Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
By A. J. Daley, C. Kollath, U. Schollwöck, G. Vidal. 2004
139 citations recorded by the source corpus.
An algorithm for the simulation of the evolution of slightly entangled quantum states has been recently proposed as a tool to study time-dependent phenomena in one-dimensional quantum systems. Its key feature is a time-evolving block-decimation (TEBD) procedure to identify and dynamically update the relevant, conveniently small, subregion of the otherwise exponentially large Hilbert space. Potential applications of the TEBD algorithm are the simulation of time-dependent Hamiltonians, transport in quantum systems far from equilibrium and dissipative quantum mechanics. In this paper we translate the TEBD algorithm into the language of matrix product states in order to both highlight and exploit its resemblances to the widely used density-matrix renormalization-group (DMRG) algorithms. The TEBD algorithm, being based on updating a matrix product state in time, is very accessible to the DMRG community and it can be enhanced by using well-known DMRG techniques, for instance in the event of good quantum numbers. More importantly, we show how it can be simply incorporated into existing DMRG implementations to produce a remarkably effective and versatile ‘adaptive time-dependent DMRG’ variant, that we also test and compare to previous proposals.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/e19058c34d4b40c2937e24483e0cf7d899027e94
Citations in the corpus
- Quantum trajectories and open many-body quantum systems (2014, unknown): “Early development of time-dependent methods has included the time-evolving block decimation (TEBD) algorithm [228, 229], and its integration with DMRG to produce an adaptive time-dependent DMRG (t-DMRG) algorithm [230, 231].”
- QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains (2016, unknown): “In contrast to the tremendous progress made in studying low-energy phenomena based on well-developed sophisticated techniques, such as Quantum Monte Carlo methods [1–3], Density Matrix Renormalisation Group [4,5], Matrix Product States [6], Dynamical Mean-Field Theory [7–9], etc.”
- Time-evolution methods for matrix-product states (2019, unknown): “2004 both for MPS[4, 7, 8] and the original classical DMRG[5, 6].”
- Real-time Dynamics in U(1) Lattice Gauge Theories with Tensor Networks (2015, unknown): “, by means of a SuzukiTrotter decomposition of the time-evolution operator acting on a pair of neighboring sites [76,77].”
- Light-cone-like spreading of correlations in a quantum many-body system (2011, unknown): “We compared the experimental results to numerical simulations of an infinite, homogeneous system at T = 0 using the adaptive time-dependent density matrix renormalization group algorith”
- Efficient Variational Quantum Simulator Incorporating Active Error Minimization (2016, unknown): “nonequilibrium dynamical mean-field theory [27], the time-dependent variational quantum Monte Carlo method [28], timedependent tensor network methods [29, 30], and of course time-dependent density functional theory [31].”