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 $U^{ab}$ larger than the intra-species repulsion $U$, they found a transition from a uniform miscible phase to phase-separation occurring at a finite value of $U$ , e.g., at around $U = 1.3$ for $\Delta = U^{ab}/U = 1.05$ and $\rho_{a} = \rho_{b} = 1/2$. 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 $U^{ab} > U > 0$.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 $\hat H$ to $|\Psi\rangle$ in the central eigensolver is reduced in cost for a speed-up of $\approx (d + 1)/2$, with $d$ 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 $T=0$ 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 $\sim\frac{1}{6}$. 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 $e^{-iHt}$ only involves the action of the generator $H$. 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 $H$ than time evolution algorithms when fixing a given amount of created entanglement.Comment: 12 pages + 6 pages appendix, 11 figure

Domain-wall melting in ultracold boson systems with holes and spin-flip defects

Quantum magnetism is a fundamental phenomenon of nature. As of late, it has garnered a lot of interest because experiments with ultracold atomic gases in optical lattices could be used as a simulator for phenomena of magnetic systems. A paradigmatic example is the time evolution of a domain-wall state of a spin-1/2 Heisenberg chain, the so-called domain-wall melting. The model can be implemented by having two species of bosonic atoms with unity filling and strong on-site repulsion U in an optical lattice. In this paper, we study the domain-wall melting in such a setup on the basis of the time-dependent density matrix renormalization group (tDMRG). We are particularly interested in the effects of defects that originate from an imperfect preparation of the initial state. Typical defects are holes (empty sites) and flipped spins. We show that the dominating effects of holes on observables like the spatially resolved magnetization can be taken account of by a linear combination of spatially shifted observables from the clean case. For sufficiently large U, further effects due to holes become negligible. In contrast, the effects of spin flips are more severe as their dynamics occur on the same time scale as that of the domain-wall melting itself. It is hence advisable to avoid preparation schemes that are based on spin-flips.Comment: 15 pages, 12 figures. Supplemental Material: 2 animations (avi) comparing the domain-wall melting with and without defects, corresponding to figures 3, 4 and the discussion in section V.B; minor improvements; published versio