arXiv:1902.07361 · Physical review. B./Physical review. B

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

Maxime Dupont

Published May 28, 2019• 2 citations

Abstract

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.

DOI: 10.1103/physrevb.99.205147

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

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Field and temperature dependence of NMR relaxation rate in the magnetic quadrupolar liquid phase of spin- 12 frustrated ferromagnetic chains

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arXiv:1902.07361 · Physical review. B./Physical review. B

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

Maxime Dupont

Published May 28, 2019• 2 citations

arXiv HTML PDF

Abstract

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.

DOI: 10.1103/physrevb.99.205147

Related papers

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

Field and temperature dependence of NMR relaxation rate in the magnetic quadrupolar liquid phase of spin- 12 frustrated ferromagnetic chains

Masahiro Sato, Toshiya Hikihara, Tsutomu Momoi

It is generally difficult experimentally to distinguish magnetic multipolar orders in spin systems. Recently, it was proposed that the temperature dependence of the nuclear magnetic resonance relaxation rate $1/{T}_{1}$ can involve an indirect but clear signature of the field-induced spin nematic or multipolar Tomonaga-Luttinger (TL) liquid phase [M. Sato, T. Momoi, and A. Furusaki, Phys. Rev. B 79, 060406(R) (2009)]. In this paper, we evaluate accurately the field and temperature dependence of $1/{T}_{1}$ in spin- $\frac{1}{2}$ frustrated ${J}_{1}$ - ${J}_{2}$ chains combining field-theoretical techniques with numerical data. Our results demonstrate that isotherms of $1/{T}_{1}$ as a function of magnetic field also exhibit distinctive nonmonotonic behavior in spin nematic TL liquid, in contrast with the standard TL liquid in the spin- $\frac{1}{2}$ Heisenberg chain. The relevance of our results to quasi-one-dimensional edge-sharing cuprate magnets, such as ${\mathrm{LiCuVO}}_{4}$ , is discussed.It is generally difficult experimentally to distinguish magnetic multipolar orders in spin systems. Recently, it was proposed that the temperature dependence of the nuclear magnetic resonance relaxation rate $1/{T}_{1}$ can involve an indirect but clear signature of the field-induced spin nematic or multipolar Tomonaga-Luttinger (TL) liquid phase [M. Sato, T. Momoi, and A. Furusaki, Phys. Rev. B 79, 060406(R) (2009)]. In this paper, we evaluate accurately the field and temperature dependence of $1/{T}_{1}$ in spin-$\frac{1}{2}$ frustrated ${J}_{1}$-${J}_{2}$ chains combining field-theoretical techniques with numerical data. Our results demonstrate that isotherms of $1/{T}_{1}$ as a function of magnetic field also exhibit distinctive nonmonotonic behavior in spin nematic TL liquid, in contrast with the standard TL liquid in the spin-$\frac{1}{2}$ Heisenberg chain. The relevance of our results to quasi-one-dimensional edge-sharing cuprate magnets, such as ${\mathrm{LiCuVO}}_{4}$, is discussed.

arXiv:1009.3206Physical Review BFeb 10, 201157 citations

Direct determination of the Tomonaga-Luttinger parameter K in quasi-one-dimensional spin systems

M. Horvatić, M. Klanjšek, E. Orignac

We test the analytical formula for the enhancement of the nuclear magnetic resonance rate ${T}_{1}^{\ensuremath{-}1}$ by the critical spin fluctuations, over the simple power-law dependence predicted for a purely one-dimensional spin system, recently derived in the random phase approximation [M. Dupont et al., Phys. Rev. B 98, 094403 (2018)]. This prediction is experimentally confirmed by excellent fits to the published temperature dependence of ${T}_{1}^{\ensuremath{-}1}$ data in the two representative spin compounds, ${({\mathrm{C}}_{7}{\mathrm{H}}_{10}\mathrm{N})}_{2}{\mathrm{CuBr}}_{4}$ (DIMPY) and ${\mathrm{BaCo}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$ , providing at the same time a direct and convenient experimental determination of the Tomonaga-Luttinger-liquid parameter $K$ , very well in agreement with theoretical predictions.We test the analytical formula for the enhancement of the nuclear magnetic resonance rate ${T}_{1}^{\ensuremath{-}1}$ by the critical spin fluctuations, over the simple power-law dependence predicted for a purely one-dimensional spin system, recently derived in the random phase approximation [M. Dupont et al., Phys. Rev. B 98, 094403 (2018)]. This prediction is experimentally confirmed by excellent fits to the published temperature dependence of ${T}_{1}^{\ensuremath{-}1}$ data in the two representative spin compounds, ${({\mathrm{C}}_{7}{\mathrm{H}}_{10}\mathrm{N})}_{2}{\mathrm{CuBr}}_{4}$ (DIMPY) and ${\mathrm{BaCo}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$, providing at the same time a direct and convenient experimental determination of the Tomonaga-Luttinger-liquid parameter $K$, very well in agreement with theoretical predictions.

arXiv:2003.05904Physical review. B./Physical review. BJun 9, 202016 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

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.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:1806.04913Physical review. B./Physical review. BSep 5, 201819 citations

Weak- versus strong-disorder superfluid—Bose glass transition in one dimension

Elmer V. H. Doggen, Gabriel Lemarié, Sylvain Capponi +1 more

Using large-scale simulations based on matrix product state and quantum Monte Carlo techniques, we study the superfluid to Bose glass transition for one-dimensional attractive hard-core bosons at zero temperature, across the full regime from weak to strong disorder. As a function of interaction and disorder strength, we identify a Berezinskii-Kosterlitz-Thouless critical line with two different regimes. At small attraction where critical disorder is weak compared to the bandwidth, the critical Luttinger parameter ${K}_{c}$ takes its universal Giamarchi-Schulz value ${K}_{c}=3/2$ . Conversely, a nonuniversal ${K}_{c}>3/2$ emerges for stronger attraction where weak-link physics is relevant. In this strong-disorder regime, the transition is characterized by self-similar power-law-distributed weak links with a continuously varying characteristic exponent $\ensuremath{\alpha}$.Using large-scale simulations based on matrix product state and quantum Monte Carlo techniques, we study the superfluid to Bose glass transition for one-dimensional attractive hard-core bosons at zero temperature, across the full regime from weak to strong disorder. As a function of interaction and disorder strength, we identify a Berezinskii-Kosterlitz-Thouless critical line with two different regimes. At small attraction where critical disorder is weak compared to the bandwidth, the critical Luttinger parameter ${K}_{c}$ takes its universal Giamarchi-Schulz value ${K}_{c}=3/2$. Conversely, a nonuniversal ${K}_{c}>3/2$ emerges for stronger attraction where weak-link physics is relevant. In this strong-disorder regime, the transition is characterized by self-similar power-law-distributed weak links with a continuously varying characteristic exponent $\ensuremath{\alpha}$.

arXiv:1704.02257Physical review. B./Physical review. BNov 9, 201735 citations

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

1/{T}_{1}

1/{T}_{1}

K

1/{T}_{1}

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

{}_{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.

1/{T}_{1}

can involve an indirect but clear signature of the field-induced spin nematic or multipolar Tomonaga-Luttinger (TL) liquid phase [M. Sato, T. Momoi, and A. Furusaki, Phys. Rev. B 79, 060406(R) (2009)]. In this paper, we evaluate accurately the field and temperature dependence of

1/{T}_{1}

in spin-

\frac{1}{2}

frustrated

{J}_{1}

{J}_{2}

chains combining field-theoretical techniques with numerical data. Our results demonstrate that isotherms of

1/{T}_{1}

as a function of magnetic field also exhibit distinctive nonmonotonic behavior in spin nematic TL liquid, in contrast with the standard TL liquid in the spin-

\frac{1}{2}

Heisenberg chain. The relevance of our results to quasi-one-dimensional edge-sharing cuprate magnets, such as

{\mathrm{LiCuVO}}_{4}

, is discussed.

{({\mathrm{C}}_{7}{\mathrm{H}}_{10}\mathrm{N})}_{2}{\mathrm{CuBr}}_{4}

(DIMPY) and

{\mathrm{BaCo}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}

, providing at the same time a direct and convenient experimental determination of the Tomonaga-Luttinger-liquid parameter

K

, very well in agreement with theoretical predictions.

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.

{K}_{c}

takes its universal Giamarchi-Schulz value

{K}_{c}=3/2

. Conversely, a nonuniversal

{K}_{c}>3/2

emerges for stronger attraction where weak-link physics is relevant. In this strong-disorder regime, the transition is characterized by self-similar power-law-distributed weak links with a continuously varying characteristic exponent $\ensuremath{\alpha}$.