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Methods to Explore the Influence of Top-down Visual Processes on Motor Behavior

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Published on: April 16, 2014

Variational Discrete Action Theory.

Zhengqian Cheng¹, Chris A Marianetti¹

¹Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, USA.

Physical Review Letters

|June 10, 2021

Summary

This summary is machine-generated.

A new variational discrete action theory (VDAT) precisely studies quantum Hamiltonians. This method offers accurate ground state properties for many-body systems, improving upon existing approximations.

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Area of Science:

Quantum many-body physics
Condensed matter theory
Computational physics

Background:

Studying ground state properties of quantum many-body Hamiltonians is computationally challenging.
Existing variational methods often involve approximations that limit accuracy.
There is a need for efficient and precise theoretical frameworks.

Purpose of the Study:

Introduce the variational discrete action theory (VDAT) for quantum many-body systems.
Develop a novel variational approach based on the sequential product density matrix (SPD) ansatz.
Provide a flexible framework for studying ground state properties with tunable accuracy.

Main Methods:

The variational discrete action theory (VDAT) is proposed.
It utilizes a sequential product density matrix (SPD) ansatz with an integer parameter N.
A discrete action and integer time Green's function are introduced for SPD evaluation.

Main Results:

VDAT is applied to the Anderson impurity model and the d=∞ Hubbard model.
For the d=∞ Hubbard model, N=2 recovers the Gutzwiller approximation (GA).
N=3 precisely describes Mott physics, matching the Gutzwiller-Baeriswyl wave function with GA-like computational cost.

Conclusions:

VDAT offers a systematically improvable approach to quantum many-body problems.
It provides a precise and efficient description of Mott physics.
VDAT serves as a flexible framework, bridging state-of-the-art and efficient computational methods.