Adaptive Time-dependent Density-matrix Renormalization Group Research Articles

Adaptive density matrix renormalization group for disordered systems

We propose a simple modification of the density matrix renormalization group (DMRG) method in order to tackle strongly disordered quantum spin chains. Our proposal, akin to the idea of the adaptive time-dependent DMRG, enables us to reach larger system sizes in the strong disorder limit by avoiding most of the metastable configurations which hinder the performance of the standard DMRG method. We benchmark our adaptive method by revisiting the random antiferromagnetic XXZ spin-1/2 chain for which we compute the random-singlet ground-state average spin-spin correlation functions and von Neumann entanglement entropy. We then apply our method to the bilinear-biquadratic random antiferromagnetic spin-1 chain tuned to the antiferromagnet and gapless highly symmetric SU(3) point. We find the new result that the mean correlation function decays algebraically with the same universal exponent $\phi=2$ as the spin-1/2 chain. We then perform numerical and analytical strong-disorder renormalization-group calculations which confirm this finding and generalize it for any highly symmetric SU($N$) random-singlet state.

Entanglement evolution across defects in critical anisotropic Heisenberg chains

We study the out-of-equilibrium time evolution after a local quench connecting two anisotropic spin-1/2 XXZ Heisenberg open chains via an impurity bond. The dynamics is obtained by means of the adaptive time-dependent density-matrix renormalization group. We show that the entanglement entropies (von Neumann and Rényi) in the presence of a weakened bond depend on the sign of the bulk interaction. For an attractive interaction (Δ < 0), the defect turns out to be irrelevant and the evolution is asymptotically equivalent to the one without defect obtained by conformal field theory. For a repulsive interaction (Δ > 0), the defect is relevant and the entanglement saturates to a finite value. This out-of-equilibrium behavior generalizes the well-known results for the ground-state entanglement entropy of the model.

Quantum Discord and Entanglement in Heisenberg XXZ Spin Chain after Quenches

Using the adaptive time-dependent density-matrix renormalization group method, the dynamics of entanglement and quantum discord of an one-dimensional spin-1/2 XXZ chain is studied when anisotropic interaction quenches are applied at different temperatures. The dynamics of the quantum discord and pairwise entanglement between the nearest qubits shows that the entanglement and quantum discord will first oscillate and then approach to a constant value. The quantum discord can be used to predict the quantum phase transition, while the entanglement cannot.

Quench dynamics of entanglement in an open anisotropic spin-12Heisenberg chain

The quantum entanglement dynamics of a one-dimensional spin-$1/2$ anisotropic $\mathit{XXZ}$ model is studied using the method of the adaptive time-dependent density-matrix renormalization group when two cases of quenches are performed in the system. An anisotropic interaction quench and the maximum number of domain walls of a staggered magnetization quench are considered. The dynamics of the pairwise entanglement between the nearest two qubits in the spin chain is investigated. The entanglement of the two spin qubits can be created and oscillates in both cases of the quench. The anisotropic interaction has a strong influence on the oscillation frequency of the entanglement.

Time evolution of correlations in strongly interacting fermions after a quantum quench

Using the adaptive time-dependent density-matrix renormalization group, we study the time evolution of density correlations of interacting spinless fermions on a one-dimensional lattice after a sudden change in the interaction strength. Over a broad range of model parameters, the correlation function exhibits a characteristic light-cone-like time evolution representative of a ballistic transport of information. Such behavior is observed both when quenching an insulator into the metallic region and also when quenching within the insulating region. However, when a metallic state beyond the quantum critical point is quenched deep into the insulating regime, no indication for ballistic transport is observed. Instead, stable domain walls in the density correlations emerge during the time evolution, consistent with the predictions of the Kibble-Zurek mechanism.

Ground-state properties of fermions in double-well optical lattices

We investigate the ground-state properties of fermions trapped in a one-dimensional double-well optical lattice by means of the density-matrix renormalization group method. A weak harmonic confinement potential inherent in real experiments, which makes the system inhomogeneous, is also considered. Under certain conditions for interactions, we find that two kinds of insulating regions coexist at half-filling and three-quarters filling due to the double-well structure and the system inhomogeneity. We further study the dynamical properties of the system by employing the adaptive time-dependent density-matrix renormalization group method. When the double-well lattice is suddenly changed into a normal single-well lattice, the two insulating regions gradually disappear under time evolution, which is accompanied by oscillating behavior of the local density characteristic of many-body fermionic systems.

The spin-current blockade in Luttinger liquid

We investigate the spin-charge separation in the Luttinger liquid with a defective bond of controllable spin-dependent hopping by using the adaptive time-dependent density-matrix renormalization group method. The model is the non-half-filled Hubbard chain with this special bond, which is found to block the relevant spin current with little influence on charge current. We have considered the pure spin and charge currents induced by the voltage biases that are applied to the ideal leads attached at the ends of this Hubbard chain. The phenomenon is so robust that one may utilize it to observe the spin-charge separation directly.

Coherence loss and recovery of an electron spin coupled inhomogeneously to a one-dimensional interacting spin bath: An adaptive time-dependent density-matrix renormalization group study

Coherence evolution and echo effect of an electron spin, which is coupled inhomogeneously to an interacting one-dimensional finite spin bath via hyperfine-type interaction, are studied using the adaptive time-dependent density-matrix renormalization group method. It is found that the interplay of the coupling inhomogeneity and the transverse intrabath interactions results in two qualitatively different coherence evolutions, namely, a coherence-preserving evolution characterized by periodic oscillation and a complete decoherence evolution. Correspondingly, the echo effects induced by an electron-spin flip at time tau exhibit stable recoherence pulse sequence for the periodic evolution and a single peak at root 2 tau for the decoherence evolution, respectively. With the diagonal intrabath interaction included, the specific feature of the periodic regime is kept, while the root 2 tau-type echo effect in the decoherence regime is significantly affected. To render the experimental verifications possible, the Hahn echo envelope as a function of tau is calculated, which eliminates the inhomogeneous broadening effect and serves for the identification of the different status of the dynamic coherence evolution, periodic versus decoherence.

Strongly Correlated Fermions after a Quantum Quench

Using the adaptive time-dependent density-matrix renormalization group method, we study the time evolution of strongly correlated spinless fermions on a one-dimensional lattice after a sudden change of the interaction strength. For certain parameter values, two different initial states (e.g., metallic and insulating) lead to observables which become indistinguishable after relaxation. We find that the resulting quasistationary state is nonthermal. This result holds for both integrable and nonintegrable variants of the system.

Separation of spin and charge in cold Fermi gases

One of the key features of one-dimensional systems is the phenomenon of spin–charge separation. We show this separation of spin and charge in real time in the 1D Hubbard model by the application of the adaptive time-dependent density-matrix renormalization group method. It is found for single particle excitations and density wave packets far beyond the low-energy Luttinger liquid theory. An experimental set-up is proposed on how to observe the spin–charge separation with ultracold Fermi gases in a harmonic trap using the presence of the Mott-insulator region. Quantitative estimates for experimental parameters are given.

Spin-Charge Separation in Cold Fermi Gases: A Real Time Analysis

Using the adaptive time-dependent density-matrix renormalization group method for the 1D Hubbard model, the splitting of local perturbations into separate wave packets carrying charge and spin is observed in real time. We show the robustness of this separation beyond the low-energy Luttinger liquid theory by studying the time evolution of single particle excitations and density wave packets. A striking signature of spin-charge separation is found in 1D cold Fermi gases in a harmonic trap at the boundary between liquid and Mott-insulating phases. We give quantitative estimates for an experimental observation of spin-charge separation in an array of atomic wires.

One-dimensional density waves of ultracold bosons in an optical lattice

We investigate the propagation of density-wave packets in a Bose-Hubbard model using the adaptive time-dependent density-matrix renormalization group method. We discuss the decay of the amplitude with time and the dependence of the velocity on density, interaction strength, and the height of the perturbation in a numerically exact way, covering arbitrary interactions and amplitudes of the perturbation. In addition, we investigate the effect of self-steepening due to the amplitude dependence of the velocity and discuss the possibilities for an experimental detection of the moving wave packet in time-of-flight pictures. By comparing the sound velocity to theoretical predictions, we determine the limits of a Gross-Pitaevskii- or Bogoliubov-type description and the regime where repulsive one-dimensional Bose gases exhibit fermionic behavior.

Real-time dynamics in spin-12chains with adaptive time-dependent density matrix renormalization group

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 |upward arrow... upward arrow downward arrow... downward arrow > in using the adaptive time-dependent density-matrix renormalization group (adaptive t-DMRG). Time scales accessible to us are of the order of 100 units of time measured in Planck's/J for almost negligible error in the observables. We find ballistic magnetization transport for small S(z) S(z) interaction and arbitrary dimerization, but almost no transport for stronger S(z) S(z) interaction, with a sharp crossover at J(z) =1 . 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. Overall, errors are extremely small before the "runaway" time.

Time-dependent density-matrix renormalization-group using adaptive effective Hilbertspaces

An algorithm for the simulation of the evolution of slightly entangled quantum states hasbeen recently proposed as a tool to study time-dependent phenomena in one-dimensionalquantum systems. Its key feature is a time-evolving block-decimation (TEBD) procedure toidentify and dynamically update the relevant, conveniently small, subregion of theotherwise exponentially large Hilbert space. Potential applications of the TEBD algorithmare the simulation of time-dependent Hamiltonians, transport in quantum systems far fromequilibrium and dissipative quantum mechanics. In this paper we translate the TEBDalgorithm into the language of matrix product states in order to both highlight and exploitits resemblances to the widely used density-matrix renormalization-group (DMRG)algorithms. The TEBD algorithm, being based on updating a matrix product state intime, is very accessible to the DMRG community and it can be enhanced byusing well-known DMRG techniques, for instance in the event of good quantumnumbers. More importantly, we show how it can be simply incorporated into existingDMRG implementations to produce a remarkably effective and versatile ‘adaptivetime-dependent DMRG’ variant, that we also test and compare to previous proposals.