"Six-vertex model and Quantum XXZ Hamiltonian"의 두 판 사이의 차이
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| 15번째 줄: | 15번째 줄: | ||
* on a square lattice with periodic boundary conditions | * on a square lattice with periodic boundary conditions | ||
| − | * on a square lattice with domain wall boundary | + | * on a square lattice with domain wall boundary conditions<br> |
| + | ** this is related to the [[alternating sign matrix theorem|Alternating sign matrix theorem]] | ||
| 32번째 줄: | 33번째 줄: | ||
<h5>anistropic one-dimensional Heisenberg model</h5> | <h5>anistropic one-dimensional Heisenberg model</h5> | ||
| − | * XXZ model | + | * XXZ model or XXZ spin chain |
| + | * http://exactitude.tistory.com/891 | ||
| + | * http://en.wikipedia.org/wiki/Heisenberg_model_(quantum) | ||
* first solved by Bethe | * first solved by Bethe | ||
* Yang and Yang | * Yang and Yang | ||
2010년 2월 26일 (금) 06:38 판
introduction
- XXZ spin chain and the six-vertex transfer matrix have the same eigenvectors
- Boltzmann weights
- monodromy matrix
- trace of monodromy matrix is the transfer matrix
- power of transfer matrix becomes the partition function
types of six vertex models
- on a square lattice with periodic boundary conditions
- on a square lattice with domain wall boundary conditions
- this is related to the Alternating sign matrix theorem
transfer matrix
- finding eigenvalues and eigenvectors of transfer matrix is crucial
- Bethe ansatz equation is used to find the eigenvectors and eigenvalues
anistropic one-dimensional Heisenberg model
- XXZ model or XXZ spin chain
- http://exactitude.tistory.com/891
- http://en.wikipedia.org/wiki/Heisenberg_model_(quantum)
- first solved by Bethe
- Yang and Yang
- ground state eigevector for Hamiltonian is a common eigenvector
partition function
free energy
- \(F=-kT \ln Z\)
correlation functions
books
- Exactly Solved Models in Statistical mechanics
- R. J. Baxter, 1982
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
encyclopedia
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/Ice-type_model
- http://en.wikipedia.org/wiki/Heisenberg_model_(quantum)
- http://en.wikipedia.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
blogs
- 구글 블로그 검색
STATISTICAL MECHANICS-A REVIEW OF
SELECTED RIGOROUS RESULTS1•2
By JOEL L. LEBOWITZ
Method for calculating finite size corrections in Bethe ansatz systems: Heisenberg chain and six-vertex model
de Vega, H. J.; Woynarovich, F.
articles
- Integrability of the Quantum XXZ Hamiltonian
- T Miwa, 2009
- Introduction to solvable lattice models in statistical and mathematical physics
- Tetsuo Deguchi, 2003
- Diagonalization of the XXZ Hamiltonian by Vertex Operators
- Authors: Brian Davies, Omar Foda, Michio Jimbo, Tetsuji Miwa, Atsushi Nakayashiki, 1993
- E. H. Lieb, Phys. Rev. Letters18, 692 (1967)
- Exact Solution of the F Model of An Antiferroelectric
- E.H. Lieb. Phys. Rev. 18 (1967), p. 1046. Full Text via CrossRef
- Exact Solution of the Two-Dimensional Slater KDP Model of a Ferroelectric
- E.H. Lieb. Phys. Rev. 19 (1967), p. 108. Full Text via CrossRef
- Exact Solution of a Two-Dimensional Model for Hydrogen-Bonded Crystals
- B. Sutherland. Phys. Rev. 19 (1967), p. 103. Full Text via CrossRef
- 논문정리
- http://www.ams.org/mathscinet/search/publications.html?pg4=ALLF&s4=
- http://www.zentralblatt-math.org/zmath/en/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://www.ams.org/mathscinet
- http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
- http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
- http://dx.doi.org/