Crossovers and critical scaling in the one-dimensional transverse-field Ising model

Abstract

We consider the scaling behavior of thermodynamic quantities in the one-dimensional transverse-field Ising model near its quantum critical point (QCP). Our study has been motivated by the question about the thermodynamical signatures of this paradigmatic quantum critical system and, more generally, by the issue of how quantum criticality accumulates entropy. We find that the crossovers in the phase diagram of temperature and (the non-thermal control parameter) transverse field obey a general scaling ansatz, and so does the critical scaling behavior of the specific heat and magnetic expansion coefficient. Furthermore, the Grüneisen ratio diverges in a power-law way when the QCP is accessed as a function of the transverse field at zero temperature, which follows the prediction of quantum critical scaling. However, at the critical field, upon decreasing the temperature, the Grüneisen ratio approaches a constant instead of showing the expected divergence. We are able to understand this unusual result in terms of a peculiar form of the quantum critical scaling function for the free energy; the contribution to the Grüneisen ratio vanishes at the linear order in a suitable Taylor expansion of the scaling function. In spite of this special form of the scaling function, we show that the entropy is still maximized near the QCP, as expected from the general scaling argument. Our results establish the telltale thermodynamic signature of a transverse-field Ising chain, and will thus facilitate the experimental identification of this model quantum-critical system in real materials.

7 pages, 5 figures

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• Quantum Ising model on the frustrated square lattice
• Universal Thermodynamic Signature of Self-dual Quantum Critical Points
• Cascade of singularities in the spin dynamics of a perturbed quantum critical Ising chain
• Magnetic excitations in the one-dimensional Heisenberg-Ising model with external fields and their experimental realizations
• Local dynamics and thermal activation in the transverse-field Ising chain
• Analytical results for the unusual Grüneisen ratio in the quantum Ising model with Dzyaloshinskii-Moriya interaction
• Signatures of quantum criticality in the complex inverse temperature plane
• Magnetization oscillations in a periodically driven transverse field Ising chain
• Universality of Heisenberg-Ising chain in external fields
• Dimensional reduction of Kitaev spin liquid at quantum criticality
• Finite-Size Scaling Theory at a Self-Dual Quantum Critical Point
• Precursor to Quantum Criticality in Ce-Au-Al Quasicrystal Approximants
• Spin dynamics and dark particle in a weak-coupled quantum Ising ladder with ${\mathcal{D}}_8^{(1)}$ spectrum