BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:A unified graph-theoretic framework for free-fermion solubility - 
 Sam Elman (UTS Sydney)
DTSTART:20230721T130000Z
DTEND:20230721T140000Z
UID:TALK203521@talks.cam.ac.uk
CONTACT:Sergii Strelchuk
DESCRIPTION:An invaluable method for probing the physics of a quantum many
 -body spin system is a mapping to a system of non-interacting fermions. Th
 e canonical transformation from spin operators to fermionic operators is\,
  of course\, the Jordan-Wigner transform\, which is both generic\, in that
  it is not dependent on fine tuning of coupling coefficients\, and generat
 or-to-generator. In recent work\, it was shown that a Jordan-Wigner-like m
 apping to free fermions is possible if and only if the frustration graph o
 f the Hamiltonian is a line graph. More recently\, a free-fermion model ou
 tside of the Jordan-Wigner framework\, called the four-fermion model\, was
  presented by Fendley in his paper Free fermions in disguise. The solution
  holistically maps the Hamiltonian to free fermions and is generic despite
  transcending the Jordan-Wigner structure. Surprisingly\, the existence of
  a solution of this form is also revealed by the structure of the Hamilton
 ians frustration graph. In this work\, we show that a quantum spin model h
 as an exact description by free fermions if its frustration graph is claw-
 free and contains a structure called simplicial clique\, which is a class 
 of graphs containing the line graph class. In this way\, we unify models w
 hich can be solved by Fendley's method and those soluble by Jordan-Wigner.
  Extending the solution method to arbitrary spatial dimensions is made pos
 sible by the identification of a new class of Hamiltonian symmetries corre
 sponding to graphical structures called generalised even holes. 
LOCATION:MR14
END:VEVENT
END:VCALENDAR