arXiv subjects

Ulrich Schollwöck

Publications and source records attributed to Ulrich Schollwöck.

85 records · Page 5Linked to original sources

arXiv2012

Quantum dynamics of a single, mobile spin impurity

Quantum magnetism describes the properties of many materials such as transition metal oxides and cuprate superconductors. One of its elementary processes is the propagation of spin excitations. Here we study the quantum dynamics of a deterministically created spin-impurity atom, as it propagates in a one-dimensional lattice system. We probe the full spatial probability distribution of the impurity at different times using single-site-resolved imaging of bosonic atoms in an optical lattice. In the Mott-insulating regime, a post-selection of the data allows to reduce the effect of temperature, giving access to a space- and time-resolved measurement of the quantum-coherent propagation of a magnetic excitation in the Heisenberg model. Extending the study to the bath's superfluid regime, we determine quantitatively how the bath strongly affects the motion of the impurity. The experimental data shows a remarkable agreement with theoretical predictions allowing us to determine the effect of temperature on the coherence and velocity of impurity motion. Our results pave the way for a new approach to study quantum magnetism, mobile impurities in quantum fluids, and polarons in lattice systems.

cond-mat.quant-gas↗

arXiv2011

Landau-Zener sweeps and sudden quenches in coupled Bose-Hubbard chains

We simulate numerically the dynamics of strongly correlated bosons in a two-leg ladder subject to a time-dependent energy bias between the two chains. When all atoms are initially in the leg with higher energy, we find a drastic reduction of the inter-chain particle transfer for slow linear sweeps, in quantitative agreement with recent experiments. This effect is preceded by a rapid broadening of the quasi-momentum distribution of atoms, signaling the presence of a bath of low-energy excitations in the chains. We further investigate the scenario of quantum quenches to fixed values of the energy bias. We find that for large enough density the momentum distribution relaxes to that of an equilibrium thermal state with the same energy.

quant-ph↗

arXiv2011

Chebyshev matrix product state approach for spectral functions

We show that recursively generated Chebyshev expansions offer numerically efficient representations for calculating zero-temperature spectral functions of one-dimensional lattice models using matrix product state (MPS) methods. The main features of this Chebychev matrix product state (CheMPS) approach are: (i) it achieves uniform resolution over the spectral function's entire spectral width; (ii) it can exploit the fact that the latter can be much smaller than the model's many-body bandwidth; (iii) it offers a well-controlled broadening scheme; (iv) it is based on a succession of Chebychev vectors |t_n>, (v) whose entanglement entropies were found to remain bounded with increasing recursion order n for all cases analyzed here; (vi) it distributes the total entanglement entropy that accumulates with increasing n over the set of Chebyshev vectors |t_n>. We present zero-temperature CheMPS results for the structure factor of spin-1/2 antiferromagnetic Heisenberg chains and perform a detailed finite-size analysis. Making comparisons to three benchmark methods, we find that CheMPS (1) yields results comparable in quality to those of correction vector DMRG, at dramatically reduced numerical cost; (2) agrees well with Bethe Ansatz results for an infinite system, within the limitations expected for numerics on finite systems; (3) can also be applied in the time domain, where it has potential to serve as a viable alternative to time-dependent DMRG (in particular at finite temperatures). Finally, we present a detailed error analysis of CheMPS for the case of the noninteracting resonant level model.

cond-mat.str-el↗

arXiv2011

Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas

The problem of how complex quantum systems eventually come to rest lies at the heart of statistical mechanics. The maximum entropy principle put forward in 1957 by E. T. Jaynes suggests what quantum states one should expect in equilibrium but does not hint as to how closed quantum many-body systems dynamically equilibrate. A number of theoretical and numerical studies accumulate evidence that under specific conditions quantum many-body models can relax to a situation that locally or with respect to certain observables appears as if the entire system had relaxed to a maximum entropy state. In this work, we report the experimental observation of the non-equilibrium dynamics of a density wave of ultracold bosonic atoms in an optical lattice in the regime of strong correlations. Using an optical superlattice, we are able to prepare the system in a well-known initial state with high fidelity. We then follow the dynamical evolution of the system in terms of quasi-local densities, currents, and coherences. Numerical studies based on the time-dependent density-matrix renormalization group method are in an excellent quantitative agreement with the experimental data. For very long times, all three local observables show a fast relaxation to equilibrium values compatible with those expected for a global maximum entropy state. We find this relaxation of the quasi-local densities and currents to initially follow a power-law with an exponent being significantly larger than for free or hardcore bosons. For intermediate times the system fulfills the promise of being a dynamical quantum simulator, in that the controlled dynamics runs for longer times than present classical algorithms based on matrix product states can efficiently keep track of.

cond-mat.quant-gas↗

arXiv2010

Coulomb interaction effects and electron spin relaxation in the 1d Kondo lattice model

We study the effects of the Coulomb interaction in the one dimensional Kondo lattice model on the phase diagram, the static magnetic susceptibility and electron spin relaxation. We show that onsite Coulomb interaction supports ferromagnetic order and nearest neighbor Coulomb interaction drives, depending on the electron filling, either a paramagnetic or ferromagnetic order. Furthermore we calculate electron quasiparticle life times, which can be related to electron spin relaxation and decoherence times, and explain their dependence on the strength of interactions and the electron filling in order to find the sweet spot of parameters where the relaxation time is maximized. We find that effective exchange processes between the electrons dominate the spin relaxation and decoherence rate.

cond-mat.str-el↗

arXiv2009

Kondo screening cloud in the single-impurity Anderson model: A density matrix renormalization group study

A magnetic moment in a metal or in a quantum dot is, at low temperatures, screened by the conduction electrons through the mechanism of the Kondo effect. This gives rise to spin-spin correlations between the magnetic moment and the conduction electrons, which can have a substantial spatial extension. We study this phenomenon, the so-called Kondo cloud, by means of the density matrix renormalization group method for the case of the single-impurity Anderson model. We focus on the question whether the Kondo screening length, typically assumed to be proportional to the inverse Kondo temperature, can be extracted from the spin-spin correlations. For several mechanisms -- the gate potential and a magnetic field -- which destroy the Kondo effect, we investigate the behavior of the screening cloud induced by these perturbations.

cond-mat.str-el↗

arXiv2009

Magnetism, coherent many-particle dynamics, and relaxation with ultracold bosons in optical superlattices

We study how well magnetic models can be implemented with ultracold bosonic atoms of two different hyperfine states in an optical superlattice. The system is captured by a two-species Bose-Hubbard model, but realizes in a certain parameter regime actually the physics of a spin-1/2 Heisenberg magnet, describing the second order hopping processes. Tuning of the superlattice allows for controlling the effect of fast first order processes versus the slower second order ones. Using the density-matrix renormalization-group method, we provide the evolution of typical experimentally available observables. The validity of the description via the Heisenberg model, depending on the parameters of the Hubbard model, is studied numerically and analytically. The analysis is also motivated by recent experiments [S. Foelling et al., Nature 448, 1029 (2007); S. Trotzky et al., Sience 319, 295 (2008)] where coherent two-particle dynamics with ultracold bosonic atoms in isolated double wells were realized. We provide theoretical background for the next step, the observation of coherent many-particle dynamics after coupling the double wells. Contrary to the case of isolated double wells, relaxation of local observables can be observed. The tunability between the Bose-Hubbard model and the Heisenberg model in this setup could be used to study experimentally the differences in equilibration processes for nonintegrable and Bethe ansatz integrable models. We show that the relaxation in the Heisenberg model is connected to a phase averaging effect, which is in contrast to the typical scattering driven thermalization in nonintegrable models. We discuss the preparation of magnetic groundstates by adiabatic tuning of the superlattice parameters.

cond-mat.stat-mech↗

arXiv2009

Spectral functions in one-dimensional quantum systems at T>0

We present for the first time time-dependent density-matrix renormalization-group simulations (t-DMRG) at finite temperatures. It is demonstrated how a combination of finite-temperature t-DMRG and time-series prediction allows for an easy and very accurate calculation of spectral functions in one-dimensional quantum systems, irrespective of their statistics, for arbitrary temperatures. This is illustrated with spin structure factors of XX and XXX spin-1/2 chains. For the XX model we can compare against an exact solution and for the XXX model (Heisenberg antiferromagnet) against a Bethe Ansatz solution and quantum Monte Carlo data.

cond-mat.str-el↗

arXiv2008

Dephasing and the steady state in quantum many-particle systems

We discuss relaxation in bosonic and fermionic many-particle systems. For integrable systems, the time evolution can cause a dephasing effect, leading for finite subsystems to certain steady states. We give an explicit derivation of those steady subsystem states and devise sufficient prerequisites for the dephasing to take place. We also find simple scenarios, in which dephasing is ineffective and discuss the dependence on dimensionality and criticality. It follows further that, after a quench of system parameters, bipartite entanglement entropy will become extensive. This provides a way of creating strong entanglement in a controlled fashion.

cond-mat.stat-mech↗

arXiv2005

Ground-state phases in antiferromagnetic spin-crossover chains

Spin-crossover molecules having a low-spin ground state and a low-lying excited high-spin state are promising components for molecular electronics. We theoretically examine one-dimensional spin-crossover chain molecules of the type of Fe-II triazole complexes. The existence of the additional low-spin/high-spin degree of freedom leads to rich behavior already in the ground state. We obtain the complete ground-state phase diagram, taking into account an elastic nearest-neighbor interaction, a ferromagnetic or antiferromagnetic exchange interaction between the magnetic ions, and an external magnetic field. Ground-state energies are calculated with high numerical precision using the density-matrix renormalization group. Besides pure low-spin, highspin, and alternating low-spin/high-spin phases we obtain a number of periodic ground states with longer periods, which we discuss in detail. For example, for antiferromagnetic coupling there exists a dimer phase with a magnetic unit cell containing two high-spin ions forming a spin singlet and a single low-spin ion, which is stabilized by the energy gain for singlet formation.

cond-mat.stat-mech↗

arXiv2004

Ageing phenomena without detailed balance: the contact process

The long-time dynamics of the 1D contact process suddenly brought out of an uncorrelated initial state is studied through a light-cone transfer-matrix renormalisation group approach. At criticality, the system undergoes ageing which is characterised through the dynamical scaling of the two-times autocorrelation and autoresponse functions. The observed non-equality of the ageing exponents a and b excludes the possibility of a finite fluctuation-dissipation ratio in the ageing regime. The scaling form of the critical autoresponse function is in agreement with the prediction of local scale-invariance.

cond-mat.stat-mech↗

arXiv2001

Universal finite-size scaling amplitudes in anisotropic scaling

Phenomenological scaling arguments suggest the existence of universal amplitudes in the finite-size scaling of certain correlation lengths in strongly anisotropic or dynamical phase transitions. For equilibrium systems, provided that translation invariance and hyperscaling are valid, the Privman-Fisher scaling form of isotropic equilibrium phase transitions is readily generalized. For non-equilibrium systems, universality is shown analytically for directed percolation and is tested numerically in the annihilation-coagulation model and in the pair contact process with diffusion. In these models, for both periodic and free boundary conditions, the universality of the finite-size scaling amplitude of the leading relaxation time is checked. Amplitude universality reveals strong transient effects along the active-inactive transition line in the pair contact process.

cond-mat.stat-mech↗

arXiv1998

Combination of Ferromagnetic and Antiferromagnetic Features in Heisenberg Ferrimagnets

We investigate the thermodynamic properties of Heisenberg ferrimagnetic mixed-spin chains both numerically and analytically with particular emphasis on the combination of ferromagnetic and antiferromagnetic features. Employing a new density-matrix renormalization-group technique as well as a quantum Monte Carlo method, we reveal the overall thermal behavior: At very low temperatures, the specific heat and the magnetic susceptibility times temperature behave like $T^{1/2}$ and $T^{-1}$, respectively, whereas at intermediate temperatures, they exhibit a Schottky-like peak and a minimum, respectively. Developing the modified spin-wave theory, we complement the numerical findings and give a precise estimate of the low-temperature behavior.

cond-mat.stat-mech↗