Dynamical properties of the $S=\frac{1}{2}$ random Heisenberg chain

Abstract

We use numerical techniques to study dynamical properties at finite temperature ($T$) of the Heisenberg spin chain with random exchange couplings, which realizes the random singlet (RS) fixed point in the low-energy limit. Specifically, we study the dynamic spin structure factor $S(q,\omega )$, which can be probed directly by inelastic neutron scattering experiments and, in the limit of small $\omega$, in nuclear magnetic resonance (NMR) experiments through the spin-lattice relaxation rate $1/T_1$. Our work combines three complementary methods: exact diagonalization, matrix-product-state algorithms, and stochastic analytic continuation of quantum Monte Carlo results in imaginary time. Unlike the uniform system, whose low-energy excitations at low $T$ are restricted to $q$ close to $0$ and $\pi$, our study reveals a continuous narrow band of low-energy excitations in $S(q,\omega )$, extending throughout the Brillouin zone. Close to $q=\pi$, the scaling properties of these excitations are well captured by the RS theory, but we also see disagreements with some aspects of the predicted $q$-dependence further away from $q=\pi$. Furthermore we find spin diffusion effects close to $q=0$ that are not contained within the RS theory but give non-negligible contributions to the mean $1/T_1$. To compare with NMR experiments, we consider the distribution of the local $1/T_1$ values, which is broad, approximately described by a stretched exponential. The mean value first decreases with $T$, but starts to increase and diverge below a crossover temperature. Although a similar divergent behavior has been found for the static uniform susceptibility, this divergent behavior of $1/T_1$ has never been seen in experiments. Our results 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.

19 pages, 14 figures

References in corpus (9)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Minimally Entangled Typical Thermal State Algorithms
• Spectral functions in one-dimensional quantum systems at T>0
• Chebyshev matrix product state approach for spectral functions
• Nearly deconfined spinon excitations in the square-lattice spin-1/2 Heisenberg antiferromagnet
• Chebyshev Matrix Product State Impurity Solver for the Dynamical Mean-Field Theory
• Using the average spectrum method to extract dynamics from quantum Monte Carlo simulations
• Correlation amplitude and entanglement entropy in random spin chains

Cited by in corpus (23)

• Dynamical Signature of Fractionalization at the Deconfined Quantum Critical Point
• Strong Disorder RG approach - a short review of recent developments
• Progress on stochastic analytic continuation of quantum Monte Carlo data
• Random-Singlet Phase in Disordered Two-Dimensional Quantum Magnets
• Dynamical Signature of Symmetry Fractionalization in Frustrated Magnets
• Spectral function of the $J_1-J_2$ Heisenberg model on the triangular lattice
• Randomness induced spin-liquid-like phase in the spin-$1/2$ $J_1-J_2$ triangular Heisenberg model
• Extreme Suppression of Antiferromagnetic Order and Critical Scaling in a Two-Dimensional Random Quantum Magnet
• Signature of a randomness-driven spin-liquid state in a frustrated magnet
• Fractional and composite excitations of antiferromagnetic quantum spin trimer chains
• NMR relaxation in the spin-1 Heisenberg chain
• Spin excitation spectra of the two dimensional $S=1/2$ Heisenberg model with a checkerboard structure
• The correlation functions of certain random antiferromagnetic spin-1/2 critical chains
• Dynamic structure factor of disordered quantum spin ladders
• Engineering entanglement Hamiltonians with strongly interacting cold atoms in optical traps
• Dynamical spin excitations of topological Haldane gapped phase in the $S=1$ Heisenberg antiferromagnetic chain with single-ion anisotropy
• From order to randomness: Onset and evolution of the random-singlet state in bond-disordered BaCu${}_2$(Si${}_{1-x}$Ge${}_x$)${}_2$O${}_7$ spin-chain compounds
• Peculiarities of magnetic ordering in the S = 5/2 two-dimensional square-lattice antimonate NaMnSbO4
• Dynamical properties of the Haldane chain with bond disorder
• Numerical study of the temperature dependence of the NMR relaxation rate across the superfluid-Bose glass transition in one dimension
• Exploration of magnetoelastic deformations in spin-chain compound CuBr${}_2$
• Competition between Neel, Haldane nematic, plaquette valence bond solid, and $(\pi ,\pi )$ valence bond solid phases in SU(N) analogs of $S=1$ square-lattice antiferromagnets
• Witnessing Disorder in Quantum Magnets