Efficient dynamical simulation of strongly correlated one-dimensional quantum systems by Clark, SR, Jaksch, D

“…For an important class of one-dimensional (11)) systems dynamical simulations have become possible since the advent of the time-evolving block decimation (TEBD) algorithm. We study the computational properties of TEBD using the Bose-Hubbard model (BHM) as a test-bed. …”

Directed percolation in nonunitary quantum cellular automata by Ramil Nigmatullin, Elisabeth Wagner, Gavin K. Brennen

“…In this work, we construct a nonunitary quantum CA that generalizes the Domany-Kinzel CA and study the resulting dynamical evolution using numerical simulations using the tensor network infinite time-evolving block decimation (iTEBD) algorithm. We demonstrate that the system undergoes the absorbing/percolating phase transition and that the addition of the Hamiltonian generates coherences, which are a distinct feature of quantum dynamics. …”
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Tensor-network approach to work statistics for one-dimensional quantum lattice systems by Jiayin Gu, Fan Zhang, H. T. Quan

“…In this approach, the dynamics is simulated with time-evolving block decimation (TEBD), and the initial thermal equilibrium state is prepared either directly with TEBD or with minimally entangled typical thermal states, which generates a set of typical states representing the Gibbs canonical ensemble. …”
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Tensor-network approaches to counting statistics for the current in a boundary-driven diffusive system by Jiayin Gu, Fan Zhang

“…Two tensor-network algorithms, namely, density matrix renormalization group and time evolving block decimation, are respectively implemented. …”
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Phonon resonances in atomic currents through Bose-Fermi mixtures in optical lattices by Bruderer, M, Johnson, T, Clark, S, Jaksch, D, Posazhennikova, A, Belzig, W

“…Numerical simulations of the full dynamics of the system based on the time-evolving block decimation algorithm reveal that the phonon resonances should be observable under the conditions of a realistic measuring procedure.…”

Measurement-induced phase transition: A case study in the nonintegrable model by density-matrix renormalization group calculations by Qicheng Tang, W. Zhu

“…As a concrete example, a one-dimensional Bose-Hubbard model is simulated by the matrix product state and time-evolving block decimation. We map out a global phase diagram in terms of the measurement rate in spatial space and time domain, which demonstrates a volume-to-area law entanglement phase transition. …”
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Signatures of the superfluid to Mott-insulator transition in the excitation spectrum of ultracold atoms by Clark, SR, Jaksch, D

“…By using the Time Evolving Block Decimation algorithm, we are able to simulate one-dimensional systems comparable in size to those in the experiment, with harmonic trapping and across many lattice depths ranging from the Mott-insulator to the superfluid regime. …”

Dissipation-induced correlations in one-dimensional bosonic systems by Kiffner, M, Hartmann, M

“…We consider dissipative and conservative two-particle interactions, and integrate the master equation describing the system dynamics via a time-evolving block-decimation (TEBD) algorithm. Our numerical simulations directly apply to stationary-light polaritons in systems where atoms and photons are confined to the hollow core of a photonic crystal fibre. …”

Observation of complex bound states in the spin-1/2 Heisenberg XXZ chain using local quantum quenches. by Ganahl, M, Rabel, E, Essler, F, Evertz, H

“…At time t=0 the field is switched off and the time evolution of observables such as the z component of spin is computed using the time evolving block decimation algorithm. We find that the observables exhibit strong signatures of linearly propagating spinon and bound state excitations. …”

Photoinduced η-pairing at finite temperatures by Satoshi Ejima, Tatsuya Kaneko, Florian Lange, Seiji Yunoki, Holger Fehske

“…The result, obtained by combining the matrix-product-state based infinite time-evolving block decimation technique and the purification method, applies to the thermodynamic limit. …”
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Signatures of the superfluid to Mott-insulator transition in the excitation spectrum of ultracold atoms by Clark, S, Jaksch, D

“…By using the Time Evolving Block Decimation algorithm, we are able to simulate one-dimensional systems comparable in size to those in the experiment, with harmonic trapping and across many lattice depths ranging from the Mott-insulator (MI) to the superfluid (SF) regime. …”

Heat transport in the XXZ spin chain: from ballistic to diffusive regimes and dephasing enhancement by Mendoza-Arenas, J, Al-Assam, S, Clark, SR, Jaksch, D

“…The non-equilibrium steady state of the chain is obtained by simulating its evolution under the corresponding Lindblad master equation, using the time evolving block decimation method. In the absence of dephasing, the heat transport is ballistic for weak interactions, while being diffusive in the strongly interacting regime, as evidenced by the heat current scaling with the system size. …”

Transport in out-of-equilibrium XXZ chains: Exact profiles of charges and currents by Bertini, B, Collura, M, De Nardis, J, Fagotti, M

“…We find excellent agreement (any discrepancy is within the numerical error) between theoretical predictions and numerical simulations of time evolution based on time-evolving block decimation algorithms. As a corollary, we unveil an exact expression for the expectation values of the charge currents in a generic stationary state.…”

Tensor network simulation of chains of non-Markovian open quantum systems by Gerald E. Fux, Dainius Kilda, Brendon W. Lovett, Jonathan Keeling

“…The method combines the process tensor formalism for general (possibly non-Markovian) open quantum systems with time-evolving block decimation for one-dimensional chains. It systematically reduces the numerical complexity originating from system-environment correlations before integrating them into the full many-body problem, making a wide range of applications numerically feasible. …”
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Solitonic excitations in the Ising anisotropic chain BaCo_{2}V_{2}O_{8} under large transverse magnetic field by Quentin Faure, Shintaro Takayoshi, Béatrice Grenier, Sylvain Petit, Stéphane Raymond, Martin Boehm, Pascal Lejay, Thierry Giamarchi, Virginie Simonet

“…The dynamical susceptibility numerically calculated with the infinite time-evolving block decimation method shows an excellent agreement with the measured spectra, which enables us to identify the dispersion branches with elementary excitations. …”
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Dynamical phase transitions in the two-dimensional transverse-field Ising model by Tomohiro Hashizume, Ian P. McCulloch, Jad C. Halimeh

“…We investigate two separate notions of dynamical phase transitions in the two-dimensional nearest-neighbor transverse-field Ising model on a square lattice using matrix product states and a hybrid infinite time-evolving block decimation algorithm, where the model is implemented on an infinitely long cylinder with a finite diameter along which periodic boundary conditions are employed. …”
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Superdiffusive Energy Transport in Kinetically Constrained Models by Marko Ljubotina, Jean-Yves Desaules, Maksym Serbyn, Zlatko Papić

“…Our state-of-the-art numerical simulations, including exact diagonalization and time-evolving block decimation methods, reveal the existence of two distinct transport regimes. …”
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Fast initialization of a high-fidelity quantum register using optical superlattices by Vaucher, B, Clark, SR, Dorner, U, Jaksch, D

“…The dynamics of the transition from a half filled to a commensurately filled lattice is analysed numerically with the help of the time evolving block decimation algorithm and analytically using the Kibble-Zurek theory. …”

Many-body localization in the infinite-interaction limit and the discontinuous eigenstate phase transition by Chun Chen, Yan Chen, Xiaoqun Wang

“…Employing exact diagonalization, Krylov-typicality technique, and time-evolving block decimation, we identify evidence for a constrained MBL phase stabilized by a pure quasirandom transverse field. …”
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Dynamical simulations of classical stochastic systems using matrix product states. by Johnson, T, Clark, S, Jaksch, D

“…We adapt the time-evolving block decimation (TEBD) algorithm, originally devised to simulate the dynamics of one-dimensional quantum systems, to simulate the time evolution of nonequilibrium stochastic systems. …”