function. We discuss the
relevance of these results for matrix product state (MPS) based DMRG-type
algorithms, and their use within dynamical mean-field theory (DMFT). We present
strong evidence that the Chebyshev recursion extracts less spectral information
from than time evolution algorithms when fixing a given amount of created
entanglement.Comment: 12 pages + 6 pages appendix, 11 figure
Topological phase transition and the effect of Hubbard interaction on the one-dimensional topological Kondo insulator
The effect of a local Kondo coupling and Hubbard interaction on the
topological phase of the one-dimensional topological Kondo insulator (TKI) is
numerically investigated using the infinite matrix-product state density-matrix
renormalization group algorithm. The groundstate of the TKI is a
symmetry-protected topological (SPT) phase protected by inversion symmetry. It
is found that on its own, the Hubbard interaction that tends to force fermions
into a one-charge per site order is insufficient to destroy the SPT phase.
However when the local Kondo Hamiltonian term that favors a topologically
trivial groundstate with a one-charge per site order is introduced, the Hubbard
interaction assists in the destruction of the SPT phase. This topological phase
transition occurs in the charge sector where the correlation length of the
charge excitation diverges while the correlation length of the spin excitation
remains finite. The critical exponents, central charge and the phase diagram
separating the SPT phase from the topologically trivial phase are presented.Comment: 15 pages, 22 figure
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