Twisted Heisenberg chain and the six-vertex model with DWBC

Abstract

In this work we establish a relation between the six-vertex model with Domain Wall Boundary Conditions (DWBC) and the $XXZ$ spin chain with anti-periodic twisted boundaries. More precisely, we demonstrate a formal relation between the zeroes of the partition function of the six-vertex model with DWBC and the zeroes of the transfer matrix eigenvalues associated with the six-vertex model with a particular non-diagonal boundary twist.

17 pages. v2: 20 pages, presentation modified, details of derivations added, references added. v3: typos fixed, minor changes, accepted for publication in JSTAT

References in corpus (4)

• Antiperiodic spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and form factors
• Functional relations from the Yang-Baxter algebra: Eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions
• Domain wall partition functions and KP
• Functional relations and the Yang-Baxter algebra

Cited by in corpus (5)

• New differential equations in the six-vertex model
• Differential approach to on-shell scalar products in six-vertex models
• A novel class of translationally invariant spin chains with long-range interactions
• Six-vertex model and non-linear differential equations I. Spectral problem
• Domain-wall boundaries through non-diagonal twists in the six-vertex model