The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
General theory of fractal path integrals with applications to many-body theories and statistical physics
Abstract
A general scheme of fractal decomposition of exponential operators is presented in any order m. Namely, exp[x(A+B)]=Sm(x)+O(xm+1) for any positive integer m, where Sm(x)=et1A et2B et3A et4B⋅⋅⋅etMA with finite M depending on m. A general recursive scheme of construction of {tj} is given explicitly. It is proven that some of {tj} should be negative for m≥3 and for any finite M (nonexistence theorem of positive decomposition). General systematic decomposition criterions based on a new type of time-ordering are also formulated. The decomposition exp[x(A+B)]=[Sm(x/n)]n +O(xm+1/nm) yields a new efficient approach to quantum Monte Carlo simulations.
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Citations
Cites
On the product of semi-groups of operators
Trotter, H. F. (1959) · Proceedings of the American Mathematical Society · doi:10.1090/s0002-9939-1959-0108732-6 · Cited by 2,282
Suzuki, M. (1976) · Communications in Mathematical Physics · doi:10.1007/bf01609348 · Cited by 895
Self-citation
Cited by
The density-matrix renormalization group in the age of matrix product states
Schollwöck, U. (2011) · Annals of Physics · doi:10.1016/j.aop.2010.09.012 · Cited by 4,818
Efficient Simulation of One-Dimensional Quantum Many-Body Systems
Vidal, G. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.040502 · Cited by 1,779
Classical Simulation of Infinite-Size Quantum Lattice Systems in Two Spatial Dimensions
Jordan, J., Orús, R., Vidal, G., Verstraete, F., & Cirac, J. I. (2008) · Physical Review Letters · doi:10.1103/physrevlett.101.250602 · Cited by 710
Efficient Quantum Algorithms for Simulating Sparse Hamiltonians
Berry, D. W., Ahokas, G., Cleve, R., & Sanders, B. C. (2007) · Communications in Mathematical Physics · doi:10.1007/s00220-006-0150-x · Cited by 692
Hybrid Quantum-Classical Algorithms and Quantum Error Mitigation
Endo, S., Cai, Z., Benjamin, S. C., & Yuan, X. (2021) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.90.032001 · Cited by 566
Metadata
- Authors
- Suzuki, M.
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1991-02-01
- Volume
- 32
- Issue
- 2
- Pages
- 400-407
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W2015711858
- Cited by
- 762
- References
- 2
- FWCI
- 6.72
- Type
- journal article
- Language
- en
- Open access
- closed
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- Suzuki, M. (1991). General theory of fractal path integrals with applications to many-body theories and statistical physics. Journal of Mathematical Physics. https://doi.org/10.1063/1.529425
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
