Critical Scaling of Entropy and Thermal Drude Weight in Anisotropic Heisenberg Antiferromagnets: A Thermodynamic Quest for Quantum Criticality

Abstract

Up to now, probing the quantum phase transition (QPT) and quantum critical (QC) phenomena at finite temperatures in one-dimensional (1D) spin systems still lacks an in-depth understanding. Herein, we study the QPT and thermodynamics of 1D spin-1/2 anisotropic Heisenberg antiferromagnetic chains by Green’s function theory. The quantum phase diagram is renormalized by the anisotropy (∆), which manifests a quantum critical point (QCP) hc = 1 + ∆ signaling the transition from gapless Tomonaga–Luttinger liquid (TLL) to gapped ferromagnetic (FM) state, demonstrated by the magnetic entropy and thermal Drude weight. At low temperatures, it is shown that two crossover temperatures fan out a QC regime and capture the QCP via the linear extrapolation to zero temperature. In addition, around QCP, the QC scaling is performed by analyzing the entropy and thermal Drude weight to extract the critical exponents (α, δ, and β) that fulfill the Essamm–Fisher scaling law, which provides a novel thermodynamic means to detect QPT for experiment. Furthermore, scaling hypothesis equations with two rescaled manners are proposed to testify the scaling analysis, for which all the data points fall on a universal curve or two independent branches for the plot against rescaled field or temperature, implying the self-consistency and reliability of the obtained critical exponents.

Geometric entropy of plant leaves: A measure of morphological complexity

“…Entropy is a ubiquitous concept that reveals a complicated picture in almost all fields ranging from information [ 30 , 31 ], thermodynamics [ 32 , 33 ], biology [ 34 , 35 ], materials [ 36 , 37 ], and economics [ 38 , 39 ]. While some of these are probability distribution functions, others are not.…”

Geometric Entropy of plant leaves: A measure of morphological complexity

“…Entropy is a ubiquitous concept that reveals a complicated picture in almost all fields ranging from information [30,31], thermodynamics [32,33], biology [34,35], materials [36,37], and economics [38,39].…”

Geometric Entropy of Plant Leaves: A Measure of Morphological Complexity

“…Entropy is a ubiquitous concept that reveals a complicated picture in almost all fields ranging from information (Yang et al 2020;Ben-Gal and Kagan 2021), thermodynamics (Tan et al 2021;Ding and Zhong 2022), biology (Wimmer et al 2021;Vanchurin et al 2022), materials (Saidi et al 2021;Sun and Dai 2021), and economics (Rosser 2016;Yan et al 2020). While some of these are probability distribution functions, others are not.…”