arXiv subjects

F. Heidrich-Meisner

Publications and source records attributed to F. Heidrich-Meisner.

At least 37 records · Page 2Linked to original sources

arXiv2015

Strongly interacting bosons on a three-leg ladder in the presence of a homogeneous flux

We perform a density-matrix renormalization-group study of strongly interacting bosons on a three-leg ladder in the presence of a homogeneous flux. Focusing on one-third filling, we explore the phase diagram in dependence of the magnetic flux and the inter-leg tunneling strength. We find several phases including a Meissner phase, vortex liquids, a vortex lattice, as well as a staggered-current phase. Moreover, there are regions where the chiral current reverses its direction, both in the Meissner and in the staggered-current phase. While the reversal in the latter case can be ascribed to spontaneous breaking of translational invariance, in the first it stems from an effective flux increase in the rung direction. Interactions are a necessary ingredient to realize either type of chiral-current reversal.

cond-mat.quant-gas↗

arXiv2015

Temporal decay of Neel order in the one-dimensional Fermi-Hubbard model

Motivated by recent experiments with ultra-cold quantum gases in optical lattices we study the decay of the staggered moment in the one-dimensional Fermi-Hubbard model starting from a perfect Neel state using exact diagonalization and the iTEBD method. This extends previous work in which the same problem has been addressed for pure spin Hamiltonians. As a main result, we show that the relaxation dynamics of the double occupancy and of the staggered moment are different. The former is controlled by the nearest-neighbor tunneling rate while the latter is much slower and strongly dependent on the interaction strength, indicating that spin excitations are important. This difference in characteristic energy scales for the fast charge dynamics and the much slower spin dynamics is also reflected in the real-time evolution of nearest-neighbor density and spin correlations. A very interesting time dependence emerges in the von Neumann entropy, which at short times increases linearly with a slope proportional to the tunneling matrix element while the long-time growth of entanglement is controlled by spin excitations. Our predictions for the different relaxation dynamics of the staggered moment and the double occupancy should be observable in state-of-the art optical lattice experiments. We further compare time averages of the double occupancy to both the expectation values in the canonical and diagonal ensemble, which quantitatively disagree with each other on finite systems. We relate the question of thermalization to the eigenstate thermalization hypothesis.

cond-mat.str-el↗

arXiv2015

Interaction quantum quenches in the one-dimensional Fermi-Hubbard model with spin imbalance

Using the time-dependent density matrix renormalization group method and exact diagonalization, we study the non-equilibrium dynamics of the one-dimensional Fermi-Hubbard model following a quantum quench or a ramp of the onsite interaction strength. For quenches from the non-interacting to the attractive regime, we investigate the dynamical emergence of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) correlations, which at finite spin polarizations are the dominant two-body correlations in the ground state, and their signatures in the pair quasi-momentum distribution function. We observe that the post-quench double occupancy exhibits a maximum as the interaction strength becomes of the order of the bandwidth. Finally, we study quenches and ramps from attractive to repulsive interactions, which imprint FFLO correlations onto repulsively bound pairs. We show that a quite short ramp time is sufficient to wipe out the characteristic FFLO features in the post-quench pair momentum distribution functions.

cond-mat.quant-gas↗

arXiv2015

Vortex and Meissner phases of strongly-interacting bosons on a two-leg ladder

We establish the phase diagram of the strongly-interacting Bose-Hubbard model defined on a two-leg ladder geometry in the presence of a homogeneous flux. Our work is motivated by a recent experiment [Atala et al., Nature Phys. 10, 588 (2014)], which studied the same system, in the complementary regime of weak interactions. Based on extensive density matrix renormalization group simulations and a bosonization analysis, we fully explore the parameter space spanned by filling, inter-leg tunneling, and flux. As a main result, we demonstrate the existence of gapless and gapped Meissner and vortex phases, with the gapped states emerging in Mott-insulating regimes. We calculate experimentally accessible observables such as chiral currents and vortex patterns.

cond-mat.quant-gas↗

arXiv2015

Spin and thermal conductivity of quantum spin ladders

We study the spin and thermal conductivity of spin-1/2 ladders at finite temperature. This is relevant for experiments with quantum magnets. Using a state-of-the-art density matrix renormalization group algorithm, we compute the current autocorrelation functions on the real-time axis and then carry out a Fourier integral to extract the frequency dependence of the corresponding conductivities. The finite-time error is analyzed carefully. We first investigate the limiting case of spin-1/2 XXZ chains, for which our analysis suggests non-zero dc-conductivities in all interacting cases irrespective of the presence or absence of spin Drude weights. For ladders, we observe that all models studied are normal conductors with no ballistic contribution. Nonetheless, only the high-temperature spin conductivity of XX ladders has a simple diffusive, Drude-like form, while Heisenberg ladders exhibit a more complicated low-frequency behavior. We compute the dc spin conductivity down to temperatures of the order of T~0.5J, where J is the exchange coupling along the legs of the ladder. We further extract mean-free paths and discuss our results in relation to thermal conductivity measurements on quantum magnets.

cond-mat.str-el↗

arXiv2015

Real-time decay of a highly excited charge carrier in the one-dimensional Holstein model

We study the real-time dynamics of a highly excited charge carrier coupled to quantum phonons via a Holstein-type electron-phonon coupling. This is a prototypical example for the non-equilibrium dynamics in an interacting many-body system where excess energy is transferred from electronic to phononic degrees of freedom. We use diagonalization in a limited functional space (LFS) to study the non-equilibrium dynamics on a finite one-dimensional chain. This method agrees with exact diagonalization and the time-evolving block decimation method, in both the relaxation regime and the long-time stationary state, and among these three methods it is the most efficient and versatile one for this problem. We perform a comprehensive analysis of the time evolution by calculating the electron, phonon and electron-phonon coupling energies, and the electronic momentum distribution function. The numerical results are compared to analytical solutions for short times, for a small hopping amplitude and for a weak electron-phonon coupling. In the latter case, the relaxation dynamics obtained from the Boltzmann equation agrees very well with the LFS data. We also study the time dependence of the eigenstates of the single-site reduced density matrix, which defines so-called optimal phonon modes. We discuss their structure in non-equilibrium and the distribution of their weights. Our analysis shows that the structure of optimal phonon modes contains very useful information for the interpretation of the numerical data.

cond-mat.str-el↗

arXiv2014

Decoherence of an entangled state of a strongly-correlated double quantum dot structure through tunneling processes

We consider two quantum dots described by the Anderson-impurity model with one electron per dot. The goal of our work is to study the decay of a maximally entangled state between the two electrons localized in the dots. We prepare the system in a perfect singlet and then tunnel-couple one of the dots to leads, which induces the non-equilibrium dynamics. We identify two cases: if the leads are subject to a sufficiently large voltage and thus a finite current, then direct tunneling processes cause decoherence and the entanglement as well as spin correlations decay exponentially fast. At zero voltage or small voltages and beyond the mixed-valence regime, virtual tunneling processes dominate and lead to a slower loss of coherence. We analyze this problem by studying the real-time dynamics of the spin correlations and the concurrence using two techniques, namely the time-dependent density matrix renormalization group method and a master-equation method. The results from these two approaches are in excellent agreement in the direct-tunneling regime for the case in which the dot is weakly tunnel-coupled to the leads. We present a quantitative analysis of the decay rates of the spin correlations and the concurrence as a function of tunneling rate, interaction strength, and voltage.

cond-mat.mes-hall↗

arXiv2014

Scaling of diffusion constants in the spin-1/2 XX ladder

We study the dynamics of spin currents in the XX spin-1/2 ladder at finite temperature. Within the framework of linear response theory, we numerically calculate autocorrelation functions for quantum systems larger than what is accessible with exact diagonalization using the concept of dynamical quantum typicality. We show that spin Drude weights vanish exponentially fast with increasing system size. As a main result, we unveil qualitatively different dependencies of the spin diffusion coefficient on the rung-interaction strength, resulting from a crossover from exponential to Gaussian dissipation as the rung coupling increases. This behavior is also derived analytically. We further discuss the relation of our results to experiments with cold atomic gases.

cond-mat.str-el↗

arXiv2014

Relaxation and thermalization in the one-dimensional Bose-Hubbard model: A case study for the interaction quantum quench from the atomic limit

Motivated by recent experiments, we study the relaxation dynamics and thermalization in the one-dimensional Bose-Hubbard model induced by a global interaction quench. Specifically, we start from an initial state that has exactly one boson per site and is the ground state of a system with infinitely strong repulsive interactions at unit filling. Using exact diagonalization and the density matrix renormalization group method, we compute the time dependence of such observables as the multiple occupancy and the momentum distribution function. Typically, the relaxation to stationary values occurs over just a few tunneling times. The stationary values are identical to the so-called diagonal ensemble on the system sizes accessible to our numerical methods and we further observe that the micro-canonical ensemble describes the steady state of many observables reasonably well for small and intermediate interaction strength. The expectation values of observables in the canonical ensemble agree quantitatively with the time averages obtained from the quench at small interaction strengths, and qualitatively provide a good description of steady-state values even in parameter regimes where the micro-canonical ensemble is not applicable due to finite-size effects. We discuss our numerical results in the framework of the eigenstate thermalization hypothesis. Moreover, we also observe that the diagonal and the canonical ensemble are practically identical for our initial conditions already on the level of their respective energy distributions for small interaction strengths. Finally, we discuss implications of our results for the interpretation of a recent sudden expansion experiment [Phys. Rev. Lett. 110, 205301 (2013)], in which the same interaction quench was realized.

cond-mat.stat-mech↗

arXiv2014

Real-time and real-space spin- and energy dynamics in one-dimensional spin-1/2 systems induced by local quantum quenches at finite temperatures

We study the spin- and energy dynamics in one-dimensional spin-1/2 systems induced by local quantum quenches at finite temperatures using a time-dependent density matrix renormalization group method. System sizes are chosen large enough to ensure that the time-dependent data for the accesible time scales represents the behavior in the thermodynamic limit. As a main result, we observe a ballistic spreading of perturbations of the energy density in the integrable spin-1/2 XXZ chain for all temperatures and exchange anisotropies, related to the divergent thermal conductivity in this model and the exact conservation of the energy current. In contrast, the spin dynamics is ballistic in the massless phase, but shows a diffusive behavior at high temperatures in the easy-axis phase in the case of a vanishing background spin density. We extract a quantitative estimate for the spin diffusion constant from the time dependence of the spatial variance of the spin density, which agrees well with values obtained from current-current correlation functions using an Einstein relation. As an example for non-integrable models, we consider two-leg ladders, for which we observe indications of diffusive energy and spin dynamics. The relevance of our results for recent experiments with quantum magnets and bosons in optical lattices is discussed.

cond-mat.str-el↗

arXiv2013

Sudden expansion of Mott insulators in one dimension

We investigate the expansion of bosons and fermions in a homogeneous lattice after a sudden removal of the trapping potential using exact numerical methods. As a main result, we show that in one dimension, both bosonic and fermionic Mott insulators expand with the same velocity, irrespective of the interaction strength, provided the expansion starts from the ground state of the trapped gas. Furthermore, their density profiles become identical during the expansion: The asymptotic density dynamics is identical to that of initially localized, non-interacting particles, and the asymptotic velocity distribution is flat. The expansion velocity for initial correlated Mott insulating states is therefore independent of the interaction strength and particle statistics. Interestingly, this non-equilibrium dynamics is sensitive to the interaction driven quantum phase transition in the Bose-Hubbard model: While being constant in the Mott phase, the expansion velocity decreases in the superfluid phase and vanishes for large systems in the non-interacting limit. These results are compared to the set-up of a recent experiment [PRL 110, 205301 (2013)], where the trap opening was combined with an interaction quench from infinitely strong interactions to finite values. We carry out an analogous analysis for a two-component Fermi gas, with similar observations. In addition, we study the effect of breaking the integrability of hard-core bosons in different ways: While the fast ballistic expansion from the ground state of Mott insulators in one dimension remains unchanged for finite interactions, we observe strong deviations from this behavior on a two-leg ladder even in the hard-core case. This change in dynamics bares similarities with the dynamics in the dimensional crossover from one to two dimensions observed in the aformentioned experimental study.

cond-mat.quant-gas↗

arXiv2013

Inducing spin-correlations and entanglement in a double quantum dot through non-equilibrium transport

For a double quantum dot system in a parallel geometry, we demonstrate that by combining the effects of a flux and driving an electrical current through the structure, the spin correlations between electrons localized in the dots can be controlled at will. In particular, a current can induce spin correlations even if the spins are uncorrelated in the initial equilibrium state. Therefore, we are able to engineer an entangled state in this double-dot structure. We take many-body correlations fully into account by simulating the real-time dynamics using the time-dependent density matrix renormalization group method. Using a canonical transformation, we provide an intuitive explanation for our results, related to Ruderman-Kittel-Kasuya-Yoshida physics driven by the bias.

cond-mat.str-el↗

arXiv2013

The Drude weight of the spin-1/2 XXZ chain: density matrix renormalization group versus exact diagonalization

We revisit the problem of the spin Drude weight D of the integrable spin-1/2 XXZ chain using two complementrary approaches, exact diagonalization (ED) and the time-dependent density-matrix renormalization group (tDMRG). We pursue two main goals. First, we present extensive results for the temperature dependence of D. By exploiting time translation invariance within tDMRG, one can extract D for significantly lower temperatures than in previous tDMRG studies. Second, we discuss the numerical quality of the tDMRG data and elaborate on details of the finite-size scaling of the ED results, comparing calculations carried out in the canonical and grand-canonical ensembles. Furthermore, we analyze the behavior of the Drude weight as the point with SU(2)-symmetric exchange is approached and discuss the relative contribution of the Drude weight to the sum rule as a function of temperature.

cond-mat.str-el↗

arXiv2012

Long-time behavior of the momentum distribution during the sudden expansion of a spin-imbalanced Fermi gas in one dimension

We study the sudden expansion of spin-imbalanced ultracold lattice fermions with attractive interactions in one dimension after turning off the longitudinal confining potential. We show that the momentum distribution functions of majority and minority fermions approach stationary values quickly due to a quantum distillation mechanism that results in a spatial separation of pairs and majority fermions. As a consequence, Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) correlations are lost during the expansion. Furthermore, we argue that the shape of the stationary momentum distribution functions can be understood by relating them to the integrals of motion in this integrable quantum system. We discuss our results in the context of proposals to observe FFLO correlations, related to recent experiments by Liao et al., Nature 467, 567 (2010).

cond-mat.str-el↗

arXiv2012

Expansion velocity of a one-dimensional, two-component Fermi gas during the sudden expansion in the ballistic regime

We show that in the sudden expansion of a spin-balanced two-component Fermi gas into an empty optical lattice induced by releasing particles from a trap, over a wide parameter regime, the radius $R_n$ of the particle cloud grows linearly in time. This allow us to define the expansion velocity $V_{ex}$ from $R_n=V_{ex}t$. The goal of this work is to clarify the dependence of the expansion velocity on the initial conditions which we establish from time-dependent density matrix renormalization group simulations, both for a box trap and a harmonic trap. As a prominent result, the presence of a Mott-insulating region leaves clear fingerprints in the expansion velocity. Our predictions can be verified in experiments with ultra-cold atoms.

cond-mat.str-el↗

arXiv2012

Frustrated spin chains in strong magnetic field: dilute two-component Bose gas regime

We study the ground state of frustrated spin-S chains in a strong magnetic field in the immediate vicinity of saturation. In strongly frustrated chains, the magnon dispersion has two degenerate minima at inequivalent momenta $\pm Q$, and just below the saturation field the system can be effectively represented as a dilute one-dimensional lattice gas of two species of bosons that correspond to magnons with momenta around $\pm Q$. We present a theory of effective interactions in such a dilute magnon gas that allows us to make quantitative predictions for arbitrary values of the spin. With the help of this method, we are able to establish the magnetic phase diagram of frustrated chains close to saturation and study phase transitions between several nontrivial states, including a two-component Luttinger liquid, a vector chiral phase, and phases with bound magnons. We study those phase transitions numerically and find a good agreement with our analytical predictions.

cond-mat.str-el↗

arXiv2012

Dimer, trimer and FFLO liquids in mass- and spin-imbalanced trapped binary mixtures in one dimension

We present a systematic investigation of attractive binary mixtures in presence of both spin- and mass-imbalance in one dimensional setups described by the Hubbard model. After discussing typical cold atomic experimental realizations and the relation between microscopic and effective parameters, we study several many-body features of trapped Fermi-Fermi and Bose-Bose mixtures such as density profiles, momentum distributions and correlation functions by means of numerical density-matrix-renormalization-group and Quantum Monte Carlo simulations. In particular, we focus on the stability of Fulde-Ferrell-Larkin-Ovchinnikov, dimer and trimer fluids in inhomogeneous situations, as typically realized in cold gas experiments due to the harmonic confinement. We finally consider possible experimental signatures of these phases both in the presence of a finite polarization and of a finite temperature.

cond-mat.quant-gas↗

arXiv2011

Resonances in a dilute gas of magnons and metamagnetism of isotropic frustrated ferromagnetic spin chains

We show that spin-S chains with SU(2)-symmetric, ferromagnetic nearest-neighbor and frustrating antiferromagnetic next-nearest-neighbor exchange interactions exhibit metamagnetic behavior under the influence of an external magnetic field for small S, in the form of a first-order transition to the fully polarized state. The corresponding magnetization jump increases gradually starting from an S-dependent critical value of exchange couplings and takes a maximum in the vicinity of a ferromagnetic Lifshitz point. The metamagnetism results from resonances in the dilute magnon gas caused by an interplay between quantum fluctuations and frustration.

cond-mat.str-el↗