Dynamical windows for real-time evolution with matrix product states

@article{Phien2013DynamicalWF,
  title={Dynamical windows for real-time evolution with matrix product states},
  author={Ho N. Phien and Guifr{\'e} Vidal and I. P. McCulloch},
  journal={Physical Review B},
  year={2013},
  volume={88},
  pages={035103}
}
We propose the use of a dynamical window to investigate the real-time evolution of quantum many-body systems in a one-dimensional lattice. In a recent paper [Phien et al., Phys. Rev. B 86, 245107 (2012)], we introduced infinite boundary conditions in order to investigate real-time evolution of an infinite system under a local perturbation. This was accomplished by restricting the update of the tensors in the matrix product state to a finite region known as a window, with left and right… 

Time evolution within a comoving window: scaling of signal fronts and magnetization plateaus after a local quench in quantum spin chains

TLDR
A modification of Matrix Product State time evolution to simulate the propagation of signal fronts on infinite one-dimensional systems and finds that for an initial Jordan-Wigner domain wall state, the complete time evolution of the normalised excess longitudinal magnetisation agrees exactly with the particle density of TB fermions.

Infinite boundary conditions for response functions and limit cycles in iDMRG, demonstrated for bilinear-biquadratic spin-1 chains

Response functions 〈Ax(t)By(0)〉 for one-dimensional strongly correlated quantum many-body systems can be computed with matrix product state (MPS) techniques. Especially, when one is interested in

Particle and energy transport in strongly driven one-dimensional quantum systems

This Dissertation concerns the transport properties of a strongly–correlated one–dimensional system of spinless fermions, driven by an external electric field which induces the flow of charges and

Infinite boundary conditions for response functions and limit cycles within the infinite-system density matrix renormalization group approach demonstrated for bilinear-biquadratic spin-1 chains

Response functions $\langle\hat{A}_x(t)\hat{B}_y(0)\rangle$ for one-dimensional strongly correlated quantum many-body systems can be computed with matrix product state (MPS) techniques. Especially,

Fast convergence of imaginary time evolution tensor network algorithms by recycling the environment

TLDR
An environment recycling scheme to speed up a class of tensor network algorithms that produce an approximation to the ground state of a local Hamiltonian by simulating an evolution in imaginary time, which confirms that a consistent choice of gauge in the bond indices confirms that the environment is essentially the same over many time steps and can thus be re-used, leading to very substantial computational savings.

Tensor networks and geometry for the modelling of disordered quantum many-body systems

TLDR
This work uses DMRG to study the one dimensional disordered Bose-Hubbard model at fillings N=L = 1=2, 1 and 2 and shows that the whole phase diagram for each can be successfully obtained by analysing entanglement properties alone.

Tensor networks for the simulation of strongly correlated systems

This thesis treats the classical simulation of strongly-interacting many-body quantum-mechanical systems in more than one dimension using matrix product states and the more general tensor product

Few-body systems capture many-body physics: Tensor network approach

Due to the presence of strong correlations, theoretical or experimental investigations of quantum many-body systems belong to the most challenging tasks in modern physics. Stimulated by tensor

Crossover of correlation functions near a quantum impurity in a Tomonaga-Luttinger liquid

An impurity in a Tomonaga-Luttinger liquid leads to a crossover between short- and long-distance regime which describes many physical phenomena. However, calculation of the entire crossover of

Matrix product state decomposition in machine learning and signal processing

TLDR
Several new algorithms are proposed for tensor object classification, which demonstrate an MPS-based approach as an efficient method against other tensor-based approaches, and new methods for colour image and video completion are introduced, which outperform the current state-of-the-art tensor completion algorithms.