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Algebraic Bethe ansatz and tensor networks

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Abstract
The algebraic Bethe ansatz is a prosperous and well-established method for solving one-dimensional quantum models exactly. The solution of the complex eigenvalue problem is thereby reduced to the solution of a set of algebraic equations. Whereas the spectrum is usually obtained directly, the eigenstates are available only in terms of complex mathematical expressions. This makes it very hard, in general, to extract properties from the states, for example, correlation functions. In our work, we apply the tools of tensor-network states to describe the eigenstates approximately as matrix product states. From the matrix product state expression, we then obtain observables like the structure factor, dimer-dimer correlation functions, chiral correlation functions, and one-particle Green function directly.
Keywords
QUANTUM RENORMALIZATION-GROUPS, MATRIX PRODUCT ANSATZ, BOND, GROUND-STATES, SYSTEMS, ANTIFERROMAGNETS, CHAIN

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Please use this url to cite or link to this publication:

Chicago
Murg, V, VE Korepin, and Frank Verstraete. 2012. “Algebraic Bethe Ansatz and Tensor Networks.” Physical Review B 86 (4).
APA
Murg, V., Korepin, V., & Verstraete, F. (2012). Algebraic Bethe ansatz and tensor networks. PHYSICAL REVIEW B, 86(4).
Vancouver
1.
Murg V, Korepin V, Verstraete F. Algebraic Bethe ansatz and tensor networks. PHYSICAL REVIEW B. 2012;86(4).
MLA
Murg, V, VE Korepin, and Frank Verstraete. “Algebraic Bethe Ansatz and Tensor Networks.” PHYSICAL REVIEW B 86.4 (2012): n. pag. Print.
@article{8589191,
  abstract     = {The algebraic Bethe ansatz is a prosperous and well-established method for solving one-dimensional quantum models exactly. The solution of the complex eigenvalue problem is thereby reduced to the solution of a set of algebraic equations. Whereas the spectrum is usually obtained directly, the eigenstates are available only in terms of complex mathematical expressions. This makes it very hard, in general, to extract properties from the states, for example, correlation functions. In our work, we apply the tools of tensor-network states to describe the eigenstates approximately as matrix product states. From the matrix product state expression, we then obtain observables like the structure factor, dimer-dimer correlation functions, chiral correlation functions, and one-particle Green function directly.},
  articleno    = {045125},
  author       = {Murg, V and Korepin, VE and Verstraete, Frank},
  issn         = {2469-9950},
  journal      = {PHYSICAL REVIEW B},
  keywords     = {QUANTUM RENORMALIZATION-GROUPS,MATRIX PRODUCT ANSATZ,BOND,GROUND-STATES,SYSTEMS,ANTIFERROMAGNETS,CHAIN},
  language     = {eng},
  number       = {4},
  pages        = {17},
  title        = {Algebraic Bethe ansatz and tensor networks},
  url          = {http://dx.doi.org/10.1103/PhysRevB.86.045125},
  volume       = {86},
  year         = {2012},
}

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