scholarly journals Matrix-product-based projected wave functions ansatz for quantum many-body ground states

2012 ◽  
Vol 86 (4) ◽  
Author(s):  
Chung-Pin Chou ◽  
Frank Pollmann ◽  
Ting-Kuo Lee
Keyword(s):  
Ground States ◽  
Wave Functions ◽  
Matrix Product ◽  
Many Body

scholarly journals Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 984
Author(s):  
Regina Finsterhölzl ◽  
Manuel Katzer ◽  
Andreas Knorr ◽  
Alexander Carmele
Keyword(s):  
Time Evolution ◽  
Nearest Neighbor ◽  
Matrix Product ◽  
Body System ◽  
Many Body ◽  
Initial State ◽  
Matrix Product States ◽  
Open Quantum ◽  
Many Body Systems ◽  
The Many

This paper presents an efficient algorithm for the time evolution of open quantum many-body systems using matrix-product states (MPS) proposing a convenient structure of the MPS-architecture, which exploits the initial state of system and reservoir. By doing so, numerically expensive re-ordering protocols are circumvented. It is applicable to systems with a Markovian type of interaction, where only the present state of the reservoir needs to be taken into account. Its adaption to a non-Markovian type of interaction between the many-body system and the reservoir is demonstrated, where the information backflow from the reservoir needs to be included in the computation. Also, the derivation of the basis in the quantum stochastic Schrödinger picture is shown. As a paradigmatic model, the Heisenberg spin chain with nearest-neighbor interaction is used. It is demonstrated that the algorithm allows for the access of large systems sizes. As an example for a non-Markovian type of interaction, the generation of highly unusual steady states in the many-body system with coherent feedback control is demonstrated for a chain length of N=30.

scholarly journals Many-body localization transition in Rokhsar-Kivelson-type wave functions

2015 ◽  
Vol 92 (21) ◽  
Author(s):  
Xiao Chen ◽  
Xiongjie Yu ◽  
Gil Young Cho ◽  
Bryan K. Clark ◽  
Eduardo Fradkin
Keyword(s):  
Wave Functions ◽  
Many Body ◽  
Localization Transition ◽  
Type Wave

Eine Approximation der Löwdinschen natürlichen Orbitale für Moleküle mit einer Green-Funktion-Methode

1972 ◽  
Vol 27 (4) ◽  
pp. 545-552 ◽  
Author(s):  
R. Albat
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Mass Operator ◽  
Ground States ◽  
Present Form ◽  
Many Body ◽  
Natural Orbitals ◽  
First Order ◽  
The Many ◽  
Closed Shells

Abstract An Approximation of Löwdin's Natural Orbitals for Molecules with a Green's Function Method The many-body-pertubation theorie of the single-particle Green's function is used to get an approximate first-order density matrix. Slightly modified SCF-orbitals form the basis for the expansion. The mass-operator in Dyson's equation is considered up to second order in the Perturbation. In the present form the method is only applicable to ground states with closed shells. The ground states of the molecules LiH and NH3 serve as examples to demonstrate the usefulness of the directly calculated natural orbitals for application in the C I-method. The natural orbitals give a much better convergence of the C I-expansion than the SCF-orbitals do.

scholarly journals Hermitizing the HAL QCD potential in the derivative expansion

2020 ◽  
Vol 2020 (2) ◽  
Author(s):  
Sinya Aoki ◽  
Takumi Iritani ◽  
Koichi Yazaki
Keyword(s):  
Phase Shift ◽  
Wave Functions ◽  
Leading Order ◽  
Many Body ◽  
Derivative Expansion ◽  
Local Part ◽  
Scattering Phase ◽  
Many Body Systems ◽  
Local Term ◽  
Better Than

Abstract A formalism is given to hermitize the HAL QCD potential, which needs to be non-Hermitian except for the leading-order (LO) local term in the derivative expansion as the Nambu– Bethe– Salpeter (NBS) wave functions for different energies are not orthogonal to each other. It is shown that the non-Hermitian potential can be hermitized order by order to all orders in the derivative expansion. In particular, the next-to-leading order (NLO) potential can be exactly hermitized without approximation. The formalism is then applied to a simple case of $\Xi \Xi (^{1}S_{0}) $ scattering, for which the HAL QCD calculation is available to the NLO. The NLO term gives relatively small corrections to the scattering phase shift and the LO analysis seems justified in this case. We also observe that the local part of the hermitized NLO potential works better than that of the non-Hermitian NLO potential. The Hermitian version of the HAL QCD potential is desirable for comparing it with phenomenological interactions and also for using it as a two-body interaction in many-body systems.

scholarly journals Hartree–Fock many-body perturbation theory for nuclear ground-states

2016 ◽  
Vol 756 ◽  
pp. 283-288 ◽  
Author(s):  
Alexander Tichai ◽  
Joachim Langhammer ◽  
Sven Binder ◽  
Robert Roth
Keyword(s):  
Perturbation Theory ◽  
Ground States ◽  
Many Body ◽  
Hartree Fock ◽  
Many Body Perturbation Theory
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