The tensor network theory library

Al-Assam, Sarah; Clark, Stephen R. L.; Jaksch, Dieter

doi:10.1088/1742-5468/aa7df3

Cited by 65 publications

(81 citation statements)

References 29 publications

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“…Furthermore in figure 7, as the simulation is only on a short timescale, we were able to use the time-evolving block decimation [38] algorithm on a Matrix Product State [39] decomposition of the trajectory wavefunctions, further increasing the available system size. These simulations were performed with the aid of the tensor network theory library [40].…”

Section: Many-body Synchronisation In the Hubbard Modelmentioning

confidence: 99%

“…752180). In carrying out this work we acknowledge the use of the University of Oxford Advanced Research Computing (ARC) facility doi:10.5281/zenodo.22558, the QuTiP Python toolbox for simulating open quantum systems http://qutip.org [45] and the Tensor Network Theory library [40] for performing the TEBD [38] algorithm which produced the data in figure 7.…”

Section: Acknowledgmentsmentioning

confidence: 99%

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Quantum synchronisation enabled by dynamical symmetries and dissipation

et al. 2020

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In nature, instances of synchronisation abound across a diverse range of environments. In the quantum regime, however, synchronisation is typically observed by identifying an appropriate parameter regime in a specific system. In this work we show that this need not be the case, identifying conditions which, when satisfied, guarantee that the individual constituents of a generic open quantum system will undergo completely synchronous limit cycles which are, to first order, robust to symmetry-breaking perturbations. We then describe how these conditions can be satisfied by the interplay between several elements: interactions, local dephasing and the presence of a strong dynamical symmetry-an operator which guarantees long-time non-stationary dynamics. These elements cause the formation of entanglement and off-diagonal long-range order which drive the synchronised response of the system. To illustrate these ideas we present two central examples: a chain of quadratically dephased spin-1s and the many-body charge-dephased Hubbard model. In both cases perfect phase-locking occurs throughout the system, regardless of the specific microscopic parameters or initial states. Furthermore, when these systems are perturbed, their nonlinear responses elicit longlived signatures of both phase and frequency-locking.

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Section: Many-body Synchronisation In the Hubbard Modelmentioning

confidence: 99%

Section: Acknowledgmentsmentioning

confidence: 99%

Quantum synchronisation enabled by dynamical symmetries and dissipation

et al. 2020

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“…In what follows, the specific algorithm we use to perform the evolutions of Eqs. (3) and (4) is timeevolution block decimation (TEBD) [20,45,46]. The TEBD algorithm uses a time step δt resulting in an error, beyond that due to compression, of OðNδt 2 Þ and requires time OðNχ 3 δt −1 Þ (see the Supplemental Material [32]).…”

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confidence: 99%

Capturing Exponential Variance Using Polynomial Resources: Applying Tensor Networks to Nonequilibrium Stochastic Processes

et al. 2015

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Estimating the expected value of an observable appearing in a nonequilibrium stochastic process usually involves sampling. If the observable's variance is high, many samples are required. In contrast, we show that performing the same task without sampling, using tensor network compression, efficiently captures high variances in systems of various geometries and dimensions. We provide examples for which matching the accuracy of our efficient method would require a sample size scaling exponentially with system size. In particular, the high-variance observable e^{-βW}, motivated by Jarzynski's equality, with W the work done quenching from equilibrium at inverse temperature β, is exactly and efficiently captured by tensor networks.

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“…We determine the ground state by performing DMRG calculations [45] with our TNT library [46]. To this end, we map the 2D lattice to a 1D chain by sequentially going through each column of the lattice from bottom to top as in [47].…”

Section: N T 7 W Q 1 F F N G U 4 a A O 4 R H C O I C 6 3 E A D M K mentioning

confidence: 99%

Characterizing the phase diagram of finite-size dipolar Bose-Hubbard systems

et al. 2020

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We use state-of-the-art density matrix renormalization group calculations in the canonical ensemble to determine the phase diagram of the dipolar Bose-Hubbard model on a finite cylinder. We consider several observables that are accessible in typical optical lattice setups and assess how well these quantities perform as order parameters. We find that, especially for small systems, the occupation imbalance is less susceptible to boundary effects than the structure factor in uncovering the presence of a periodic density modulation. By analysing the non-local correlations, we find that the appearance of supersolid order is very sensitive to boundary effects, which may render it difficult to observe in quantum gas lattice experiments with a few tens of particles. Finally, we show how density measurements readily obtainable on a quantum gas microscope allow distinguishing between superfluid and solid phases using unsupervised machine-learning techniques. arXiv:1909.09099v1 [cond-mat.quant-gas]

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The tensor network theory library

Cited by 65 publications

References 29 publications

Quantum synchronisation enabled by dynamical symmetries and dissipation

Quantum synchronisation enabled by dynamical symmetries and dissipation

Capturing Exponential Variance Using Polynomial Resources: Applying Tensor Networks to Nonequilibrium Stochastic Processes

Characterizing the phase diagram of finite-size dipolar Bose-Hubbard systems

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