Quantum correlation functions through tensor network path integral
- URL: http://arxiv.org/abs/2308.10540v2
- Date: Wed, 30 Aug 2023 08:16:02 GMT
- Title: Quantum correlation functions through tensor network path integral
- Authors: Amartya Bose
- Abstract summary: tensor networks are utilized for calculating equilibrium correlation function for open quantum systems.
The influence of the solvent on the quantum system is incorporated through an influence functional.
The design and implementation of this method is discussed along with illustrations from rate theory, symmetrized spin correlation functions, dynamical susceptibility calculations and quantum thermodynamics.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Tensor networks have historically proven to be of great utility in providing
compressed representations of wave functions that can be used for calculation
of eigenstates. Recently, it has been shown that a variety of these networks
can be leveraged to make real time non-equilibrium simulations of dynamics
involving the Feynman-Vernon influence functional more efficient. In this work,
tensor networks are utilized for calculating equilibrium correlation function
for open quantum systems using the path integral methodology. These correlation
functions are of fundamental importance in calculations of rates of reactions,
simulations of response functions and susceptibilities, spectra of systems,
etc. The influence of the solvent on the quantum system is incorporated through
an influence functional, whose unconventional structure motivates the design of
a new optimal matrix product-like operator that can be applied to the so-called
path amplitude matrix product state. This complex time tensor network path
integral approach provides an exceptionally efficient representation of the
path integral enabling simulations for larger systems strongly interacting with
baths and at lower temperatures out to longer time. The design and
implementation of this method is discussed along with illustrations from rate
theory, symmetrized spin correlation functions, dynamical susceptibility
calculations and quantum thermodynamics.
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