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

 

 

transfer matrix

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

 

 

 

 

free energy

• \(F=-kT \ln Z\)

 

 

 

 

 

 

 

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

• 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/