Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session DD01: V: Poster Session I (8:30am-9:30 am, PST)
8:30 AM,
Monday, March 20, 2023
Abstract: DD01.00039 : Memory efficient Fock-space recursion scheme for many-fermion correlation functions*
Presenter:
prabhakar .
(NISER Bhubhaneswar)
Author:
prabhakar .
(NISER Bhubhaneswar)
Collaboration:
NA
properties of many-body quantum systems. The density of states, electronic
conductivity can be directly computed from one and two body excitations
(few-body Green’s functions) in the many-particle ground state. To compute
this few-body Green’s function exactly for lattice fermion systems, one needs
to calculate many-body Green’s functions in vacuum. To compute many-
body Green’s functions in vacuum, we need to invert the resolvent operator
defined as [ω + iη − H]−1 in the relevant particle number sectors of the Fock
space, where ω, η , and H are the frequency, regulator and Hubbard Hamil-
tonian respectively. However, exponential Hilbert space growth limits such
calculations to small system sizes. In our work, we have developed a new
algorithm that allows a mapping between the Hilbert space of an L size pe-
riodic chain of spinless fermions to an abstract one-dimensional Fock-space
lattice with open boundary conditions. At half-filling, our method allows
O(1/L) suppression in RAM usage in the exact computation of many-body
correlations in a vacuum, as compared to brute force methods. We named
this method as Fock-space recursive Green’s functions (F-RGF) method.
We derive exact relations for computing few-body Green’s functions from
the above-mentioned resolvent calculations. While our relations are general
for arbitrary p-body excitations in many-body ground states, for demon-
stration purposes, we compute two-hole excitation spectra in partially-filled
many-body ground states for the Hubbard model that are relevant to spec-
troscopies that measures local few-body density of states.
*Department of Atomic Energy, India under Project No. 12- R&D-NIS-5.00-0100.
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