Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1208.6117 · Physical Review Letters

Quantum-Critical Spin Dynamics in Quasi-One-Dimensional Antiferromagnets

S. Mukhopadhyay, M. Klanjšek, Mihael S. Grbić, Rémi Blinder, H. Mayaffre, C. Berthier, M. Horvatić, M. A. Contínentino, Armando Paduan-Filho, BRUNETTO CHIARI, O. Piovesana

Published Oct 26, 2012• 54 citations
arXivHTMLPDF

Abstract

By means of nuclear spin-lattice relaxation rate ${T}_{1}^{\ensuremath{-}1}$, we follow the spin dynamics as a function of the applied magnetic field in two gapped quasi-one-dimensional quantum antiferromagnets: the anisotropic spin-chain system ${\mathrm{NiCl}}_{2}\mathrm{\text{\ensuremath{-}}}4\mathrm{SC}({\mathrm{NH}}_{2}{)}_{2}$ and the spin-ladder system $({\mathrm{C}}_{5}{\mathrm{H}}_{12}\mathrm{N}{)}_{2}\mathrm{Cu}{\mathrm{Br}}_{4}$. In both systems, spin excitations are confirmed to evolve from magnons in the gapped state to spinons in the gapless Tomonaga-Luttinger-liquid state. In between, ${T}_{1}^{\ensuremath{-}1}$ exhibits a pronounced, continuous variation, which is shown to scale in accordance with quantum criticality. We extract the critical exponent for ${T}_{1}^{\ensuremath{-}1}$, compare it to the theory, and show that this behavior is identical in both studied systems, thus demonstrating the universality of quantum-critical behavior.

DOI
10.1103/physrevlett.109.177206

Related papers

Nuclear Magnetic Resonance Study of the S=1/2 Heisenberg Ladder Cu2(C5H12N2)2Cl4 : Quantum Phase Transition and Critical Dynamics

G. Chaboussant, Y. Fagot‐Révurat, M.-H. Julien +5 more

We present an extensive NMR study of the spin-1/2 antiferromagnetic Heisenberg ladder $\mathrm{Cu}{}_{2}({\mathrm{C}}_{5}{\mathrm{H}}_{12}{\mathrm{N}}_{2}{)}_{2}\mathrm{Cl}{}_{4}$ in a magnetic field range 4.5--16.7 T. By measuring the proton NMR relaxation rate $1/{T}_{1}$ and varying the magnetic field around the critical field ${H}_{c1}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\Delta}/g{\ensuremath{\mu}}_{B}\ensuremath{\approx}7.5\mathrm{T}$, we have studied the transition from a gapped spin liquid ground state to a gapless magnetic regime which can be described as a Luttinger liquid. We identify an intermediate regime $T\ensuremath{\ge}|{H\ensuremath{-}H}_{c1}|$, where the spin dynamics is (possibly) only controlled by the $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ critical point ${H}_{c1}$.

arXiv:cond-mat/9711124•Physical Review Letters•Mar 23, 1998•108 citations

Quantum criticality of spinons

Feng He, Yuzhu Jiang, Yi-Cong Yu +2 more

Magnon bound states emerging in one-dimensional (1D) spin chains still lack a rigorous understanding. In this Rapid Communication we show that the length-1 spin strings significantly dominate the critical properties of spinons, magnons, and free fermions in the 1D antiferromagnetic spin-1/2 chain. Using the Bethe ansatz solution, we analytically calculate the scaling functions of the thermal and magnetic properties of the model, providing a rigorous understanding of the quantum criticality of spinons. It turns out that the double maxima in specific heat elegantly mark two crossover temperatures fanning out from the critical point, indicating three quantum phases: the Tomonaga-Luttinger liquid (TLL), the quantum critical, and fully polarized ferromagnetic phases. For the TLL phase, the Wilson ratio ${R}_{W}=4{K}_{s}$ remains almost temperature independent, where ${K}_{s}$ is the Luttinger parameter. Furthermore, by applying our results, we precisely determine the quantum scalings and critical exponents of all magnetic properties in the ideal 1D spin-1/2 antiferromagnet $\mathrm{Cu}(\mathrm{C}{}_{4}\mathrm{H}{}_{4}\mathrm{N}{}_{2})(\mathrm{NO}{}_{3}){}_{2}$, recently studied by Kono et al. [Phys. Rev. Lett. 114, 037202 (2015)]. We further find that the magnetization maximum used in experiments is not a good quantity to map out the finite-temperature TLL phase boundary.

arXiv:1702.05903•Physical review. B./Physical review. B•Dec 7, 2017•23 citations

Temperature dependence of the NMR relaxation rate 1/T1 for quantum spin chains

Maxime Dupont, Sylvain Capponi, Nicolas Laflorencie

Quasi-one-dimensional (1D) antiferromagnets are good candidates to realize a Tomonaga-Luttinger liquid (TLL), describing 1D interacting quantum systems, provided 3D coupling remains small as compared to temperature. In systems such as NiCl${}_{2}$-4SC(NH${}_{2}$)${}_{2}$ (DTN), made of weakly coupled spin $S=1$ chains, interchain coupling plays an important role at low temperature as it leads to antiferromagnetic long-range order below $1$ K, corresponding to a Bose-Einstein condensate of magnons. Using time-dependent numerical simulations at finite temperature, the authors compute here the nuclear magnetic resonance (NMR) relaxation rate $1/{T}_{1}$, a key experimental quantity, and address the question of the low-temperature crossover between TLL predictions and the higher-temperature regime in purely $1$D quantum spins chains. They also comment on the experimental observation of the TLL regime, possibly masked by $3$D long-range order in materials such as DTN.

arXiv:1606.09502•Physical review. B./Physical review. B•Oct 11, 2016•26 citations

Magnon-induced nuclear relaxation in the quantum critical region of a Heisenberg linear chain

Michael J. R. Hoch

The low-temperature properties of spin-1/2 one-dimensional (1D) Heisenberg antiferromagnetic (HAF) chains which have relatively small exchange couplings between the spins can be tuned using laboratory-scale magnetic fields. Magnetization measurements, made as a function of temperature, provide phase diagrams for these systems and establish the quantum critical point (QCP). The evolution of the spin dynamics behavior with temperature and applied field in the quantum critical (QC) region, near the QCP, is of particular interest and has been experimentally investigated in a number of 1D HAFs using neutron scattering and nuclear magnetic resonance as the preferred techniques. In the QC phase both quantum and thermal spin fluctuations are present. As a result of extended spin correlations in the chains, magnon excitations are important at finite temperatures. An expression for the NMR spin-lattice relaxation rate $1/{T}_{1}$ of probe nuclei in the QC phase of 1D HAFs is obtained by considering Raman scattering processes which induce nuclear spin flips. The relaxation rate expression, which involves the temperature and the chemical potential, predicts scaling behavior of $1/{T}_{1}$ consistent with recent experimental findings for quasi-1D HAF systems. A simple relationship between $1/{T}_{1}$ and the deviation of the magnetization from saturation (${M}_{S}\ensuremath{-}M$) is predicted for the QC region.

Physical review. B./Physical review. B•Jul 27, 2017•2 citations

Critical properties of gapped spin-chains and ladders in a magnetic field

R. Chitra, Thierry Giamarchi

An interesting feature of spin- chains with a gap is that they undergo a commensurate-incommensurate transition in the presence of an external magnetic field H. The system is in a gapless incommensurate regime for all values of the magnetic field between the lower critical field ${\mathrm{H}}_{\mathrm{c}1}$ and an upper critical field ${\mathrm{H}}_{\mathrm{c}2}$, where it is gapless and has power-law correlations. We calculate the critical exponents for such a generic gapped system in the incommensurate regime at the critical field ${\mathrm{H}}_{\mathrm{c}1}$ and in its vicinity. Our analysis also applies to the spin- ladder. We compute the full dynamical susceptibilities at finite temperature. We use the same to discuss the thermal broadening of various modes and obtain the low-temperature behavior of the nuclear spin relaxation rate ${\mathrm{T}}_{1}^{\mathrm{\ensuremath{-}}1}$. We discuss the results obtained here for the special cases of the dimerized chain, frustrated chain, and the spin- ladder.

arXiv:cond-mat/9611114•Physical review. B, Condensed matter•Mar 1, 1997•218 citations

Dynamical response and dimensional crossover for spatially anisotropic antiferromagnets

Maxime Dupont, Sylvain Capponi, Nicolas Laflorencie +1 more

At low temperature, critical one-dimensional (1D) quantum systems, such as spin chains, are theoretically described by the Tomonaga-Luttinger liquid (TLL) theory. In realistic quasi-1D materials, however, residual couplings are always present, and these systems eventually escape the theoretical 1D world to get eventually ordered at lower temperature. In order to define a genuine ``1D temperature window'' in quasi-1D systems for dynamical quantities such as the NMR relaxation rate or the dynamical structure factor that is probed by inelastic neutron scattering, the authors present a comprehensive theoretical study based on analytical as well as numerical approaches. They are able to describe the full temperature crossover for weakly coupled chains and, in particular, the universal 1D window where the TLL picture can be experimentally observed.

arXiv:1806.04913•Physical review. B./Physical review. B•Sep 5, 2018•19 citations
By means of nuclear spin-lattice relaxation rate T1\ensuremath−1{T}_{1}^{\ensuremath{-}1}T1\ensuremath−1​, we follow the spin dynamics as a function of the applied magnetic field in two gapped quasi-one-dimensional quantum antiferromagnets: the anisotropic spin-chain system NiCl2\ensuremath-4SC(NH2)2{\mathrm{NiCl}}_{2}\mathrm{\text{\ensuremath{-}}}4\mathrm{SC}({\mathrm{NH}}_{2}{)}_{2}NiCl2​\ensuremath-4SC(NH2​)2​ and the spin-ladder system (C5H12N)2CuBr4({\mathrm{C}}_{5}{\mathrm{H}}_{12}\mathrm{N}{)}_{2}\mathrm{Cu}{\mathrm{Br}}_{4}(C5​H12​N)2​CuBr4​. In both systems, spin excitations are confirmed to evolve from magnons in the gapped state to spinons in the gapless Tomonaga-Luttinger-liquid state. In between, T1\ensuremath−1{T}_{1}^{\ensuremath{-}1}T1\ensuremath−1​ exhibits a pronounced, continuous variation, which is shown to scale in accordance with quantum criticality. We extract the critical exponent for T1\ensuremath−1{T}_{1}^{\ensuremath{-}1}T1\ensuremath−1​, compare it to the theory, and show that this behavior is identical in both studied systems, thus demonstrating the universality of quantum-critical behavior.
We present an extensive NMR study of the spin-1/2 antiferromagnetic Heisenberg ladder Cu2(C5H12N2)2Cl4\mathrm{Cu}{}_{2}({\mathrm{C}}_{5}{\mathrm{H}}_{12}{\mathrm{N}}_{2}{)}_{2}\mathrm{Cl}{}_{4}Cu2​(C5​H12​N2​)2​Cl4​ in a magnetic field range 4.5--16.7 T. By measuring the proton NMR relaxation rate 1/T11/{T}_{1}1/T1​ and varying the magnetic field around the critical field ${H}_{c1}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\Delta}/g{\ensuremath{\mu}}_{B}\ensuremath{\approx}7.5\mathrm{T}$, we have studied the transition from a gapped spin liquid ground state to a gapless magnetic regime which can be described as a Luttinger liquid. We identify an intermediate regime $T\ensuremath{\ge}|{H\ensuremath{-}H}_{c1}|$, where the spin dynamics is (possibly) only controlled by the T=0T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0T=0 critical point Hc1{H}_{c1}Hc1​.
Magnon bound states emerging in one-dimensional (1D) spin chains still lack a rigorous understanding. In this Rapid Communication we show that the length-1 spin strings significantly dominate the critical properties of spinons, magnons, and free fermions in the 1D antiferromagnetic spin-1/2 chain. Using the Bethe ansatz solution, we analytically calculate the scaling functions of the thermal and magnetic properties of the model, providing a rigorous understanding of the quantum criticality of spinons. It turns out that the double maxima in specific heat elegantly mark two crossover temperatures fanning out from the critical point, indicating three quantum phases: the Tomonaga-Luttinger liquid (TLL), the quantum critical, and fully polarized ferromagnetic phases. For the TLL phase, the Wilson ratio RW=4Ks{R}_{W}=4{K}_{s}RW​=4Ks​ remains almost temperature independent, where Ks{K}_{s}Ks​ is the Luttinger parameter. Furthermore, by applying our results, we precisely determine the quantum scalings and critical exponents of all magnetic properties in the ideal 1D spin-1/2 antiferromagnet Cu(C4H4N2)(NO3)2\mathrm{Cu}(\mathrm{C}{}_{4}\mathrm{H}{}_{4}\mathrm{N}{}_{2})(\mathrm{NO}{}_{3}){}_{2}Cu(C4​H4​N2​)(NO3​)2​, recently studied by Kono et al. [Phys. Rev. Lett. 114, 037202 (2015)]. We further find that the magnetization maximum used in experiments is not a good quantity to map out the finite-temperature TLL phase boundary.
Quasi-one-dimensional (1D) antiferromagnets are good candidates to realize a Tomonaga-Luttinger liquid (TLL), describing 1D interacting quantum systems, provided 3D coupling remains small as compared to temperature. In systems such as NiCl2{}_{2}2​-4SC(NH2{}_{2}2​)2{}_{2}2​ (DTN), made of weakly coupled spin S=1S=1S=1 chains, interchain coupling plays an important role at low temperature as it leads to antiferromagnetic long-range order below 111 K, corresponding to a Bose-Einstein condensate of magnons. Using time-dependent numerical simulations at finite temperature, the authors compute here the nuclear magnetic resonance (NMR) relaxation rate 1/T11/{T}_{1}1/T1​, a key experimental quantity, and address the question of the low-temperature crossover between TLL predictions and the higher-temperature regime in purely 111D quantum spins chains. They also comment on the experimental observation of the TLL regime, possibly masked by 333D long-range order in materials such as DTN.
The low-temperature properties of spin-1/2 one-dimensional (1D) Heisenberg antiferromagnetic (HAF) chains which have relatively small exchange couplings between the spins can be tuned using laboratory-scale magnetic fields. Magnetization measurements, made as a function of temperature, provide phase diagrams for these systems and establish the quantum critical point (QCP). The evolution of the spin dynamics behavior with temperature and applied field in the quantum critical (QC) region, near the QCP, is of particular interest and has been experimentally investigated in a number of 1D HAFs using neutron scattering and nuclear magnetic resonance as the preferred techniques. In the QC phase both quantum and thermal spin fluctuations are present. As a result of extended spin correlations in the chains, magnon excitations are important at finite temperatures. An expression for the NMR spin-lattice relaxation rate 1/T11/{T}_{1}1/T1​ of probe nuclei in the QC phase of 1D HAFs is obtained by considering Raman scattering processes which induce nuclear spin flips. The relaxation rate expression, which involves the temperature and the chemical potential, predicts scaling behavior of 1/T11/{T}_{1}1/T1​ consistent with recent experimental findings for quasi-1D HAF systems. A simple relationship between 1/T11/{T}_{1}1/T1​ and the deviation of the magnetization from saturation (${M}_{S}\ensuremath{-}M$) is predicted for the QC region.
An interesting feature of spin- chains with a gap is that they undergo a commensurate-incommensurate transition in the presence of an external magnetic field H. The system is in a gapless incommensurate regime for all values of the magnetic field between the lower critical field Hc1{\mathrm{H}}_{\mathrm{c}1}Hc1​ and an upper critical field Hc2{\mathrm{H}}_{\mathrm{c}2}Hc2​, where it is gapless and has power-law correlations. We calculate the critical exponents for such a generic gapped system in the incommensurate regime at the critical field Hc1{\mathrm{H}}_{\mathrm{c}1}Hc1​ and in its vicinity. Our analysis also applies to the spin- ladder. We compute the full dynamical susceptibilities at finite temperature. We use the same to discuss the thermal broadening of various modes and obtain the low-temperature behavior of the nuclear spin relaxation rate ${\mathrm{T}}_{1}^{\mathrm{\ensuremath{-}}1}$. We discuss the results obtained here for the special cases of the dimerized chain, frustrated chain, and the spin- ladder.
At low temperature, critical one-dimensional (1D) quantum systems, such as spin chains, are theoretically described by the Tomonaga-Luttinger liquid (TLL) theory. In realistic quasi-1D materials, however, residual couplings are always present, and these systems eventually escape the theoretical 1D world to get eventually ordered at lower temperature. In order to define a genuine ``1D temperature window'' in quasi-1D systems for dynamical quantities such as the NMR relaxation rate or the dynamical structure factor that is probed by inelastic neutron scattering, the authors present a comprehensive theoretical study based on analytical as well as numerical approaches. They are able to describe the full temperature crossover for weakly coupled chains and, in particular, the universal 1D window where the TLL picture can be experimentally observed.