Thermodynamic limit and surface energy of the XXZ spin chain with arbitrary boundary fields

Abstract

In two previous papers [26, 27], the exact solutions of the spin-1/2 chains with arbitrary boundary fields were constructed via the off-diagonal Bethe ansatz (ODBA). Here we introduce a method to approach the thermodynamic limit of those models. The key point is that at a sequence of degenerate points of the crossing parameter η=η_m, the off-diagonal Bethe ansatz equations (BAEs) can be reduced to the conventional ones. This allows us to extrapolate the formulae derived from the reduced BAEs to arbitrary ηcase with O(N^{-2}) corrections in the thermodynamic limit N\to\infty. As an example, the surface energy of the XXZ spin chain model with arbitrary boundary magnetic fields is derived exactly. This approach can be generalized to all the ODBA solvable models.

Published version

References in corpus (5)

• Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
• Bethe ansatz solution of zero-range process with nonuniform stationary state
• Exact solution of the one-dimensional Hubbard model with arbitrary boundary magnetic fields
• Bethe ansatz solution of discrete time stochastic processes with fully parallel update
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Cited by in corpus (26)

• Modified algebraic Bethe ansatz for XXZ chain on the segment - I - triangular cases
• Modified algebraic Bethe ansatz for XXZ chain on the segment - II - general cases
• Bethe states of the XXZ spin-1/2 chain with arbitrary boundary fields
• Exact solution of the Izergin-Korepin model with general non-diagonal boundary terms
• Thermodynamic limit and boundary energy of the SU(3) spin chain with non-diagonal boundary fields
• Quantum impurity in a Luttinger liquid: Exact solution of the Kane-Fisher model
• Exact surface energy and helical spinons in the XXZ spin chain with arbitrary non-diagonal boundary fields
• Exact solution of the spin-s Heisenberg chain with generic non-diagonal boundaries
• Exact boundary free energy of the open XXZ chain with arbitrary boundary conditions
• Entanglement and boundary entropy in quantum spin chains with arbitrary direction of the boundary magnetic fields
• Thermodynamic limit and twisted boundary energy of the XXZ spin chain with antiperiodic boundary condition
• Entanglement entropy in quantum spin chains with broken parity number symmetry
• Surface energy of the one-dimensional supersymmetric $t-J$ model with unparallel boundary fields
• Surface energy and elementary excitations of the XXZ spin chain with arbitrary boundary fields
• On the complete-spectrum characterization of quantum integrable spin chains via the inhomogeneous T-Q relation
• Thermodynamic limit and boundary energy of the spin-1 Heisenberg chain with non-diagonal boundary fields
• Thermodynamic limit of the spin-$\frac{1}{2}$ XYZ spin chain with the antiperiodic boundary condition
• A representation basis for the quantum integrable spin chain associated with the su(3) algebra
• Bethe states of the trigonometric SU(3) spin chain with generic open boundaries
• Ground state solutions of inhomogeneous Bethe equations
• Root patterns and exact surface energy of the spin-1 Heisenberg model with generic open boundaries
• Exact solution of the trigonometric SU(3) spin chain with generic off-diagonal boundary reflections
• Non-linear integral equations for the XXX spin-1/2 quantum chain with non-diagonal boundary fields
• Exact physical quantities of the XYZ spin chain in the thermodynamic limit
• Exact surface energy of the Hubbard model with nonparallel boundary magnetic fields
• A note on a boundary sine-Gordon model at the free-Fermion point