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:cond-mat/9904290 · Physical Review Letters

Dynamics and Transport in Random Antiferromagnetic Spin Chains

Kedar Damle, Olexei I. Motrunich, David A. Huse

Published Apr 10, 2000• 51 citations
arXivHTMLPDF

Abstract

We present the first results on the low-frequency dynamical and transport properties of random antiferromagnetic spin chains at low temperature (T). We obtain the momentum and frequency dependent dynamic structure factor in the random singlet (RS) phases of both spin-1/2 and spin-1 chains, as well as in the random dimer phase of spin-1/2 chains. We also show that the RS phases are unusual "spin-metals" with divergent low-frequency conductivity at T = 0, and follow the spin conductivity through "metal-insulator" transitions tuned by the strength of dimerization or Ising anisotropy in the spin-1/2 case and by the strength of disorder in the spin-1 case.

DOI
10.1103/physrevlett.84.3434

Related papers

Dynamics and transport in random quantum systems governed by strong-randomness fixed points

Olexei I. Motrunich, Kedar Damle, David A. Huse

We present results on the low-frequency dynamical and transport properties of random quantum systems whose low temperature $(T),$ low-energy behavior is controlled by strong-disorder fixed points. We obtain the momentum- and frequency-dependent dynamic structure factor in the random singlet (RS) phases of both spin-1/2 and spin-1 random antiferromagnetic chains, as well as in the random dimer and Ising antiferromagnetic phases of spin-1/2 random antiferromagnetic chains. We show that the RS phases are unusual ``spin metals'' with divergent low-frequency spin conductivity at $T=0,$ and we also follow the conductivity through ``metal-insulator'' transitions tuned by the strength of dimerization or Ising anisotropy in the spin-1/2 case, and by the strength of disorder in the spin-1 case. We work out the average spin and energy autocorrelations in the one-dimensional random transverse-field Ising model in the vicinity of its quantum critical point. All of the above calculations are valid in the frequency-dominated regime $\ensuremath{\omega}\ensuremath{\gtrsim}T,$ and rely on previously available renormalization group schemes that describe these systems in terms of the properties of certain strong-disorder fixed-point theories. In addition, we obtain some information about the behavior of the dynamic structure factor and dynamical conductivity in the opposite ``hydrodynamic'' regime $\ensuremath{\omega}<T$ for the special case of spin-1/2 chains close to the planar limit (the quantum $x\ensuremath{-}y$ model) by analyzing the corresponding quantities in an equivalent model of spinless fermions with weak repulsive interactions and particle-hole symmetric disorder.

arXiv:cond-mat/0005543•Physical review. B, Condensed matter•Mar 13, 2001•80 citations

Signatures of infinite randomness in transport properties of strongly disordered spin chains

L. F. C. Faria, Victor L. Quito, João C. Getelina +2 more

We study the spin transport properties of some disordered spin chains with a special focus on the distribution of the frequency-dependent spin conductivity. In the cases of interest here, the systems are governed by an effectively infinite disorder at low energies. A hallmark of this behavior is the wide discrepancy between the average and the typical values of some physical quantities, which are described by extremely broad distributions. We show that such is also the case of the spin conductivity, whose average value is metallic but whose typical one, the physically relevant quantity, is insulating. This solves the apparent contradiction between the prediction of a spin metallic phase of the spin-1/2 disordered XX chain and its known localized behavior (after a mapping to free fermions). Our results are based on analytical and numerical implementations of a strong-disorder renormalization group as well as exact diagonalization studies. We present our analyses in very general terms, valid for systems of any spin $S$ value, but the cases of $S=1/2$ and 1 are studied in greater detail.

arXiv:2312.07474•Physical review. B./Physical review. B•Jun 12, 2026•0 citations

Dynamical properties of the S=12 random Heisenberg chain

Yu-Rong Shu, Maxime Dupont, Dao‐Xin Yao +2 more

We study dynamical properties at finite temperature $(T)$ of Heisenberg spin chains with random antiferromagnetic exchange couplings, which realize the random singlet phase in the low-energy limit, using three complementary numerical methods: exact diagonalization, matrix-product-state algorithms, and stochastic analytic continuation of quantum Monte Carlo results in imaginary time. Specifically, we investigate the dynamic spin structure factor $S(q,\ensuremath{\omega})$ and its $\ensuremath{\omega}\ensuremath{\rightarrow}0$ limit, which are closely related to inelastic neutron scattering and nuclear magnetic resonance (NMR) experiments (through the spin-lattice relaxation rate $1/{T}_{1})$. Our study reveals a continuous narrow band of low-energy excitations in $S(q,\ensuremath{\omega})$, extending throughout the $q$ space, instead of being restricted to $q\ensuremath{\approx}0$ and $q\ensuremath{\approx}\ensuremath{\pi}$ as found in the uniform system. Close to $q=\ensuremath{\pi}$, the scaling properties of these excitations are well captured by the random-singlet theory, but disagreements also exist with some aspects of the predicted $q$ dependence further away from $q=\ensuremath{\pi}$. Furthermore we also find spin diffusion effects close to $q=0$ that are not contained within the random-singlet theory but give non-negligible contributions to the mean $1/{T}_{1}$. To compare with NMR experiments, we consider the distribution of the local relaxation rates $1/{T}_{1}$. We show that the local $1/{T}_{1}$ values are broadly distributed, approximately according to a stretched exponential. The mean $1/{T}_{1}$ first decreases with $T$, but below a crossover temperature it starts to increase and likely diverges in the limit of a small nuclear resonance frequency ${\ensuremath{\omega}}_{0}$. Although a similar divergent behavior has been predicted and experimentally observed for the static uniform susceptibility, this divergent behavior of the mean $1/{T}_{1}$ has never been experimentally observed. Indeed, we show that the divergence of the mean $1/{T}_{1}$ is due to rare events in the disordered chains and is concealed in experiments, where the typical $1/{T}_{1}$ value is accessed.

arXiv:1712.01701•Physical review. B./Physical review. B•Mar 28, 2018•31 citations

Random antiferromagnetic quantum spin chains

Daniel S. Fisher

The properties of spin-1/2 antiferromagnetic chains with various types of random exchange coupling are studied via an asymptotically exact decimation renormalization-group transformation, which is a generalization of that introduced by Dasgupta and Ma. Random-singlet phases occur in which each spin is paired with one other spin that may be very far away; more exotic phases also occur. The behavior of typical and mean correlation functions is analyzed and found to be very different, with very small sets of spins dominating the latter at long distances as well as the low-temperature thermodynamics. Some of the phase transitions that occur between antiferromagnetically ordered phases and random singlet or other antiferromagnetic phases are also analyzed. For example, if a small uniaxial anisotropy perturbation is added to a random Heisenberg antiferromagnetic chain, a transition occurs from a random-singlet phase to an Ising antiferromagnetic phase, as the anisotropy changes sign from easy plane to easy axis. The staggered magnetization vanishes at the transition with critical exponent \ensuremath{\beta}=8/(1+ \ensuremath{\surd}7 ). Possible implications for the properties of random quantum magnetic systems in higher dimensions are briefly discussed.

Physical review. B, Condensed matter•Aug 1, 1994•651 citations

Dynamical structure factor of random antiferromagnetic Heisenberg spin chains

Zhaoxin Xu, He-Ping Ying, Xin Wan

Combining quantum Monte Carlo simulations with the maximum entropy method, we study the dynamical structure factor $S(k,ω)$ of spin-1/2 antiferromagnetic Heisenberg chains with various random bond distributions. We emphasize the crossover behavior in the dynamical properties from pure chain to disorder-dominated random singlet phase due to bond randomness. For the distribution corresponding to the infinite randomness fixed point, $S(k,ω)$ develops broad non-spinon excitations as well as the random-singlet peak near $(k, ω) = (π, 0)$, consistent with the known results obtained by the real-space renormalization group method. For weak disorder, however, we find clear signature of spinon excitations, reminiscent of pure spin chains, blurred by disorder. We discuss the implication for experiments on random-bond antiferromagnetic spin chains, realizable, e.g., in BaCu$_2$(Si$_x$Ge$_{1-x}$)$_2$O$_7$.

arXiv:cond-mat/0703772•Mar 29, 2007•0 citations

Strongly disordered antiferromagnetic spin-1 chains with random anisotropy

A. Saguia, B. Boechat, M. A. Contínentino

The zero-temperature phase diagram of the anisotropic, strongly disordered antiferromagnetic quantum spin-1 chain is investigated, within the framework of a real-space renormalization-group approach. In the presence of uniform anisotropy there occurs a phase transition from a random singlet phase to an Ising antiferromagnetic phase controlled by a fixed point that does not have Heisenberg symmetry. We find evidence of a fixed point due to randomness in the anisotropy similar to that which occurs for quantum Heisenberg spin-$\frac{1}{2}$ chains.

Physical review. B, Condensed matter•Jul 1, 1998•22 citations
We present the first results on the low-frequency dynamical and transport properties of random antiferromagnetic spin chains at low temperature (T). We obtain the momentum and frequency dependent dynamic structure factor in the random singlet (RS) phases of both spin-1/2 and spin-1 chains, as well as in the random dimer phase of spin-1/2 chains. We also show that the RS phases are unusual "spin-metals" with divergent low-frequency conductivity at T = 0, and follow the spin conductivity through "metal-insulator" transitions tuned by the strength of dimerization or Ising anisotropy in the spin-1/2 case and by the strength of disorder in the spin-1 case.
We present results on the low-frequency dynamical and transport properties of random quantum systems whose low temperature (T),(T),(T), low-energy behavior is controlled by strong-disorder fixed points. We obtain the momentum- and frequency-dependent dynamic structure factor in the random singlet (RS) phases of both spin-1/2 and spin-1 random antiferromagnetic chains, as well as in the random dimer and Ising antiferromagnetic phases of spin-1/2 random antiferromagnetic chains. We show that the RS phases are unusual ``spin metals'' with divergent low-frequency spin conductivity at T=0,T=0,T=0, and we also follow the conductivity through ``metal-insulator'' transitions tuned by the strength of dimerization or Ising anisotropy in the spin-1/2 case, and by the strength of disorder in the spin-1 case. We work out the average spin and energy autocorrelations in the one-dimensional random transverse-field Ising model in the vicinity of its quantum critical point. All of the above calculations are valid in the frequency-dominated regime $\ensuremath{\omega}\ensuremath{\gtrsim}T,$ and rely on previously available renormalization group schemes that describe these systems in terms of the properties of certain strong-disorder fixed-point theories. In addition, we obtain some information about the behavior of the dynamic structure factor and dynamical conductivity in the opposite ``hydrodynamic'' regime $\ensuremath{\omega}<T$ for the special case of spin-1/2 chains close to the planar limit (the quantum $x\ensuremath{-}y$ model) by analyzing the corresponding quantities in an equivalent model of spinless fermions with weak repulsive interactions and particle-hole symmetric disorder.
We study the spin transport properties of some disordered spin chains with a special focus on the distribution of the frequency-dependent spin conductivity. In the cases of interest here, the systems are governed by an effectively infinite disorder at low energies. A hallmark of this behavior is the wide discrepancy between the average and the typical values of some physical quantities, which are described by extremely broad distributions. We show that such is also the case of the spin conductivity, whose average value is metallic but whose typical one, the physically relevant quantity, is insulating. This solves the apparent contradiction between the prediction of a spin metallic phase of the spin-1/2 disordered XX chain and its known localized behavior (after a mapping to free fermions). Our results are based on analytical and numerical implementations of a strong-disorder renormalization group as well as exact diagonalization studies. We present our analyses in very general terms, valid for systems of any spin SSS value, but the cases of S=1/2S=1/2S=1/2 and 1 are studied in greater detail.
We study dynamical properties at finite temperature (T)(T)(T) of Heisenberg spin chains with random antiferromagnetic exchange couplings, which realize the random singlet phase in the low-energy limit, using three complementary numerical methods: exact diagonalization, matrix-product-state algorithms, and stochastic analytic continuation of quantum Monte Carlo results in imaginary time. Specifically, we investigate the dynamic spin structure factor $S(q,\ensuremath{\omega})$ and its $\ensuremath{\omega}\ensuremath{\rightarrow}0$ limit, which are closely related to inelastic neutron scattering and nuclear magnetic resonance (NMR) experiments (through the spin-lattice relaxation rate 1/T1)1/{T}_{1})1/T1​). Our study reveals a continuous narrow band of low-energy excitations in $S(q,\ensuremath{\omega})$, extending throughout the qqq space, instead of being restricted to $q\ensuremath{\approx}0$ and $q\ensuremath{\approx}\ensuremath{\pi}$ as found in the uniform system. Close to $q=\ensuremath{\pi}$, the scaling properties of these excitations are well captured by the random-singlet theory, but disagreements also exist with some aspects of the predicted qqq dependence further away from $q=\ensuremath{\pi}$. Furthermore we also find spin diffusion effects close to q=0q=0q=0 that are not contained within the random-singlet theory but give non-negligible contributions to the mean 1/T11/{T}_{1}1/T1​. To compare with NMR experiments, we consider the distribution of the local relaxation rates 1/T11/{T}_{1}1/T1​. We show that the local 1/T11/{T}_{1}1/T1​ values are broadly distributed, approximately according to a stretched exponential. The mean 1/T11/{T}_{1}1/T1​ first decreases with TTT, but below a crossover temperature it starts to increase and likely diverges in the limit of a small nuclear resonance frequency ${\ensuremath{\omega}}_{0}$. Although a similar divergent behavior has been predicted and experimentally observed for the static uniform susceptibility, this divergent behavior of the mean 1/T11/{T}_{1}1/T1​ has never been experimentally observed. Indeed, we show that the divergence of the mean 1/T11/{T}_{1}1/T1​ is due to rare events in the disordered chains and is concealed in experiments, where the typical 1/T11/{T}_{1}1/T1​ value is accessed.
The properties of spin-1/2 antiferromagnetic chains with various types of random exchange coupling are studied via an asymptotically exact decimation renormalization-group transformation, which is a generalization of that introduced by Dasgupta and Ma. Random-singlet phases occur in which each spin is paired with one other spin that may be very far away; more exotic phases also occur. The behavior of typical and mean correlation functions is analyzed and found to be very different, with very small sets of spins dominating the latter at long distances as well as the low-temperature thermodynamics. Some of the phase transitions that occur between antiferromagnetically ordered phases and random singlet or other antiferromagnetic phases are also analyzed. For example, if a small uniaxial anisotropy perturbation is added to a random Heisenberg antiferromagnetic chain, a transition occurs from a random-singlet phase to an Ising antiferromagnetic phase, as the anisotropy changes sign from easy plane to easy axis. The staggered magnetization vanishes at the transition with critical exponent \ensuremath{\beta}=8/(1+ \ensuremath{\surd}7 ). Possible implications for the properties of random quantum magnetic systems in higher dimensions are briefly discussed.
Combining quantum Monte Carlo simulations with the maximum entropy method, we study the dynamical structure factor S(k,ω)S(k,ω)S(k,ω) of spin-1/2 antiferromagnetic Heisenberg chains with various random bond distributions. We emphasize the crossover behavior in the dynamical properties from pure chain to disorder-dominated random singlet phase due to bond randomness. For the distribution corresponding to the infinite randomness fixed point, S(k,ω)S(k,ω)S(k,ω) develops broad non-spinon excitations as well as the random-singlet peak near (k,ω)=(π,0)(k, ω) = (π, 0)(k,ω)=(π,0), consistent with the known results obtained by the real-space renormalization group method. For weak disorder, however, we find clear signature of spinon excitations, reminiscent of pure spin chains, blurred by disorder. We discuss the implication for experiments on random-bond antiferromagnetic spin chains, realizable, e.g., in BaCu2_22​(Six_xx​Ge1−x_{1-x}1−x​)2_22​O7_77​.
The zero-temperature phase diagram of the anisotropic, strongly disordered antiferromagnetic quantum spin-1 chain is investigated, within the framework of a real-space renormalization-group approach. In the presence of uniform anisotropy there occurs a phase transition from a random singlet phase to an Ising antiferromagnetic phase controlled by a fixed point that does not have Heisenberg symmetry. We find evidence of a fixed point due to randomness in the anisotropy similar to that which occurs for quantum Heisenberg spin-12\frac{1}{2}21​ chains.