arXiv:cond-mat/0101422 · Journal of the Physical Society of Japan

NMR Relaxation Rate for One-Dimensional Multicomponent Spin-Orbital Systems

Akira Kawaguchi, Tatsuya Fujii, Norio Kawakami

Published Sep 1, 2000• 5 citations

Abstract

The NMR relaxation rate $1/T_{1}$ is studied for one-dimensional multicomponent spin-orbital systems. By combining the bosonization techniques and the exact solution of the SU($n$) model, we evaluate the power-law exponent and the enhancement factor for $1/T_1$ at low temperatures. We discuss how the band splitting affects the relaxation rate, and find that $1/T_{1}$ may be enhanced around the critical value of the band splitting. The crossover behavior in $1/T_1$ around the critical point is discussed in terms of the low-frequency dynamical spin susceptibility. The effect of the hole-doping is also addressed.

DOI: 10.1143/jpsj.69.3055

Related papers

Magnetic properties of the one-dimensional multicomponent spin-gap system

Akira Kawaguchi, Tatsuya Fujii, Norio Kawakami

arXiv:cond-mat/0101423Physical review. B, Condensed matterMar 19, 20014 citations

Temperature dependence of the NMR spin-lattice relaxation rate for spin- 1 2 chains

Emanuele Coira, Peter Barmettler, Thierry Giamarchi +1 more

arXiv:1606.03985Physical review. B./Physical review. BOct 11, 201624 citations

Numerical study of the temperature dependence of the NMR relaxation rate across the superfluid–Bose glass transition in one dimension

Maxime Dupont

arXiv:1902.07361Physical review. B./Physical review. BMay 28, 20192 citations

Thermal tensor network approach for spin-lattice relaxation in quantum magnets

Ning Xi, Yuan Gao, Huihang Lin +8 more

arXiv:2403.11895Physical review. B./Physical review. BMar 4, 20260 citations

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

Maxime Dupont, Sylvain Capponi, Nicolas Laflorencie

arXiv:1606.09502Physical review. B./Physical review. BOct 11, 201626 citations

NMR relaxation rates in a spin- 12 antiferromagnetic chain

Victor Barzykin

arXiv:cond-mat/0011453Physical review. B, Condensed matterMar 21, 200134 citations

arXiv:cond-mat/0101422 · Journal of the Physical Society of Japan

NMR Relaxation Rate for One-Dimensional Multicomponent Spin-Orbital Systems

Akira Kawaguchi, Tatsuya Fujii, Norio Kawakami

Published Sep 1, 2000• 5 citations

arXiv HTML PDF

Abstract

The NMR relaxation rate

1/T_{1}

is studied for one-dimensional multicomponent spin-orbital systems. By combining the bosonization techniques and the exact solution of the SU(

n

) model, we evaluate the power-law exponent and the enhancement factor for

1/T_1

at low temperatures. We discuss how the band splitting affects the relaxation rate, and find that

1/T_{1}

may be enhanced around the critical value of the band splitting. The crossover behavior in

1/T_1

around the critical point is discussed in terms of the low-frequency dynamical spin susceptibility. The effect of the hole-doping is also addressed.

DOI: 10.1143/jpsj.69.3055

Related papers

Magnetic properties of the one-dimensional multicomponent spin-gap system

Akira Kawaguchi, Tatsuya Fujii, Norio Kawakami

Magnetic properties of a one-dimensional multicomponent quantum-spin system with an excitation gap are studied based on the integrable spin model introduced by Bariev et al. [Z. Phys. B 96, 395 (1995)]. By exactly computing the magnetization, we show how a characteristic structure with plateaus and cusps appears in the magnetization process. To study the low-energy dynamics of the system, we apply a finite-size scaling analysis to the excitation spectrum, and thereby evaluate the power-law exponent as well as the enhancement factor for the low-temperature NMR relaxation rate ${1/T}_{1}.$ We discuss the critical properties of ${1/T}_{1}$ around plateaus and cusps in the magnetization curve.Magnetic properties of a one-dimensional multicomponent quantum-spin system with an excitation gap are studied based on the integrable spin model introduced by Bariev et al. [Z. Phys. B 96, 395 (1995)]. By exactly computing the magnetization, we show how a characteristic structure with plateaus and cusps appears in the magnetization process. To study the low-energy dynamics of the system, we apply a finite-size scaling analysis to the excitation spectrum, and thereby evaluate the power-law exponent as well as the enhancement factor for the low-temperature NMR relaxation rate ${1/T}_{1}.$ We discuss the critical properties of ${1/T}_{1}$ around plateaus and cusps in the magnetization curve.

arXiv:cond-mat/0101423Physical review. B, Condensed matterMar 19, 20014 citations

Temperature dependence of the NMR spin-lattice relaxation rate for spin- 1 2 chains

Emanuele Coira, Peter Barmettler, Thierry Giamarchi +1 more

Recent developments in density matrix renormalization group/matrix product state techniques allow today for a quantitative computation of dynamical correlations at finite temperature in low-dimensional quantum spin systems. By combining numerical results and field theoretical asymptotic methods, e.g., bosonization, it is now possible to give a full description of the dynamical quantity one is interested in for the range of temperatures experimentally accessible. This enhances of course the possibility of one-to-one comparisons with experiments without having to resort to uncontrolled approximations. Here, the authors focus on the temperature dependence of the NMR spin-lattice relaxation rate $1/{T}_{1}$ in spin- $\frac{1}{2}$ chain systems. This quantity is directly related to local, dynamical spin-spin correlation functions. The results agree in the low-temperature regime with bosonization predictions, and show interesting deviations from this behavior at intermediate temperatures.Recent developments in density matrix renormalization group/matrix product state techniques allow today for a quantitative computation of dynamical correlations at finite temperature in low-dimensional quantum spin systems. By combining numerical results and field theoretical asymptotic methods, e.g., bosonization, it is now possible to give a full description of the dynamical quantity one is interested in for the range of temperatures experimentally accessible. This enhances of course the possibility of one-to-one comparisons with experiments without having to resort to uncontrolled approximations. Here, the authors focus on the temperature dependence of the NMR spin-lattice relaxation rate $1/{T}_{1}$ in spin-$\frac{1}{2}$ chain systems. This quantity is directly related to local, dynamical spin-spin correlation functions. The results agree in the low-temperature regime with bosonization predictions, and show interesting deviations from this behavior at intermediate temperatures.

arXiv:1606.03985Physical review. B./Physical review. BOct 11, 201624 citations

Numerical study of the temperature dependence of the NMR relaxation rate across the superfluid–Bose glass transition in one dimension

Maxime Dupont

We study the nuclear magnetic resonance (NMR) spin-lattice relaxation rate $1/{T}_{1}$ in random one-dimensional spin chains as a function of the temperature and disorder strength. In the zero temperature limit, the system displays a disorder-induced quantum phase transition between a critical Tomonaga-Luttinger liquid (TLL) phase and a localized Bose glass phase. The $1/{T}_{1}$ is investigated across this transition using large-scale simulations based on matrix product state techniques. We find that this quantity can detect the transition and probe the value of the dimensionless TLL parameter $K$ . We also compute the NMR relaxation rate distributions for each temperature and disorder strength considered. In particular, we discuss the applicability of the stretched exponential fit to the return-to-equilibrium function to extract the $1/{T}_{1}$ experimentally. The results presented here should provide valuable insights in regards of future NMR experiments in realistic disordered spin compounds.We study the nuclear magnetic resonance (NMR) spin-lattice relaxation rate $1/{T}_{1}$ in random one-dimensional spin chains as a function of the temperature and disorder strength. In the zero temperature limit, the system displays a disorder-induced quantum phase transition between a critical Tomonaga-Luttinger liquid (TLL) phase and a localized Bose glass phase. The $1/{T}_{1}$ is investigated across this transition using large-scale simulations based on matrix product state techniques. We find that this quantity can detect the transition and probe the value of the dimensionless TLL parameter $K$. We also compute the NMR relaxation rate distributions for each temperature and disorder strength considered. In particular, we discuss the applicability of the stretched exponential fit to the return-to-equilibrium function to extract the $1/{T}_{1}$ experimentally. The results presented here should provide valuable insights in regards of future NMR experiments in realistic disordered spin compounds.

arXiv:1902.07361Physical review. B./Physical review. BMay 28, 20192 citations

Thermal tensor network approach for spin-lattice relaxation in quantum magnets

Ning Xi, Yuan Gao, Huihang Lin +8 more

Low-dimensional quantum magnets, particularly those with strong spin frustration, are characterized by their notable spin fluctuations. Nuclear magnetic resonance (NMR) serves as a sensitive probe of low-energy fluctuations that offers valuable insight into rich magnetic phases and emergent phenomena in quantum magnets. Although experimentally accessible, the numerical simulation of NMR relaxation rates, specifically the spin-lattice relaxation rate $1/T_1$ , remains a significant challenge. Analytical continuation based on Monte Carlo calculations are hampered by the notorious negative sign for frustrated systems, and the real-time simulations incur significant costs to capture low-energy fluctuations. Here we propose computing the relaxation rate using thermal tensor networks (TTNs), which provides a streamlined approach by calculating its imaginary-time proxy. We showcase the accuracy and versatility of our methodology by applying it to one-dimensional spin chains and two-dimensional lattices, where we find that the critical exponents $η$ and $zν$ can be extracted from the low-temperature scalings of the simulated $1/T_1$ near quantum critical points. Our results also provide insights into the low-dimensional and frustrated magnetic materials, elucidating universal scaling behaviors in the Ising chain compound CoNb $_2$ O $_6$ and revealing the renormalized classical behaviors in the triangular-lattice antiferromagnet Ba $_8$ CoNb $_6$ O $_{24}$ . We apply the approach to effective model of the family of frustrated magnets AYbCh $_2$ (A = Na, K, Cs, and Ch = O, S, Se), and find dramatic changes from spin ordered to the proposed quantum spin liquid phase. Overall, with high reliability and accuracy, the TTN methodology offers a systematic strategy for studying the intricate dynamics observed across a broad spectrum of quantum magnets and related fields.Low-dimensional quantum magnets, particularly those with strong spin frustration, are characterized by their notable spin fluctuations. Nuclear magnetic resonance (NMR) serves as a sensitive probe of low-energy fluctuations that offers valuable insight into rich magnetic phases and emergent phenomena in quantum magnets. Although experimentally accessible, the numerical simulation of NMR relaxation rates, specifically the spin-lattice relaxation rate $1/T_1$, remains a significant challenge. Analytical continuation based on Monte Carlo calculations are hampered by the notorious negative sign for frustrated systems, and the real-time simulations incur significant costs to capture low-energy fluctuations. Here we propose computing the relaxation rate using thermal tensor networks (TTNs), which provides a streamlined approach by calculating its imaginary-time proxy. We showcase the accuracy and versatility of our methodology by applying it to one-dimensional spin chains and two-dimensional lattices, where we find that the critical exponents $η$ and $zν$ can be extracted from the low-temperature scalings of the simulated $1/T_1$ near quantum critical points. Our results also provide insights into the low-dimensional and frustrated magnetic materials, elucidating universal scaling behaviors in the Ising chain compound CoNb$_2$O$_6$ and revealing the renormalized classical behaviors in the triangular-lattice antiferromagnet Ba$_8$CoNb$_6$O$_{24}$. We apply the approach to effective model of the family of frustrated magnets AYbCh$_2$ (A = Na, K, Cs, and Ch = O, S, Se), and find dramatic changes from spin ordered to the proposed quantum spin liquid phase. Overall, with high reliability and accuracy, the TTN methodology offers a systematic strategy for studying the intricate dynamics observed across a broad spectrum of quantum magnets and related fields.

arXiv:2403.11895Physical review. B./Physical review. BMar 4, 20260 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.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:1606.09502Physical review. B./Physical review. BOct 11, 201626 citations

NMR relaxation rates in a spin- 12 antiferromagnetic chain

Victor Barzykin

We consider the low-temperature behavior of NMR relaxation rates ${T}_{1}$ and ${T}_{2G}$ in the spin- $1/2$ antiferromagnetic chain. We find that ${T}_{1}\ensuremath{\propto}\mathrm{const}$ and ${T}_{2G}\ensuremath{\propto}\sqrt{T},$ with logarithmic corrections. We determine both constants and logarithmic terms by matching perturbative renormalization-group with exact results, so that the final expressions for the relaxation rates do not contain any free parameters. Our theoretical results are in excellent agreement with NMR experiments in ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}.$ We consider the low-temperature behavior of NMR relaxation rates ${T}_{1}$ and ${T}_{2G}$ in the spin-$1/2$ antiferromagnetic chain. We find that ${T}_{1}\ensuremath{\propto}\mathrm{const}$ and ${T}_{2G}\ensuremath{\propto}\sqrt{T},$ with logarithmic corrections. We determine both constants and logarithmic terms by matching perturbative renormalization-group with exact results, so that the final expressions for the relaxation rates do not contain any free parameters. Our theoretical results are in excellent agreement with NMR experiments in ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}.$

arXiv:cond-mat/0011453Physical review. B, Condensed matterMar 21, 200134 citations

The NMR relaxation rate

1/T_{1}

is studied for one-dimensional multicomponent spin-orbital systems. By combining the bosonization techniques and the exact solution of the SU(

n

) model, we evaluate the power-law exponent and the enhancement factor for

1/T_1

at low temperatures. We discuss how the band splitting affects the relaxation rate, and find that

1/T_{1}

may be enhanced around the critical value of the band splitting. The crossover behavior in

1/T_1

around the critical point is discussed in terms of the low-frequency dynamical spin susceptibility. The effect of the hole-doping is also addressed.

{1/T}_{1}.

We discuss the critical properties of

{1/T}_{1}

around plateaus and cusps in the magnetization curve.

1/{T}_{1}

in spin-

\frac{1}{2}

chain systems. This quantity is directly related to local, dynamical spin-spin correlation functions. The results agree in the low-temperature regime with bosonization predictions, and show interesting deviations from this behavior at intermediate temperatures.

We study the nuclear magnetic resonance (NMR) spin-lattice relaxation rate

1/{T}_{1}

in random one-dimensional spin chains as a function of the temperature and disorder strength. In the zero temperature limit, the system displays a disorder-induced quantum phase transition between a critical Tomonaga-Luttinger liquid (TLL) phase and a localized Bose glass phase. The

1/{T}_{1}

is investigated across this transition using large-scale simulations based on matrix product state techniques. We find that this quantity can detect the transition and probe the value of the dimensionless TLL parameter

K

. We also compute the NMR relaxation rate distributions for each temperature and disorder strength considered. In particular, we discuss the applicability of the stretched exponential fit to the return-to-equilibrium function to extract the

1/{T}_{1}

experimentally. The results presented here should provide valuable insights in regards of future NMR experiments in realistic disordered spin compounds.

1/T_1

, remains a significant challenge. Analytical continuation based on Monte Carlo calculations are hampered by the notorious negative sign for frustrated systems, and the real-time simulations incur significant costs to capture low-energy fluctuations. Here we propose computing the relaxation rate using thermal tensor networks (TTNs), which provides a streamlined approach by calculating its imaginary-time proxy. We showcase the accuracy and versatility of our methodology by applying it to one-dimensional spin chains and two-dimensional lattices, where we find that the critical exponents

η

and

zν

can be extracted from the low-temperature scalings of the simulated

1/T_1

near quantum critical points. Our results also provide insights into the low-dimensional and frustrated magnetic materials, elucidating universal scaling behaviors in the Ising chain compound CoNb

_2

_6

and revealing the renormalized classical behaviors in the triangular-lattice antiferromagnet Ba

_8

CoNb

_6

_{24}

. We apply the approach to effective model of the family of frustrated magnets AYbCh

_2

(A = Na, K, Cs, and Ch = O, S, Se), and find dramatic changes from spin ordered to the proposed quantum spin liquid phase. Overall, with high reliability and accuracy, the TTN methodology offers a systematic strategy for studying the intricate dynamics observed across a broad spectrum of quantum magnets and related fields.

{}_{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.

We consider the low-temperature behavior of NMR relaxation rates

{T}_{1}

and

{T}_{2G}

in the spin-

1/2

antiferromagnetic chain. We find that ${T}_{1}\ensuremath{\propto}\mathrm{const}$ and ${T}_{2G}\ensuremath{\propto}\sqrt{T},$ with logarithmic corrections. We determine both constants and logarithmic terms by matching perturbative renormalization-group with exact results, so that the final expressions for the relaxation rates do not contain any free parameters. Our theoretical results are in excellent agreement with NMR experiments in

{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}.