© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:1709.00274 · Science Advances

Quantum criticality in the spin-1/2 Heisenberg chain system copper pyrazine dinitrate

Oliver Breunig, Markus Garst, Andreas Klümper, J. Rohrkamp, Mark M. Turnbull, T. Lorenz

Published Dec 1, 2017• 71 citations

Abstract

Low-dimensional quantum magnets promote strong correlations between magnetic moments that lead to fascinating quantum phenomena. A particularly interesting system is the antiferromagnetic spin-1/2 Heisenberg chain because it is exactly solvable by the Bethe-Ansatz method. It is approximately realized in the magnetic insulator copper pyrazine dinitrate, providing a unique opportunity for a quantitative comparison between theory and experiment. We investigate its thermodynamic properties with a particular focus on the field-induced quantum phase transition. Thermal expansion, magnetostriction, specific heat, magnetization, and magnetocaloric measurements are found to be in excellent agreement with exact Bethe-Ansatz predictions. Close to the critical field, thermodynamics obeys the expected quantum critical scaling behavior, and in particular, the magnetocaloric effect and the Grüneisen parameters diverge in a characteristic manner. Beyond its importance for quantum magnetism, our study establishes a paradigm of a quantum phase transition, which illustrates fundamental principles of quantum critical thermodynamics.

DOI: 10.1126/sciadv.aao3773

Related papers

Dynamics of a Heisenberg spin chain in the quantum critical regime: NMR experiment versus effective field theory

H. Kühne, Andrei A. Zvyagin, M. Günther +5 more

A comprehensive comparison between the magnetic field- and temperature-dependent low-frequency spin dynamics in the antiferromagnetic spin-1/2 Heisenberg chain system copper pyrazine dinitrate, probed via the $^{13}\mathrm{C}$ nuclear magnetic resonance relaxation rate ${T}_{1}^{\ensuremath{-}1}$, and the field theoretical approach in the Luttinger liquid regime was performed. We found very good agreement between experiment and theory in the investigated temperature and field range. Our results demonstrate how spin-spin interactions strongly affect the spin dynamics of Heisenberg spin chain compounds in the vicinity of the quantum critical point.

arXiv:1007.3608•Physical Review B•Mar 14, 2011•26 citations

Magnetization Study of the Quantum Critical Behavior of the One Dimensional Spin-1/2 Heisenberg Antiferromagnet CuPzN

Yohei Kono, Toshiro Sakakibara, Christopher Aoyama +3 more

High-precision DC magnetization (M) measurements have been performed on a single crystal of copper pyrazine dinitrate (CuPzN) in magnetic fields H up to 14.7 T at temperatures down to 0.08 K. This material is one of the best realizations of a one-dimensional (1D) S = 1/2 Heisenberg antiferromagnet. At the base temperature, full saturation of M is observed above Hs = 13.97 T with the M(H) curve closely following a prediction based on the Bethe ansatz. The peak in M(T ), which appears at about 7 K in zero field, moves to lower temperatures with increasing H and vanishes into a temperature region well below 0.08 K at H ∼ Hs; as a result, M(T ) exhibits a strong upturn as T → 0 at this field, in agreement with a theoretical prediction. These results constitute an observation of field-induced quantum critical behavior in bulk magnetization.

International Conference on Strongly Correlated Electron Systems (SCES)•Jun 16, 2014•1 citation

Extended Quantum Critical Phase in a Magnetized Spin- 1 2 Antiferromagnetic Chain

M. B. Stone, Daniel H. Reich, C. Broholm +4 more

Measurements are reported of the magnetic field dependence of excitations in the quantum critical state of the spin S=1/2 linear chain Heisenberg antiferromagnet copper pyrazine dinitrate (CuPzN). The complete spectrum was measured at k(B)T/J< or =0.025 for H=0 and H=8.7 T, where the system is approximately 30% magnetized. At H=0, the results are in agreement with exact calculations of the dynamic spin correlation function for a two-spinon continuum. At H=8.7 T, there are multiple overlapping continua with incommensurate soft modes. The boundaries of these continua confirm long-standing predictions, and the intensities are consistent with exact diagonalization and Bethe ansatz calculations.

arXiv:cond-mat/0303364•Physical Review Letters•Jul 17, 2003•139 citations

Quantum critical dynamics of an S=12 antiferromagnetic Heisenberg chain studied by C13 NMR spectroscopy

H. Kühne, H.‐H. Klauß, Simon Grossjohann +6 more

We present a $^{13}\text{C}$ NMR study of the magnetic field driven transition to complete polarization of the $S=\frac{1}{2}$ antiferromagnetic Heisenberg chain system copper pyrazine dinitrate $\text{Cu}({\text{C}}_{4}{\text{H}}_{4}{\text{N}}_{2}){({\text{NO}}_{3})}_{2}$ (CuPzN). The static local magnetization as well as the low-frequency spin dynamics, probed via the nuclear spin-lattice relaxation rate ${T}_{1}^{\ensuremath{-}1}$, were explored from the low to the high field limit and at temperatures from the quantum regime $({k}_{B}T⪡J)$ up to the classical regime $({k}_{B}T⪢J)$. The experimental data show very good agreement with quantum Monte Carlo calculations over the complete range of parameters investigated. Close to the critical field, as derived from static experiments, a pronounced maximum in ${T}_{1}^{\ensuremath{-}1}$ is found which we interpret as the finite-temperature manifestation of a diverging density of zero-energy magnetic excitations at the field-driven quantum critical point.

arXiv:0804.2170•Physical Review B•Jul 13, 2009•32 citations

Field-Induced Quantum Criticality and Universal Temperature Dependence of the Magnetization of a Spin- 1/2 Heisenberg Chain

Yohei Kono, T. Sakakibara, Christopher Aoyama +4 more

High-precision dc magnetization measurements have been made on Cu(C4H4N2) (NO3)2 in magnetic fields up to 14.7 T, slightly above the saturation field Hs=13.97 T, in the temperature range from 0.08 to 15 K. The magnetization curve and differential susceptibility at the lowest temperature show excellent agreement with exact theoretical results for the spin-1/2 Heisenberg antiferromagnet in one dimension. A broad peak is observed in magnetization measured as a function of temperature, signaling a crossover to a low-temperature Tomonaga-Luttinger-liquid regime. With an increasing field, the peak moves gradually to lower temperatures, compressing the regime, and, at Hs, the magnetization exhibits a strong upturn. This quantum critical behavior of the magnetization and that of the specific heat withstand quantitative tests against theory, demonstrating that the material is a practically perfect one-dimensional spin-1/2 Heisenberg antiferromagnet.

Physical Review Letters•Jan 22, 2015•70 citations

Thermodynamics of quantum Heisenberg spin chains

Tao Xiang

Thermodynamic properties of the quantum Heisenberg spin chains with $S=1/2,$ 1, and $3/2$ are investigated using the transfer-matrix renormalization-group method. The temperature dependence of the magnetization, susceptibility, specific heat, spin-spin correlation length, and several other physical quantities in a zero or finite applied field are calculated and compared. Our data agree well with the Bethe ansatz, exact diagonalization, and quantum Monte Carlo results and provide further insight into the quantum effects in the antiferromagnetic Heisenberg spin chains.

arXiv:cond-mat/9808179•Physical review. B, Condensed matter•Oct 1, 1998•92 citations

Low-dimensional quantum magnets promote strong correlations between magnetic moments that lead to fascinating quantum phenomena. A particularly interesting system is the antiferromagnetic spin-1/2 Heisenberg chain because it is exactly solvable by the Bethe-Ansatz method. It is approximately realized in the magnetic insulator copper pyrazine dinitrate, providing a unique opportunity for a quantitative comparison between theory and experiment. We investigate its thermodynamic properties with a particular focus on the field-induced quantum phase transition. Thermal expansion, magnetostriction, specific heat, magnetization, and magnetocaloric measurements are found to be in excellent agreement with exact Bethe-Ansatz predictions. Close to the critical field, thermodynamics obeys the expected quantum critical scaling behavior, and in particular, the magnetocaloric effect and the Grüneisen parameters diverge in a characteristic manner. Beyond its importance for quantum magnetism, our study establishes a paradigm of a quantum phase transition, which illustrates fundamental principles of quantum critical thermodynamics.

A comprehensive comparison between the magnetic field- and temperature-dependent low-frequency spin dynamics in the antiferromagnetic spin-1/2 Heisenberg chain system copper pyrazine dinitrate, probed via the

^{13}\mathrm{C}

nuclear magnetic resonance relaxation rate ${T}_{1}^{\ensuremath{-}1}$, and the field theoretical approach in the Luttinger liquid regime was performed. We found very good agreement between experiment and theory in the investigated temperature and field range. Our results demonstrate how spin-spin interactions strongly affect the spin dynamics of Heisenberg spin chain compounds in the vicinity of the quantum critical point.

High-precision DC magnetization (M) measurements have been performed on a single crystal of copper pyrazine dinitrate (CuPzN) in magnetic fields H up to 14.7 T at temperatures down to 0.08 K. This material is one of the best realizations of a one-dimensional (1D) S = 1/2 Heisenberg antiferromagnet. At the base temperature, full saturation of M is observed above Hs = 13.97 T with the M(H) curve closely following a prediction based on the Bethe ansatz. The peak in M(T ), which appears at about 7 K in zero field, moves to lower temperatures with increasing H and vanishes into a temperature region well below 0.08 K at H ∼ Hs; as a result, M(T ) exhibits a strong upturn as T → 0 at this field, in agreement with a theoretical prediction. These results constitute an observation of field-induced quantum critical behavior in bulk magnetization.

Measurements are reported of the magnetic field dependence of excitations in the quantum critical state of the spin S=1/2 linear chain Heisenberg antiferromagnet copper pyrazine dinitrate (CuPzN). The complete spectrum was measured at k(B)T/J< or =0.025 for H=0 and H=8.7 T, where the system is approximately 30% magnetized. At H=0, the results are in agreement with exact calculations of the dynamic spin correlation function for a two-spinon continuum. At H=8.7 T, there are multiple overlapping continua with incommensurate soft modes. The boundaries of these continua confirm long-standing predictions, and the intensities are consistent with exact diagonalization and Bethe ansatz calculations.

We present a

^{13}\text{C}

NMR study of the magnetic field driven transition to complete polarization of the

S=\frac{1}{2}

antiferromagnetic Heisenberg chain system copper pyrazine dinitrate

\text{Cu}({\text{C}}_{4}{\text{H}}_{4}{\text{N}}_{2}){({\text{NO}}_{3})}_{2}

(CuPzN). The static local magnetization as well as the low-frequency spin dynamics, probed via the nuclear spin-lattice relaxation rate ${T}_{1}^{\ensuremath{-}1}$, were explored from the low to the high field limit and at temperatures from the quantum regime

({k}_{B}T⪡J)

up to the classical regime

({k}_{B}T⪢J)

. The experimental data show very good agreement with quantum Monte Carlo calculations over the complete range of parameters investigated. Close to the critical field, as derived from static experiments, a pronounced maximum in ${T}_{1}^{\ensuremath{-}1}$ is found which we interpret as the finite-temperature manifestation of a diverging density of zero-energy magnetic excitations at the field-driven quantum critical point.

High-precision dc magnetization measurements have been made on Cu(C4H4N2) (NO3)2 in magnetic fields up to 14.7 T, slightly above the saturation field Hs=13.97 T, in the temperature range from 0.08 to 15 K. The magnetization curve and differential susceptibility at the lowest temperature show excellent agreement with exact theoretical results for the spin-1/2 Heisenberg antiferromagnet in one dimension. A broad peak is observed in magnetization measured as a function of temperature, signaling a crossover to a low-temperature Tomonaga-Luttinger-liquid regime. With an increasing field, the peak moves gradually to lower temperatures, compressing the regime, and, at Hs, the magnetization exhibits a strong upturn. This quantum critical behavior of the magnetization and that of the specific heat withstand quantitative tests against theory, demonstrating that the material is a practically perfect one-dimensional spin-1/2 Heisenberg antiferromagnet.

Thermodynamic properties of the quantum Heisenberg spin chains with

S=1/2,

1, and

3/2

are investigated using the transfer-matrix renormalization-group method. The temperature dependence of the magnetization, susceptibility, specific heat, spin-spin correlation length, and several other physical quantities in a zero or finite applied field are calculated and compared. Our data agree well with the Bethe ansatz, exact diagonalization, and quantum Monte Carlo results and provide further insight into the quantum effects in the antiferromagnetic Heisenberg spin chains.