scholarly journals Self-consistent effective Hamiltonian theory for fermionic many-body systems

2020 ◽  
pp. 2150019
Author(s):  
Xindong Wang ◽  
Hai-Ping Cheng
Keyword(s):  
Hubbard Model ◽  
Order Parameter ◽  
Cooper Pair ◽  
Effective Hamiltonian ◽  
Two Dimensional ◽  
Body System ◽  
Many Body ◽  
Hamiltonian Theory ◽  
Self Consistent ◽  
Many Body Systems

Using a separable many-body variational wavefunction, we formulate a self-consistent effective Hamiltonian theory for fermionic many-body system. The theory is applied to the two-dimensional (2D) Hubbard model as an example to demonstrate its capability and computational effectiveness. Most remarkably for the Hubbard model in 2D, a highly unconventional quadruple-fermion non-Cooper pair order parameter is discovered.

scholarly journals From dynamical localization to bunching in interacting Floquet systems

2018 ◽  
Vol 5 (2) ◽  
Author(s):  
Yuval Baum ◽  
Everard van Nieuwenburg ◽  
Gil Refael
Keyword(s):  
Hubbard Model ◽  
Dynamical Localization ◽  
Body System ◽  
Many Body ◽  
Many Body Systems

We show that a quantum many-body system may be controlled by means of Floquet engineering, i.e., their properties may be controlled and manipulated by employing periodic driving. We present a concrete driving scheme that allows control over the nature of mobile units and the amount of diffusion in generic many-body systems. We demonstrate these ideas for the Fermi-Hubbard model, where the drive renders doubly occupied sites (doublons) the mobile excitations in the system. In particular, we show that the amount of diffusion in the system and the level of fermion-pairing may be controlled and understood solely in terms of the doublon dynamics. We find that under certain circumstances the diffusion in 11D systems may be eliminated completely for extremely long times. We conclude our work by generalizing these ideas to generic many-body systems.

scholarly journals Mathematical Theory of Locally Coherent Quantum Many-Body Fermionic System

2020 ◽  
Author(s):  
Xindong Wang
Keyword(s):  
Excited States ◽  
Energy Functional ◽  
Gauge Fields ◽  
Effective Hamiltonian ◽  
Many Body ◽  
Fermionic System ◽  
Hamiltonian Theory ◽  
System P ◽  
Fermionic Systems ◽  
Self Consistent

Recently Wang and Cheng proposed a self-consistent effective Hamiltonian theory (SCEHT) for many-body fermionic systems (Wang & Cheng, 2019). This paper attempts to provide a mathematical foundation to the formulation of the SCEHT that enables further study of excited states of the system in a more systematic and theoretical manner. Gauge fields are introduced and correct total energy functional in relations to the coupling gauge field is given. We also provides a Monte-Carlo numerical scheme for the search of the ground state that goes beyond the SCEHT.

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 Ergodicity in a two-dimensional self-gravitating many-body system

2016 ◽  
Vol 380 (3) ◽  
pp. 337-348 ◽  
Author(s):  
C.H. Silvestre ◽  
T.M. Rocha Filho
Keyword(s):  
Two Dimensional ◽  
Body System ◽  
Many Body

scholarly journals On the widths and binding energies of K− nuclear states and the role of K− multi-nucleon interactions

2018 ◽  
Vol 181 ◽  
pp. 01009
Author(s):  
Jaroslava Hrtankova ◽  
Jiří Mareš
Keyword(s):  
Bound States ◽  
Binding Energies ◽  
Many Body ◽  
Nucleon Interaction ◽  
Substantial Impact ◽  
Coupled Channels ◽  
Self Consistent ◽  
Interaction Term ◽  
Many Body Systems

We report on our recent self-consistent calculations of K− nuclear quasi-bound states using K− optical potentials derived from chirally motivated meson-baryon coupled channels models [1, 2]. The K− single-nucleon potentials were supplemented by a phenomenological K− multi-nucleon interaction term introduced to achieve good fits to K− atom data. We demonstrate a substantial impact of the K− multi-nucleon absorption on the widths of K− nuclear states. If such states ever exist in nuclear many-body systems, their widths are excessively large to allow observation.

scholarly journals Thermalization of Finite Many-Body Systems by a Collision Model

Entropy ◽  
2019 ◽  
Vol 21 (12) ◽  
pp. 1182 ◽  
Author(s):  
Onat Arısoy ◽  
Steve Campbell ◽  
Özgür E. Müstecaplıoğlu
Keyword(s):  
Weak Coupling ◽  
Target System ◽  
Model Description ◽  
Body System ◽  
Weak Coupling Regime ◽  
Many Body ◽  
Collision Model ◽  
System Transition ◽  
Many Body Systems ◽  
Thermal States

We construct a collision model description of the thermalization of a finite many-body system by using careful derivation of the corresponding Lindblad-type master equation in the weak coupling regime. Using the example of a two-level target system, we show that collision model thermalization is crucially dependent on the various relevant system and bath timescales and on ensuring that the environment is composed of ancillae which are resonant with the system transition frequencies. Using this, we extend our analysis to show that our collision model can lead to thermalization for certain classes of many-body systems. We establish that for classically correlated systems our approach is effective, while we also highlight its shortcomings, in particular with regards to reaching entangled thermal states.

Coherence Length in a Two-Dimensional Anisotropic Model of Superconductivity

1998 ◽  
Vol 12 (32) ◽  
pp. 3475-3483 ◽  
Author(s):  
L. Bujkiewicz ◽  
L. Jacak
Keyword(s):  
Coherence Length ◽  
Order Parameter ◽  
Cooper Pair ◽  
Mean Square ◽  
Two Dimensional ◽  
Anisotropic Model ◽  
Wide Range ◽  
Order Of Magnitude ◽  
Range Of Values

The coherence length as a mean-square radius of a Cooper pair is calculated for various forms of the anisotropic order parameter. A wide range of values of this quantity is obtained and the smallest values are of the order of magnitude of a few lattice spacings.

TWO-DIMENSIONAL QUARTER-FILLED EXTENDED HUBBARD MODEL AT STRONG COUPLING

2005 ◽  
Vol 19 (01n03) ◽  
pp. 213-216
Author(s):  
W. F. LEE ◽  
H. Q. LIN
Keyword(s):  
Hubbard Model ◽  
Correlation Functions ◽  
Nearest Neighbor ◽  
Spin Correlation ◽  
Perturbation Approach ◽  
Effective Hamiltonian ◽  
Two Dimensional ◽  
Extended Hubbard Model ◽  
Neighbor Interaction ◽  
Electron Hopping

In this paper, we generalized the perturbation approach to study the quasi-two-dimension extended Hubbard model. This model is characterizing by intra-chain electron hopping t, on-site Column interaction U, nearest-neighbor interaction V, and inter-chain electron hopping t′ and nearest-neighbor interaction V′. An effective Hamiltonian up to sixth-order in t/U, t/V, t/V′, t′/U, t′/V and t′/V′ expansion was obtained and the spin-spin correlation functions were calculated. We presented results for t=t′, V=V′.

Self‐Consistent Approximations in Many‐Body Systems

1969 ◽  
Vol 10 (9) ◽  
pp. 1804-1808
Author(s):  
M. Revzen ◽  
L. E. H. Trainor
Keyword(s):  
Many Body ◽  
Self Consistent ◽  
Consistent Approximations ◽  
Many Body Systems
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