Block Decimation Method Research Articles

Quantum spinon oscillations in a finite one-dimensional transverse Ising model

The full quantum dynamics of a spinon under external magnetic fields is investigated by using the time-evolving block decimation (TEBD) method within the microcanonical picture of transport. We show that the center of the spinon oscillates back and forth in the absence of dissipation. The quantum many-body behavior can be understood in a single-particle picture of transport and Bloch oscillations, where quantum fluctuations induce finite life times. Transport, oscillations and lifetimes can be tuned to some degree separately by external fields. Other nontrivial dynamics such as resonance as well as chaos have also been discussed.

Noise correlations of one-dimensional Bose mixtures in optical lattices

We study the noise correlations of one-dimensional binary Bose mixtures, as a probe of their quantum phases. In previous work, we found a rich structure of many-body phases in such mixtures, such as paired and counterflow superfluidity. Here we investigate the signature of these phases in the noise correlations of the atomic cloud after time-of-flight expansion, using both Luttinger liquid theory and the time-evolving block decimation (TEBD) method. We find that paired and counterflow superfluidity exhibit distinctive features in the noise spectra. We treat both extended and inhomogeneous systems, and our numerical work shows that the essential physics of the extended systems is present in the trapped-atom systems of current experimental interest. For paired and counterflow superfluid phases, we suggest methods for extracting Luttinger parameters from noise correlation spectroscopy.

Interaction-induced anomalous transport behavior in one-dimensional optical lattices

The non-equilibrium dynamics of spin impurity atoms in a strongly interacting one-dimensional (1D) Bose gas under the gravity field is studied. We show that due to the non-equilibrium preparation of the initial state as well as the interaction between the impurity atoms and other bosons, a counterintuitive phenomenon may emerge: the impurity atoms could propagate upwards automatically in the gravity field . The effects of the strength of interaction, the gradient of the gravity field, as well as the different configurations of the initial state are investigated by studying the time-dependent evolution of the 1D strongly interacting bosonic system using time-evolving block decimation (TEBD) method. A profound connection between this counterintuitive phenomenon and the repulsive bound pair is also revealed.

Multipartite entanglement measures and quantum criticality from matrix and tensor product states

We compute the multipartite entanglement measures such as the global entanglement of various one- and two-dimensional quantum systems to probe the quantum criticality based on the matrix and tensor product states (MPSs/TPSs). We use infinite time-evolving block decimation (iTEBD) method to find the ground states numerically in the form of MPSs/TPSs, and then evaluate their entanglement measures by the method of tensor renormalization group (TRG). We find these entanglement measures can characterize the quantum phase transitions by their derivative discontinuity right at the critical points in all models considered here. We also comment on the scaling behaviors of the entanglement measures by the ideas of quantum state renormalization group transformations.

Bose-Hubbard ground state: Extended Bogoliubov and variational methods compared with time-evolving block decimation

We determine the ground-state properties of a gas of interacting bosonic atoms in a one-dimensional optical lattice. The system is modeled by the Bose-Hubbard Hamiltonian. We show how to apply the time-evolving block decimation method to systems with periodic boundary conditions and employ it as a reference to find the ground state of the Bose-Hubbard model. Results are compared with recently proposed approximate methods, such as Hartree-Fock-Bogoliubov (HFB) theories generalized for strong interactions and the variational Bijl-Dingle-Jastrow method. We find that all HFB methods do not bring any improvement to the Bogoliubov theory and therefore provide correct results only in the weakly interacting limit, where the system is deeply in the superfluid regime. On the other hand, the variational Bijl-Dingle-Jastrow method is applicable for much stronger interactions but is essentially limited to the superfluid regime as it reproduces the superfluid--Mott-insulator transition only qualitatively.

Heavily Damped Motion of One-Dimensional Bose Gases in an Optical Lattice

We study the dynamics of strongly correlated one-dimensional Bose gases in a combined harmonic and optical lattice potential subjected to sudden displacement of the confining potential. Using the time-evolving block decimation method, we perform a first-principles quantum many-body simulation of the experiment of Fertig et al. [Phys. Rev. Lett. 94, 120403 (2005)] across different values of the lattice depth ranging from the superfluid to the Mott insulator regimes. We find good quantitative agreement with this experiment: the damping of the dipole oscillations is significant even for shallow lattices, and the motion becomes overdamped with increasing lattice depth as observed. We show that the transition to overdamping is attributed to the decay of superfluid flow accelerated by quantum fluctuations, which occurs well before the emergence of Mott insulator domains.

Creating a supersolid in one-dimensional Bose mixtures

We identify a one-dimensional supersolid phase in a binary mixture of near-hard-core bosons with weak, local interspecies repulsion. We find realistic conditions under which such a phase, defined here as the coexistence of quasisuperfluidity and quasi-charge-density-wave order, can be produced and observed in finite ultracold atom systems in a harmonic trap. Our analysis is based on Luttinger liquid theory supported by numerical calculations using the time-evolving block decimation method. Clear experimental signatures of these two orders can be found, respectively, in time-of-flight interference patterns and the structure factor $S(k)$ derived from density correlations.

Reentrant quantum phase transition in double-well optical lattices

We study the quantum phases of bosons confined to a combined potential of a one-dimensional double-well optical lattice and a parabolic trap (two-legged ladders). We apply the time-evolving block decimation method to the corresponding ladders described by a two-legged Bose-Hubbard model. In the absence of a parabolic trap, the system of bosons in the double-well optical lattice exhibits a reentrant quantum phase transition between Mott insulator and superfluid phases at unit filling as the tilt of the double wells is increased. We show that this reentrant phase transition still occurs in the presence of a parabolic trap, and we suggest that it can be detected experimentally by measuring matter-wave interference patterns.

Band offset in GaAs/AlxGa1-xAs multiple quantum wells calculated with the sp3s* tight-binding model.

By incorporating a block-decimation method to the ${\mathit{sp}}^{3}$${\mathit{s}}^{\mathrm{*}}$ tight-binding model, we have studied the evolution of ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As electronic band structure as a function of Al composition, including the compositional correlation effect. Using the experimental data of a GaAs/AlAs multiple quantum well, we obtain the band edges of an ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As alloy as functions of x, from which the band offsets \ensuremath{\Delta}${\mathit{E}}_{\mathit{V}}$ and \ensuremath{\Delta}${\mathit{E}}_{\mathit{C}}$ as well as the band-offset coefficient Q=\ensuremath{\Delta}${\mathit{E}}_{\mathit{C}}$/(\ensuremath{\Delta}${\mathit{E}}_{\mathit{C}}$+\ensuremath{\Delta}${\mathit{E}}_{\mathit{V}}$) are derived for arbitrary Al concentration. The result agrees well with experiment.

Study of Electronic Spectra in Inhomogeneous Disordered Chains by Renormalization-Group Block-Decimation Method

We have generalized the renormalization-group block-decimation method to study the spectra of the inhomogeneous disordered binary alloy chains. The numerical results for the densities of states in periodically modulated disordered chains are obtained.

Renormalisation-group block-decimation method for the disordered one-dimensional system

Using a block-decimation scheme the authors have derived a recursion relation to renormalise the Green's function equation of motion for disordered one-dimensional systems. The short-range correlation and the cluster states can be well treated by this method.