arXiv subjects

Ulrich Schollwoeck

Publications and source records attributed to Ulrich Schollwoeck.

At least 19 recordsLinked to original sources

arXiv2012

Nature of the Spin Liquid Ground State of the S=1/2 Kagome Heisenberg Model

We perform a density-matrix renormalization group (DMRG) study of the S=1/2 Heisenberg antiferromagnet on the kagome lattice to identify the conjectured spin liquid ground state. Exploiting SU(2) spin symmetry, which allows us to keep up to 16,000 DMRG states, we consider cylinders with circumferences up to 17 lattice spacings and find a spin liquid ground state with an estimated per site energy of -0.4386(5), a spin gap of 0.13(1), very short-range decay in spin, dimer and chiral correlation functions and finite topological entanglement gamma consistent with gamma=ld 2, ruling out gapless, chiral or non-topological spin liquids. At the same time, DMRG results provide strong evidence for a gapped topological Z2 spin liquid.

cond-mat.str-el↗

arXiv2012

Hybrid NRG-DMRG approach to real-time dynamics of quantum impurity systems

A hybrid approach to nonequilibrium dynamics of quantum impurity systems is presented. The numerical renormalization group serves as a means to generate a suitable low-energy Hamiltonian, allowing for an accurate evaluation of the real-time dynamics of the problem up to exponentially long times using primarily the time-adaptive density-matrix renormalization group. We extract the decay time of the interaction-enhanced oscillations in the interacting resonant-level model and show their quadratic divergence with the interaction strength U. Our numerical analysis is in excellent agreement with analytic predictions based on an expansion in 1/U.

cond-mat.str-el↗

arXiv2011

Signatures of Delocalization in the Fermionic 1D Hubbard Model with Box Disorder: Comparative Study with DMRG and R-DMFT

We investigate the 1D Anderson-Hubbard model at half filling with box-disorder. The ground state phase diagram is obtained by means of real-space dynamical mean-field theory (R-DMFT) and the density matrix renormalization group (DMRG). We find Mott insulating and Anderson localized regimes as well as a strong indication of a delocalized phase for intermediate interaction and disorder strength within accessible system sizes. These phases are characterized and distinguished by qualitatively different scaling behavior of the local density of states, the energy gap in the excitation spectrum and the inverse participation number.

cond-mat.str-el↗

arXiv2011

The density-matrix renormalization group in the age of matrix product states

The density-matrix renormalization group method (DMRG) has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems. In the further development of the method, the realization that DMRG operates on a highly interesting class of quantum states, so-called matrix product states (MPS), has allowed a much deeper understanding of the inner structure of the DMRG method, its further potential and its limitations. In this paper, I want to give a detailed exposition of current DMRG thinking in the MPS language in order to make the advisable implementation of the family of DMRG algorithms in exclusively MPS terms transparent. I then move on to discuss some directions of potentially fruitful further algorithmic development: while DMRG is a very mature method by now, I still see potential for further improvements, as exemplified by a number of recently introduced algorithms.

cond-mat.str-el↗

arXiv2010

Effect of Electron-Electron Interactions on the Charge Carrier Transitions in trans-Polyacetylene

By employing a newly developed dynamical simulation method, which is a combination of classical molecular dynamics (MD) and the adaptive time-dependent density matrix renormalization group (TDDMRG), we investigate the dynamics of charge carrier transitions in trans-polyacetylene (PA) with the inclusion of both electron-phonon and electron -electron interactions. The calculations are performed within a modified Su-Schrieffer-Heeger (SSH) model in which electron-electron interactions are taken into account via the combination with extended Hubbard model (EHM). We find that removing an electron from a trans-PA chain bearing a positively charged polaron leads to the formation of a pair of charged solitons. Furthermore, we study the effect of electron-electron interactions on such charge carrier transitions in trans-PA. Our results show that increasing the on-site Coulomb interaction U and the nearest-neighbor Coulomb repulsion V will not change the qualitative behavior of the transition from a polaron to a soliton pair in the evolution process but will quantitatively reduce the moving velocities of the both formed solitons significantly and change the conditions for the soliton collisions.

cond-mat.mtrl-sci↗

arXiv2008

Dynamical simulations of charged soliton transport in conjugated polymers with the inclusion of electron-electron interactions

We present numerical studies of the transport dynamics of a charged soliton in conjugated polymers under the influence of an external time-dependent electric field. All relevant electron-phonon and electron-electron interactions are nearly fully taken into account by simulating the monomer displacements with classical molecular dynamics (MD) and evolving the wavefunction for the $π$ electrons by virtue of the adaptive time-dependent density matrix renormalization group (TDDMRG) simultaneously and nonadiabatically. It is found that after a smooth turn-on of the external electric field the charged soliton is accelerated at first up to a stationary constant velocity as one entity consisting of both the charge and the lattice deformation. An ohmic region (6 mV/$\textÅ$ $\leq E_0\leq$ 12 mV/$\textÅ$) where the stationary velocity increases linearly with the electric field strength is observed. The relationship between electron-electron interactions and charged soliton transport is also investigated in detail. We find that the dependence of the stationary velocity of a charged soliton on the on-site Coulomb interactions $U$ and the nearest-neighbor interactions $V$ is due to the extent of delocalization of the charged soliton defect.

cond-mat.str-el↗

arXiv2008

Dynamical simulations of polaron transport in conjugated polymers with the inclusion of electron-electron interactions

Dynamical simulations of polaron transport in conjugated polymers in the presence of an external time-dependent electric field have been performed within a combined extended Hubbard model (EHM) and Su-Schrieffer-Heeger (SSH) model. Nearly all relevant electron-phonon and electron-electron interactions are fully taken into account by solving the time-dependent Schrödinger equation for the $π$-electrons and the Newton's equation of motion for the backbone monomer displacements by virtue of the combination of the adaptive time-dependent density matrix renormalization group (TDDMRG) and classical molecular dynamics (MD). We find that after a smooth turn-on of the external electric field the polaron is accelerated at first and then moves with a nearly constant velocity as one entity consisting of both the charge and the lattice deformation. An ohmic region (3 mV/$\textÅ$ $\leq E_0\leq$ 9 mV/$\textÅ$) where the stationary velocity increases linearly with the electric field strength is observed for the case of $U$=2.0 eV and $V$=1.0 eV. The maximal velocity is well above the speed of sound. Below 3 mV/$\textÅ$ the polaron velocity increases nonlinearly and in high electric fields with strength $E_0\geq$ 10.0 mV/$\textÅ$ the polaron will become unstable and dissociate. The relationship between electron-electron interaction strengths and polaron transport is also studied in detail. We find that the the on-site Coulomb interactions $U$ will suppress the polaron transport and small nearest-neighbor interactions $V$ values are also not beneficial to the polaronic motion while large $V$ values favor the polaron transport.

cond-mat.mtrl-sci↗

arXiv2008

Mixture of bosonic and spin-polarized fermionic atoms in an optical lattice

We investigate the properties of trapped Bose-Fermi mixtures for experimentally relevant parameters in one dimension. The effect of the attractive Bose-Fermi interaction onto the bosons is to deepen the parabolic trapping potential, and to reduce the bosonic repulsion in higher order, leading to an increase in bosonic coherence. The opposite effect was observed in ${}^{87}$Rb - ${}^{40}$K experiments, most likely due to a sharp rise in temperature. We also discuss low-temperature features, such as a bosonic Mott insulator transition driven by the fermion concentration, and the formation of composite particles such as polarons and molecules.

cond-mat.other↗

arXiv2007

Excitations in two-component Bose-gases

In this paper, we study a strongly correlated quantum system that has become amenable to experiment by the advent of ultracold bosonic atoms in optical lattices, a chain of two different bosonic constituents. Excitations in this system are first considered within the framework of bosonization and Luttinger liquid theory which are applicable if the Luttinger liquid parameters are determined numerically. The occurrence of a bosonic counterpart of fermionic spin-charge separation is signalled by a characteristic two-peak structure in the spectral functions found by dynamical DMRG in good agreement with analytical predictions. Experimentally, single-particle excitations as probed by spectral functions are currently not accessible in cold atoms. We therefore consider the modifications needed for current experiments, namely the investigation of the real-time evolution of density perturbations instead of single particle excitations, a slight inequivalence between the two intraspecies interactions in actual experiments, and the presence of a confining trap potential. Using time-dependent DMRG we show that only quantitative modifications occur. With an eye to the simulation of strongly correlated quantum systems far from equilibrium we detect a strong dependence of the time-evolution of entanglement entropy on the initial perturbation, signalling limitations to current reasonings on entanglement growth in many-body systems.

cond-mat.stat-mech↗

arXiv2006

d-wave resonating valence bond states of fermionic atoms in optical lattices

We study controlled generation and measurement of superfluid d-wave resonating valence bond (RVB) states of fermionic atoms in 2D optical lattices. Starting from loading spatial and spin patterns of atoms in optical superlattices as pure quantum states from a Fermi gas, we adiabatically transform this state to an RVB state by change of the lattice parameters. Results of exact time-dependent numerical studies for ladders systems are presented, suggesting generation of RVB states on timescale smaller than typical experimental decoherence times.

cond-mat.str-el↗

arXiv2006

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.

cond-mat.stat-mech↗

arXiv2005

Entanglement and boundary critical phenomena

We investigate boundary critical phenomena from a quantum information perspective. Bipartite entanglement in the ground state of one-dimensional quantum systems is quantified using the Renyi entropy S_alpha, which includes the von Neumann entropy (alpha=1) and the single-copy entanglement (alpha=infinity) as special cases. We identify the contribution from the boundary entropy to the Renyi entropy, and show that there is an entanglement loss along boundary renormalization group (RG) flows. This property, which is intimately related to the Affleck-Ludwig g-theorem, can be regarded as a consequence of majorization relations between the spectra of the reduced density matrix along the boundary RG flows. We also point out that the bulk contribution to the single-copy entanglement is half of that to the von Neumann entropy, whereas the boundary contribution is the same.

cond-mat.str-el↗

arXiv2004

Exotic Heavy-Fermion State in Filled Skutterudite SmOs4Sb12

Specific heat and transport measurements have revealed an unconventional heavy-fermion (HF) state in SmOs4Sb12 single crystals. The electronic specific-heat coefficient (gamma=0.82 J/K^2mol) and the coefficient (A) of the quadratic temperature dependence of electrical resistivity are largely enhanced, although the ratio A/gamma^2 is reduced from the Kadowaki-Woods ratio of HF materials. Both gamma and A do not show any significant decrease in applied field in contrast with Ce-based HF compounds, suggesting an unconventional origin of the heavy quasiparticles. A weak ferromagnetic ordering sets in below about 3 K, probably originating in the itinerant quasiparticles.

cond-mat.str-el↗

arXiv2004

Real-time dynamics in spin-1/2 chains with adaptive time-dependent DMRG

We investigate the influence of different interaction strengths and dimerizations on the magnetization transport in antiferromagnetic spin-1/2 XXZ-chains. We focus on the real-time evolution of the inhomogeneous initial state with all spins pointing up along the z axis in the left half and down in the right half of the chain, using the adaptive time-dependent density-matrix renormalization group (adaptive t-DMRG). We find on time-scales accessible to us ballistic magnetization transport for small Sz-Sz-interaction and arbitrary dimerization, but almost no transport for stronger Sz-Sz-interaction, with a sharp crossover at Jz=1. At Jz=1 results indicate superdiffusive transport. Additionally, we perform a detailed analysis of the error made by the adaptive time-dependent DMRG using the fact that the evolution in the XX-model is known exactly. We find that the error at small times is dominated by the error made by the Trotter decomposition, whereas for longer times the DMRG truncation error becomes the most important, with a very sharp crossover at some "runaway" time.

cond-mat.stat-mech↗

arXiv2004

The density-matrix renormalization group

The density-matrix renormalization group (DMRG) is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription. This algorithm has achieved unprecedented precision in the description of one-dimensional quantum systems. It has therefore quickly acquired the status of method of choice for numerical studies of one-dimensional quantum systems. Its applications to the calculation of static, dynamic and thermodynamic quantities in such systems are reviewed. The potential of DMRG applications in the fields of two-dimensional quantum systems, quantum chemistry, three-dimensional small grains, nuclear physics, equilibrium and non-equilibrium statistical physics, and time-dependent phenomena is discussed. This review also considers the theoretical foundations of the method, examining its relationship to matrix-product states and the quantum information content of the density matrices generated by DMRG.

cond-mat.str-el↗

arXiv2003

Electronic transport calculations for self-assembled mono-layers of 1,4-phenylene diisocyanide on Au(111) contacts

We report on electronic transport calculations for self-assembled mono-layers (SAM) of 1,4-phenylene diisocyanide on Au(111) contacts. Experimentally one observes more structure (i.e peaks) within the measured conductance curve for this molecule with two cyanide end-groups, compared to measurements with molecules having thiol end-groups. The calculations are performed on the semi-empiric extended Hückel level using elastic scattering quantum chemistry (ESQC) and we investigate three possible explanations for the experimental findings. Comparing the experimental and theoretical data, we are able to rule out all but one of the scenarios. The observed additional peaks are found to be only reproduced by a mono-layer with additional molecules perturbing the periodicity. It is conjectured that the weaker coupling to Au of cyanide end-groups compared to thiol end-groups might be responsible for such perturbations.

cond-mat.mes-hall↗

arXiv2003

Non-Hermitian Luttinger Liquids and Vortex Physics

As a model of two thermally excited flux liquids connected by a weak link, we study the effect of a single line defect on vortex filaments oriented parallel to the surface of a thin planar superconductor. When the applied field is tilted relative to the line defect, the physics is described by a nonhermitian Luttinger liquid of interacting quantum bosons in one spatial dimension with a point defect. We analyze this problem using a combination of analytic and numerical density matrix renormalization group methods, uncovering a delicate interplay between enhancement of pinning due to Luttinger liquid effects and depinning due to the tilted magnetic field. Interactions dramatically improve the ability of a single columnar pin to suppress vortex tilt when the Luttinger liquid parameter g is less than or equal to one.

cond-mat.mes-hall↗

arXiv2001

On the choice of the density matrix in the stochastic TMRG

In applications of the density matrix renormalization group to nonhermitean problems, the choice of the density matrix is not uniquely prescribed by the algorithm. We demonstrate that for the recently introduced stochastic transfer matrix DMRG (stochastic TMRG) the necessity to use open boundary conditions makes asymmetrical reduced density matrices, as used for renormalization in quantum TMRG, an inappropriate choice. An explicit construction of the largest left and right eigenvectors of the full transfer matrix allows us to show why symmetrical density matrices are the correct physical choice.

cond-mat.stat-mech↗