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Scalable semidefinite programming approach to variational embedding for quantum many-body problems

Journal Article · · Journal of Computational Physics
 [1];  [2]
  1. University of Chicago, IL (United States)
  2. University of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
+ Show Author Affiliations
In quantum embedding theories, a quantum many-body system is divided into localized clusters of sites which are treated with an accurate ‘high-level’ theory and glued together self-consistently by a less accurate ‘low-level’ theory at the global scale. The recently introduced variational embedding approach for quantum many-body problems combines the insights of semidefinite relaxation and quantum embedding theory to provide a lower bound on the ground-state energy that improves as the cluster size is increased. The variational embedding method is formulated as a semidefinite program (SDP), which can suffer from poor computational scaling when treated with black-box solvers. Here, we exploit the interpretation of this SDP as an embedding method to develop an algorithm which alternates parallelizable local updates of the high-level quantities with updates that enforce the low-level global constraints. Moreover, we show how translation invariance in lattice systems can be exploited to reduce the complexity of projecting a key matrix to the positive semidefinite cone.
Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
National Science Foundation (NSF); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), High Energy Physics (HEP)
Grant/Contract Number:
AC02-05CH11231; SC0022232
OSTI ID:
2477264
Journal Information:
Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 510; ISSN 0021-9991
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

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Figures / Tables (8)

Figure 4.1(p. 13)figure Figure 4.1
Figure 4.2(p. 13)figure Figure 4.2
Table 1(p. 13)table Table 1
Table 2(p. 13)table Table 2
Figure 4.3(p. 14)figure Figure 4.3
Table 3(p. 14)table Table 3
Figure 4.4(p. 15)figure Figure 4.4
Table 4(p. 16)table Table 4

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Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
97 MATHEMATICS AND COMPUTING
Augmented Lagrangian
Quantum embedding
Quantum many-body problem
Semidefinite programming