Thermodynamics and short-range correlations of the XXZ chain close to its triple point

Abstract

The XXZ quantum spin chain has a triple point in its ground state $h$-$1/\Delta$ phase diagram. This first order critical point is located at the joint end point of the two second order phase transition lines marking the transition from the gapless phase to the fully polarized phase and to the Néel ordered phase, respectively. We explore the magnetization and the short-range correlation functions in its vicinity using the exact solution of the model. In the critical regime above the triple point we observe a strong variation of all physical quantities on a low energy scale of order $1/\Delta$ induced by the transversal quantum fluctuations. We interpret this phenomenon starting from a strong-coupling perturbation theory about the highly degenerate ground state of the Ising chain at the triple point. From the perturbation theory we identify the relevant scaling of the magnetic field and of the temperature. Applying the scaling to the exact solutions we obtain explicit formulae for the magnetization and short-range correlation functions at low temperatures.

18 pages, 7 figures, v2: figures rearranged, v3: a typo corrected

References in corpus (4)

• Integral representations for correlation functions of the XXZ chain at finite temperature
• Factorization of the finite temperature correlation functions of the XXZ chain in a magnetic field
• Short-distance thermal correlations in the XXZ chain
• Finite Temperature Dynamical Structure Factor of the Heisenberg-Ising Chain

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• Orbital multicriticality in spin gapped quasi-1D antiferromagnets
• Dynamic structure factor of the spin-1/2 XXZ chain in a transverse field
• An integrable spin chain with Hilbert space fragmentation and solvable real time dynamics
• Integrable spin chains and cellular automata with medium range interaction
• Integrable models on Rydberg atom chains
• Efficient Eigenstate Preparation in an Integrable Model with Hilbert Space Fragmentation