Cylinder partition function of the 6-vertex model from algebraic geometry

Abstract

We compute the exact partition function of the isotropic 6-vertex model on a cylinder geometry with free boundary conditions, for lattices of intermediate size, using Bethe ansatz and algebraic geometry. We perform the computations in both the open and closed channels. We also consider the partial thermodynamic limits, whereby in the open (closed) channel, the open (closed) direction is kept small while the other direction becomes large. We compute the zeros of the partition function in the two partial thermodynamic limits, and compare with the condensation curves.

arXiv commentMore explanations added, a new appendix added, published version

References in corpus (26)

• Unified Approach to Thermodynamic Bethe Ansatz and Finite Size Corrections for Lattice Models and Field Theories
• What is an integrable quench?
• One-point Functions in Defect CFT and Integrability
• One-point Functions in AdS/dCFT from Matrix Product States
• A Gaudin-like determinant for overlaps of Néel and XXZ Bethe states
• AdS/dCFT one-point functions of the SU(3) sector
• Determinant formula for the six-vertex model with reflecting end
• Integrable vertex and loop models on the square lattice with open boundaries via reflection matrices
• Néel-XXZ state overlaps: odd particle numbers and Lieb-Liniger scaling limit
• Surface free energy of the open XXZ spin-1/2 chain
• Fast analytic solver of rational Bethe equations
• Overlaps between eigenstates of the XXZ spin-1/2 chain and a class of simple product states
• Algebraic Bethe ansatz for singular solutions
• Phase diagram of the chromatic polynomial on a torus
• Exact Potts Model Partition Functions for Strips of the Triangular Lattice
• Character decomposition of Potts model partition functions. I. Cyclic geometry
• A distribution approach to finite-size corrections in Bethe Ansatz solvable models
• Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. IV. Chromatic polynomial with cyclic boundary conditions
• On Generalized $Q$-systems
• On zero-remainder conditions in the Bethe ansatz
• Algebraic geometry and Bethe ansatz (I) the quotient ring for BAE
• Exact boundary free energy of the open XXZ chain with arbitrary boundary conditions
• Counting solutions of the Bethe equations of the quantum group invariant open XXZ chain at roots of unity
• Discrete Symmetries and S Matrix of the XXZ Chain
• Phase diagram of the triangular-lattice Potts antiferromagnet
• A generalized Beraha conjecture for non-planar graphs

Cited by in corpus (8)

• Boundary states, overlaps, nesting and bootstrapping AdS/dCFT
• Rational $Q$-systems, Higgsing and Mirror Symmetry
• Geometric Algebra and Algebraic Geometry of Loop and Potts Models
• Spin-$s$ Rational $Q$-system
• The $A_m^{(1)}$ Q-system
• Exact Spin Correlators of Integrable Quantum Circuits from Algebraic Geometry
• Two-dimensional massive integrable models on a torus
• On the Q operator and the spectrum of the XXZ model at root of unity