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Variational Study of Fermionic and Bosonic Systems with Non-Gaussian States: Theory and Applications
2017-11-14  【 】【打印】【关闭

CAS Key Laboratory of Theoretical Physics

Institute of Theoretical Physics

Chinese Academy of Sciences

Lunch Seminar

Title

题目

Variational Study of Fermionic and Bosonic Systems with Non-Gaussian States: Theory and Applications

Speaker

报告人

石弢

Affiliation

所在单位

ITP

Date

日期

2017年11月14日(周 二)中午12:00

Venue

地点

Conference Hall 322, ITP/理论物理所322报告厅

 

Abstract

摘要

We present a new variational method for investigating the ground state and out of equilibrium dynamics of quantum many-body bosonic and fermionic systems. Our approach is based on constructing variational wavefunctions which extend Gaussian states by including generalized canonical transformations between the elds. The key advantage of such states compared to simple Gaussian states is presence of non-factorizable correlations and the possibility of describing states with strong entanglement between particles. In contrast to the commonly used canonical transformations, such as the polaron or Lang-Firsov transformations, we allow parameters of the transformations to be time dependent, which extends their regions of applicability. We derive equations of motion for the parameters characterizing the states both in real and imaginary time using the di erential structure of the variational manifold. The ground state can be found by following the imaginary time evolution until it converges to a steady state. Collective excitations in the system can be obtained by linearizing the real-time equations of motion in the vicinity of the imaginary time steady-state solution. Our formalism allows us not only to determine the energy spectrum of quasiparticles and their lifetime, but to obtain the complete spectral functions and to explore far out of equilibrium dynamics such as coherent evolution following a quantum quench. We illustrate and benchmark this framework with several examples: a single polaron in the Holstein and Su-Schrieer-Heeger models, non-equilibrium dynamics in the spin-boson and Kondo models, the superconducting to charge density wave phase transitions in the Holstein model.

Contact Person

所内联系人

周森
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