Abstract Focusing on novel highly correlated low‐dimensional systems, we investigate a class of quasione‐dimensional systems with an even number of spin‐½ sites per unit cell, for which we find, here, that it does not give a gap in the exact excitation spectrum. The unit cells of these systems are formed by two different structural units, each with an odd number of sites. We find the instability of these systems against the regular oscillations of the interactions between structural units and estimate numerically the corresponding critical exponents for the ground‐state energies. In contrast to the well‐known spin‐Peierls instability, this type of structural instability does not change the symmetry of the above systems. We also present a class of disordered one‐dimensional spin systems formed by different types of structural units with odd numbers of spins to demonstrate a critical behavior similar to a homogeneous spin‐½ chain in the limit of weak interactions between structural units.
We investigate the spin-Peierls instability of some periodic 1D Heisenberg spin systems having a gapless energy spectrum at different values of coupling J between the unit cells. Using the density-matrix renormalization group method we numerically study the dependence of critical exponents p of spin-Peierls transition of above spin systems on the value of J. In contrast to chain systems, we find significantly non-monotonous dependence p (J) for three-legs ladder system. In the limit of weak coupling J we derive effective spin s chain Hamiltonians describing the low-energy states of the system considered by means of perturbation theory. The value of site spin s coincides with the value of the ground-state spin of the isolated unit cell of the system considered. This means that at small J values all the systems with the singlet ground state and the same half-integer value of s should have a similar critical behavior which is in agreement with our numerical study. The presence of gapped excitations inside the unit cells at small values of J should give, for our spin systems, at least one intermediate plateau in field dependence of magnetization at low temperatures. The stability of this plateau against the increase of the values of J and temperature is studied using the quantum Monte-Carlo method.
A class of frustrated one-dimensional periodic Heisenberg spin systems formed either by triangular unit cells with spin 1/2 or by composite unit cells formed by two different structural units, triangles and small linear segments formed by an odd number of spin-1/2 is investigated. Based on perturbative processing and numerical calculations of the density matrix renormalization group method, the gapless character of the exact energy spectrum of excitation for these systems was found. Their instability with respect to regular (Peierls) oscillations of interactions between structural units is demonstrated. The corresponding critical exponents for the energies of the ground state are estimated numerically. For some frustrated systems, a quantum phase transition associated with the spin symmetry of the ground state, caused by frustration, has been discovered.
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/T1). 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/T1. To compare with NMR experiments, we consider the distribution of the local relaxation rates
1/T1. We show that the local
1/T1 values are broadly distributed, approximately according to a stretched exponential. The mean
1/T1 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/T1 has never been experimentally observed. Indeed, we show that the divergence of the mean
1/T1 is due to rare events in the disordered chains and is concealed in experiments, where the typical
1/T1 value is accessed.
Low-dimensional spin systems, consisting of arrays of spins arranged in chains or ladders, have been investigated intensively in recent years using both exactly solvable theoretical models as well as a variety of experimental techniques. In case of random variations of the exchange couplings the renormalization group theory predicts the existence of a random-singlet (RS) state, corresponding to spins coupled at all possible distances and energy scales. The scarce availability of suitable random systems, however, has so far prevented the experimental identification of this peculiar magnetic ground state. In a combined effort using nuclear magnetic resonance (NMR), dc magnetometry and numerical simulations, we now find compelling evidence for the formation of a random-singlet state in this class of materials. Randomness seems to generate a broad distribution of local magnetic fields, in turn reflected in stretched exponential NMR relaxations. This distribution exhibits a progressive broadening with decreasing temperature, caused by the growing inequivalence of magnetic sites, as expected from the RS theory. Our findings suggest that NMR is the tool of choice for probing the low-energy physics also in other disordered magnets, where extended-scale excitations are dominant.
One-dimensional Heisenberg spin 1/2 chains with random ferro- and antiferromagnetic bonds are realized in systems such as
Sr3CuPt1−xIrxO6. We have investigated numerically the thermodynamic properties of a generic random bond model and of a realistic model of
Sr3CuPt1−xIrxO6 by the quantum Monte Carlo loop algorithm. For the first time we demonstrate the separation into three different temperature regimes for the original Hamiltonian based on an exact treatment, especially we show that the intermediate temperature regime is well-defined and observable in both the specific heat and the magnetic susceptibility. The crossover between the regimes is indicated by peaks in the specific heat. The uniform magnetic susceptibility shows Curie-like behavior in the high-, intermediate- and low-temperature regime, with different values of the Curie constant in each regime. We show that these regimes are overlapping in the realistic model and give numerical data for the analysis of experimental tests.