Six-vertex model and Quantum XXZ Hamiltonian

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 

 

transfer matrix

• finding eigenvalues and eigenvectors of transfer matrix is crucial
• Bethe ansatz equation is used to find the eigenvectors and eigenvalues

 

 

 

 

free energy

• \(F=-kT \ln Z\)

 

 

 

 

 

related items

• Bethe ansatz

 

 

books

• 찾아볼 수학책

• 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/http://en.wikipedia.org/wiki/Ice-type_model
• http://en.wikipedia.org/wiki/
• Princeton companion to mathematics(Companion_to_Mathematics.pdf)

 

 

blogs

• 구글 블로그 검색
  
  • http://blogsearch.google.com/blogsearch?q=
  • http://blogsearch.google.com/blogsearch?q=
  • http://blogsearch.google.com/blogsearch?q=

 

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. 18 (1967), p. 1046. Full Text via CrossRef
E.H. Lieb. Phys. Rev. 19 (1967), p. 108. 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=
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• http://dx.doi.org/