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

2015 ◽  
Vol 91 (11) ◽  
Author(s):  
Ho N. Phien ◽  
Ian P. McCulloch ◽  
Guifré Vidal
Keyword(s):  
Time Evolution ◽  
Fast Convergence ◽  
Imaginary Time ◽  
Network Algorithms ◽  
Tensor Network

scholarly journals Time-dependent study of disordered models with infinite projected entangled pair states

2019 ◽  
Vol 6 (3) ◽  
Author(s):  
Claudius Hubig ◽  
J. Ignacio Cirac
Keyword(s):  
Time Evolution ◽  
Ground State ◽  
Heisenberg Model ◽  
Infinite System ◽  
Square Lattice ◽  
Imaginary Time ◽  
Time Dynamics ◽  
Tensor Network ◽  
Disordered Models ◽  
Short Time

Infinite projected entangled pair states (iPEPS), the tensor network ansatz for two-dimensional systems in the thermodynamic limit, already provide excellent results on ground-state quantities using either imaginary-time evolution or variational optimisation. Here, we show (i) the feasibility of real-time evolution in iPEPS to simulate the dynamics of an infinite system after a global quench and (ii) the application of disorder-averaging to obtain translationally invariant systems in the presence of disorder. To illustrate the approach, we study the short-time dynamics of the square lattice Heisenberg model in the presence of a bi-valued disorder field.

scholarly journals Geometry of variational methods: dynamics of closed quantum systems

2020 ◽  
Vol 9 (4) ◽  
Author(s):  
Lucas Hackl ◽  
Tommaso Guaita ◽  
Tao Shi ◽  
Jutho Haegeman ◽  
Eugene Demler ◽  
...  
Keyword(s):  
Variational Methods ◽  
Time Evolution ◽  
Coherent States ◽  
Geometric Approach ◽  
Quantum Systems ◽  
Imaginary Time ◽  
Excitation Spectra ◽  
Spectral Functions ◽  
Geometric Framework ◽  
Gaussian States

We present a systematic geometric framework to study closed quantum systems based on suitably chosen variational families. For the purpose of (A) real time evolution, (B) excitation spectra, (C) spectral functions and (D) imaginary time evolution, we show how the geometric approach highlights the necessity to distinguish between two classes of manifolds: Kähler and non-Kähler. Traditional variational methods typically require the variational family to be a Kähler manifold, where multiplication by the imaginary unit preserves the tangent spaces. This covers the vast majority of cases studied in the literature. However, recently proposed classes of generalized Gaussian states make it necessary to also include the non-Kähler case, which has already been encountered occasionally. We illustrate our approach in detail with a range of concrete examples where the geometric structures of the considered manifolds are particularly relevant. These go from Gaussian states and group theoretic coherent states to generalized Gaussian states.

scholarly journals Publisher Correction: Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution

2020 ◽  
Vol 16 (2) ◽  
pp. 231-231 ◽  
Author(s):  
Mario Motta ◽  
Chong Sun ◽  
Adrian T. K. Tan ◽  
Matthew J. O’Rourke ◽  
Erika Ye ◽  
...  
Keyword(s):  
Time Evolution ◽  
Quantum Computer ◽  
Imaginary Time ◽  
Thermal States

scholarly journals Benchmarking Quantum Chemistry Computations with Variational, Imaginary Time Evolution, and Krylov Space Solver Algorithms

2021 ◽  
pp. 2100012
Author(s):  
Kübra Yeter‐Aydeniz ◽  
Bryan T. Gard ◽  
Jacek Jakowski ◽  
Swarnadeep Majumder ◽  
George S. Barron ◽  
...  
Keyword(s):  
Quantum Chemistry ◽  
Time Evolution ◽  
Imaginary Time ◽  
Krylov Space
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