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A quantum magnetic analogue to the critical point of water
J. Larrea Jiménez, S. P. G. Crone, E. Fogh, M. E. Zayed, R. Lortz, E. Pomjakushina, K. Conder, A. M. Läuchli, L. Weber, S. Wessel, A. Honecker, B. Normand, Ch. Rüegg, P. Corboz, H. M. Rønnow, F. Mila
TL;DR
The paper addresses the challenge of characterizing low-temperature behavior near quantum phase transitions. It combines high-precision specific-heat measurements with finite-temperature tensor-network calculations, while noting that some very-low-temperature features remain difficult to confirm.
Problem
Characterizing low-temperature behavior near quantum phase transitions is challenging for tensor-network calculations, limiting confirmation of some features.
Method
The study combines frequency-scanned a.c. calorimetry with finite-temperature iPEPS calculations to evaluate thermal properties of SrCu2(BO3)2.
Results
The calorimetry determines heat capacity C(P, H, T) with 5% accuracy relative to an adiabatic technique.
Takeaways & Limitations
The combined methodology supports accurate thermal-property measurements and thermodynamic calculations in the thermodynamic limit.
Takeaways & Limitations
Low-temperature numerical studies are challenging, and the plaquette-phase results below T/J_D ~0.03 cannot confirm an associated Ising transition.
Abstract
from arXiv · showhide
At the familiar liquid-gas phase transition in water, the density jumps discontinuously at atmospheric pressure, but the line of these first-order transitions defined by increasing pressures terminates at the critical point, a concept ubiquitous in statistical thermodynamics. In correlated quantum materials, a critical point was predicted and measured terminating the line of Mott metal-insulator transitions, which are also first-order with a discontinuous charge density. In quantum spin systems, continuous quantum phase transitions (QPTs) have been investigated extensively, but discontinuous QPTs have received less attention. The frustrated quantum antiferromagnet SrCu$_2$(BO$_3$)$_2$ constitutes a near-exact realization of the paradigmatic Shastry-Sutherland model and displays exotic phenomena including magnetization plateaux, anomalous thermodynamics and discontinuous QPTs. We demonstrate by high-precision specific-heat measurements under pressure and applied magnetic field that, like water, the pressure-temperature phase diagram of SrCu$_2$(BO$_3$)$_2$ has an Ising critical point terminating a first-order transition line, which separates phases with different densities of magnetic particles (triplets). We achieve a quantitative explanation of our data by detailed numerical calculations using newly-developed finite-temperature tensor-network methods. These results open a new dimension in understanding the thermodynamics of quantum magnetic materials, where the anisotropic spin interactions producing topological properties for spintronic applications drive an increasing focus on first-order QPTs.
Methods
The study combines high-pressure, high-field a.c. calorimetry on SrCu2(BO3)2 with finite-temperature iPEPS calculations. The experimental method determines heat capacity accurately, while numerical analyses address phase-dependent tensor representations and low-temperature limitations.
- Specific-heat measurements: Three SrCu2(BO3)2 crystal slabs were measured using 2ω a.c. calorimetry under pressures up to 26.5 kbar.The slabs had 7.6–9.0 mm2 ab-plane cross-sections, 0.5–1.0 mm thicknesses, and masses of 15–36 mg.
- Specific-heat measurements: Heat capacity was extracted from isothermal frequency scans by fitting the standard steady-state equation and selecting the pressure-dependent working frequency fC.The analysis improved corrections for heat losses, pressure-dependent contributions, and thermal equilibration.
- Specific-heat measurements: The measured heat capacity was determined with 5% accuracy relative to an adiabatic technique.Measurements used fixed frequency fC at constant field after establishing negligible pressure- and field-induced changes in relevant steady-state parameters.
- iPEPS: Finite-temperature iPEPS represented thermal states through imaginary-time evolution of a purified density operator, with bond dimension D controlling accuracy.The calculations used local simple updates near the quantum phase transition and exploited the model’s global U(1) symmetry.
- iPEPS limitations: Numerical reliability was limited at low temperatures: dimer-phase instabilities were mitigated with a small Dzyaloshinskii-Moriya interaction, while plaquette-phase results focused on T/JD >∼0.03.A feature near T/JD = 0.02 could not be confidently identified as an Ising transition because corresponding spin-correlation behavior was absent.