Ground State of the Quantum Symmetric Finite Size XXZ Spin Chain with Anisotropy Parameter $\Delta =1/2$

Abstract

We find an analytic solution of the Bethe Ansatz equations (BAE) for the special case of a finite XXZ spin chain with free boundary conditions and with a complex surface field which provides for $U_q(sl(2))$ symmetry of the Hamiltonian. More precisely, we find one nontrivial solution, corresponding to the ground state of the system with anisotropy parameter $\Delta =1/2$ corresponding to $q^3=-1$.

6 pages

References in corpus (1)

• Minimal Models of Integrable Lattice Theory and Truncated Functional Equations

Cited by in corpus (25)

• T-systems and Y-systems in integrable systems
• The quantum symmetric XXZ chain at Delta=-1/2, alternating sign matrices and plane partitions
• Thermal entanglement in three-qubit Heisenberg models
• The Importance of being Odd
• Spin chains and combinatorics: twisted boundary conditions
• Non-local space-time supersymmetry on the lattice
• The XXZ spin chain at $\Delta =-1/2$: Bethe roots, symmetric functions and determinants
• Universal finite-size scaling amplitudes in anisotropic scaling
• Exact Ground State and Finite Size Scaling in a Supersymmetric Lattice Model
• A possible combinatorial point for XYZ-spin chain
• Finite Size XXZ Spin Chain with Anisotropy Parameter $\Delta =1/2$
• Finite lattice Bethe ansatz systems and the Heun equation
• Bethe roots and refined enumeration of alternating-sign matrices
• Counting solutions of the Bethe equations of the quantum group invariant open XXZ chain at roots of unity
• Auxiliary matrices for the six-vertex model and the algebraic Bethe ansatz
• Auxiliary matrices on both sides of the equator
• The Finite Size SU(3) Perk-Schultz Model with Deformation Parameter q=exp(i 2 pi/3)
• The nineteen-vertex model and alternating sign matrices
• The Wave Functions for the Free-Fermion Part of the Spectrum of the $S{U}_q(N)$ Quantum Spin Models
• Bethe ansatz solvability and supersymmetry of the $M_2$ model of single fermions and pairs
• Free fermion branches in some quantum spin models
• Exact densities of loops in O(1) dense loop model and of clusters in critical percolation on a cylinder
• On Baxter's Q operator of the higher spin XXZ chain at the Razumov-Stroganov point
• Laws of large numbers in the Raise and Peel model
• Exact densities of loops in O(1) dense loop model and of clusters in critical percolation on a cylinder II: rotated lattice