A Q-operator for the quantum transfer matrix

Abstract

Baxter's Q-operator for the quantum transfer matrix of the XXZ spin-chain is constructed employing the representation theory of quantum groups. The spectrum of this Q-operator is discussed and novel functional relations which describe the finite temperature regime of the XXZ spin-chain are derived. For non-vanishing magnetic field the previously known Bethe ansatz equations can be replaced by a system of quadratic equations which is an important advantage for numerical studies. For vanishing magnetic field and rational coupling values it is argued that the quantum transfer matrix exhibits a loop algebra symmetry closely related to the one of the classical six-vertex transfer matrix at roots of unity.

20 pages, v2: some minor style improvements

References in corpus (17)

• Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation
• Thermodynamics of the Anisotropic Spin-1/2 Heisenberg Chain and Related Quantum Chains
• Quantum Integrable Systems and Elliptic Solutions of Classical Discrete Nonlinear Equations
• Integral representations for correlation functions of the XXZ chain at finite temperature
• Bethe Equations "on the Wrong Side of Equator"
• Integrability of quantum chains: theory and applications to the spin-1/2 $XXZ$ chain
• Reduced qKZ equation and correlation functions of the XXZ model
• A Generalized Q-operator for U_q(\hat(sl_2)) Vertex Models
• A Q-Operator Identity for the Correlation Functions of the Infinite XXZ Spin-Chain
• The 1/2-XXZ spin-chain at finite magnetic field: Crossover phenomena driven by temperature
• A Q-operator for the twisted XXX model
• The twisted XXZ chain at roots of unity revisited
• Auxiliary matrices for the six-vertex model at roots of unity II
• Auxiliary matrices for the six-vertex model and the algebraic Bethe ansatz
• Temperature dependent spatial oscillations in the correlations of the XXZ spin chain
• Auxiliary matrices on both sides of the equator
• Solving Baxter's TQ-equation via representation theory

Cited by in corpus (5)

• Functional relations from the Yang-Baxter algebra: Eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions
• The Baxter's Q-operator for the W-algebra $W_N$
• Bethe Ansatz and Q-operator for the open ASEP
• Universal R-matrix and functional relations
• Exact Large Deviations of the Current in the Asymmetric Simple Exclusion Process with Open Boundaries