6533b82ffe1ef96bd1295d69
RESEARCH PRODUCT
Surface free energy of the open XXZ spin-1/2 chain
Balázs PozsgayKarol K. Kozlowskisubject
Statistics and ProbabilityPhysicsHigh Energy Physics - TheoryPartition function (statistical mechanics)Statistical Mechanics (cond-mat.stat-mech)Nonlinear Sciences - Exactly Solvable and Integrable SystemsDiagonalMathematical analysisFOS: Physical sciencesBoundary (topology)Statistical and Nonlinear PhysicsMathematical Physics (math-ph)Function (mathematics)Integral equationHigh Energy Physics - Theory (hep-th)Chain (algebraic topology)Periodic boundary conditionsExactly Solvable and Integrable Systems (nlin.SI)Statistics Probability and UncertaintyCondensed Matter - Statistical MechanicsMathematical PhysicsSpin-½description
We study the boundary free energy of the XXZ spin-$\tf{1}{2}$ chain subject to diagonal boundary fields. We first show that the representation for its finite Trotter number approximant obtained by Bortz, Frahm and G\"{o}hmann is related to the partition function of the six-vertex model with reflecting ends. Building on the Tsuchiya determinant representation for the latter quantity we are able to take the infinite Trotter number limit. This yields a representation for the surface free energy which involves the solution of the non-linear integral equation that governs the thermodynamics of the XXZ spin-1/2 chain subject to periodic boundary conditions. We show that this integral representation allows one to extract the low-$T$ asymptotic behavior of the boundary magnetization at finite external magnetic field on the one hand and numerically plot this function on the other hand.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-01-01 |