The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
Solving gapped Hamiltonians locally
Open accessAbstract
We show that any short-range Hamiltonian with a gap between the ground and excited states can be written as a sum of local operators, such that the ground state is an approximate eigenvector of each operator separately. We then show that the ground state of any such Hamiltonian is close to a generalized matrix product state. The range of the given operators needed to obtain a good approximation to the ground state is proportional to the square of the logarithm of the system size times a characteristic ``factorization length.'' Applications to many-body quantum simulation are discussed. We also consider density matrices of systems at non zero temperature.
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Citations
Cites
Density matrix formulation for quantum renormalization groups
White, S. R. (1992) · Physical Review Letters · doi:10.1103/physrevlett.69.2863 · Cited by 7,702
The finite group velocity of quantum spin systems
Lieb, E. H., & Robinson, D. W. (1972) · Communications in Mathematical Physics · doi:10.1007/bf01645779 · Cited by 1,463
Cited by
Georgescu, I. M., Ashhab, S., & Nori, F. (2014) · Reviews of Modern Physics · doi:10.1103/revmodphys.86.153 · Cited by 2,932
“…studied, and several methods have been developed (see, e.g., (Berry et al., 2007; Bravyi et al., 2008; Bremner et al., 2005; Brown et al., 2011; Dodd et al., 2002; Dür et al., 2008; Hastings, 2006; Wang and Zanardi, 2002; Wocjan et al., 2002a,b,c)), but it still remains a difficult problem.”
MethodOrús, R. (2014) · Annals of Physics · doi:10.1016/j.aop.2014.06.013 · Cited by 2,255
Verstraete, F., Murg, V., & Cirac, J. I. (2008) · Advances in Physics · doi:10.1080/14789940801912366 · Cited by 1,762
An area law for one-dimensional quantum systems
Hastings, M. B. (2007) · Journal of Statistical Mechanics: Theory and Experiment · doi:10.1088/1742-5468/2007/08/p08024 · Cited by 1,131
Self-citationMatrix product states and projected entangled pair states: Concepts, symmetries, theorems
Cirac, J. I., Pérez-García, D., Schuch, N., & Verstraete, F. (2021) · Reviews of Modern Physics · doi:10.1103/revmodphys.93.045003 · Cited by 769
Metadata
- Authors
- Hastings, M. B.
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2006-02-22
- Volume
- 73
- Issue
- 8
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W1969631049
- Cited by
- 239
- References
- 2
- FWCI
- 5.80
- Type
- journal article
- Language
- en
- Open access
- green
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