Antiferromagnetic Heisenberg Chain Research Articles

Synthesis, coordination modes, structures, and magnetic properties of halogen-substituted 2-hydroxypyridine copper(II) chloride coordination compounds

A family of 6-X-2-hydroxyprydine/pyridone (6-X-2-HOpy/pyridone) Cu(II) compounds, [Cu(6-X-2-HOpy)2Cl2] (1 X = F; 2 X = Cl) and [(6-X-2-pyridone)CuCl(μ-Cl)]2 (3 X = Cl; 4 X = Br), has been prepared. Solution-based infrared spectra displayed a correlation between tautomeric state, primarily driven by halogen identity, and coordination mode with neutral nitrogen coordination mode favored as Br ≪ Cl < F. The tautomeric state of 6-Cl-2-HOpy is influenced by metal ion concentration (M) with lactam concentration increasing as M increases. Compound 1 has F–F contacts less than the sum of the van der Waals radii but falls outside of the typical halogen bonding angle parameters, R–X•••Y = R–Y•••X = 138.2°. Compounds 1 and 2 exhibit weak antiferromagnetic exchanges, fit with a one-dimensional quantum Heisenberg antiferromagnetic linear chain (1D-QHAF) model and J/kB = −1.99(1) K and −0.92(7) K, respectively. Compounds 3 and 4 exhibit a dominating ferromagnetic exchange and an antiferromagnetic exchange and were qualitatively fit to a ferromagnetic linear chain with an interchain interaction model. This model does not accurately represent the physical parameters of the system and was used to show that both exchanges exist and are nontrivial.

Thermally Ultrarobust S = 1/2 Tetrazolinyl Radicals: Synthesis, Electronic Structure, Magnetism, and Nanoneedle Assemblies on Silicon Surface.

Open-shell organic molecules, including S = 1/2 radicals, may provide enhanced properties for several emerging technologies; however, relatively few synthesized to date possess robust thermal stability and processability. We report the synthesis of S = 1/2 biphenylene-fused tetrazolinyl radicals 1 and 2. Both radicals possess near-perfect planar structures based on their X-ray structures and density-functional theory (DFT) computations. Radical 1 possesses outstanding thermal stability as indicated by the onset of decomposition at 269 °C, based on thermogravimetric analysis (TGA) data. Both radicals possess very low oxidation potentials <0 V (vs. SCE) and their electrochemical energy gaps, Ecell ≈ 0.9 eV, are rather low. Magnetic properties of polycrystalline 1 are characterized by superconducting quantum interference device (SQUID) magnetometry revealing a one-dimensional S = 1/2 antiferromagnetic Heisenberg chain with exchange coupling constant J'/k ≈ -22.0 K. Radical 1 in toluene glass possesses a long electron spin coherence time, Tm ≈ 7 μs in the 40-80 K temperature range, a property advantageous for potential applications as a molecular spin qubit. Radical 1 is evaporated under ultrahigh vacuum (UHV) forming assemblies of intact radicals on a silicon substrate, as confirmed by high-resolution X-ray photoelectron spectroscopy (XPS). Scanning electron microscope (SEM) images indicate that the radical molecules form nanoneedles on the substrate. The nanoneedles are stable for at least 64 hours under air as monitored by using X-ray photoelectron spectroscopy. Electron paramagnetic resonance (EPR) studies of the thicker assemblies, prepared by UHV evaporation, indicate radical decay according to first-order kinetics with a long half-life of 50 ± 4 days at ambient conditions.

State space geometry of the spin-1 antiferromagnetic Heisenberg chain

We study the phase diagram of the spin-1 antiferromagnetic Heisenberg chain with uniaxial anisotropy and applied magnetic field in terms of the genuine multipartite entanglement as witnessed by the mean quantum Fisher information density. By considering the manifold generated by the staggered magnetization operator, we connect the state space curvature in the vicinity of the ground state of the Heisenberg chain to the genuine multipartite entanglement. Our analysis demonstrates that the quantum critical points and symmetry protected topological (SPT) phase exhibit large state space curvature, while the separable phases are completely flat, offering insight into the physical interpretation of state space curvature. We further show that the entanglement in the SPT phase is enhanced by the presence of uniaxial anisotropy and undiminished in the presence of uniform magnetic fields. The magnon condensate phase induced by large fields is shown to emanate from the Gaussian critical point and exhibits massive multipartite entanglement over a robust region of the parameter space.

Duality, criticality, anomaly, and topology in quantum spin-1 chains

In quantum spin-1 chains, there is a nonlocal unitary transformation known as the Kennedy-Tasaki transformation ${U}_{\mathrm{KT}}$, which defines a duality between the Haldane phase and the ${\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ symmetry-breaking phase. In this paper, we find that ${U}_{\mathrm{KT}}$ also defines a duality between a topological Ising critical phase and a trivial Ising critical phase, which provides a ``hidden symmetry breaking'' interpretation of the topological criticality. Moreover, since the duality relates different phases of matter, we argue that a model with self-duality (i.e., invariant under ${U}_{\mathrm{KT}}$) is natural to be at a critical or multicritical point. We study concrete examples to demonstrate this argument. In particular, when $H$ is the Hamiltonian of the spin-1 antiferromagnetic Heisenberg chain, we prove that the self-dual model $H+{U}_{\mathrm{KT}}H{U}_{\mathrm{KT}}$ is exactly equivalent to a gapless spin-$1/2$ XY chain, which also implies an emergent quantum anomaly. On the other hand, we show that the topological and trivial Ising critical phases that are dual to each other meet at a multicritical point which is indeed self-dual.

Study of Interacting Heisenberg Antiferromagnet Spin-1/2 and 1 Chains

Haldane conjectures the fundamental difference in the energy spectrum of the Heisenberg antiferromagnetic (HAF) of the spin S chain is that the half-integer and the integer S chain have gapless and gapped energy spectrums, respectively. The ground state (gs) of the HAF spin-1/2 and spin-1 chains have a quasi-long-range and short-range correlation, respectively. We study the effect of the exchange interaction between an HAF spin-1/2 and an HAF spin-1 chain forming a normal ladder system and its gs properties. The inter-chain exchange interaction J⊥ can be either ferromagnetic (FM) or antiferromagnetic (AFM). Using the density matrix renormalization group method, we show that in the weak AFM/FM coupling limit of J⊥, the system behaves like two decoupled chains. However, in the large AFM J⊥ limit, the whole system can be visualized as weakly coupled spin-1/2 and spin-1 pairs which behave like an effective spin-1/2 HAF chain. In the large FM J⊥ limit, coupled spin-1/2 and spin-1 pairs can form pseudo spin-3/2 and the whole system behaves like an effective spin-3/2 HAF chain. We also derive the effective model Hamiltonian in both strong FM and AFM rung exchange coupling limits.

Characteristic quantum phase in Heisenberg antiferromagnetic chain with exchange and single-ion anisotropies.

We investigate the ground-state phase diagram for a spin-one quantum Heisenberg antiferromagnetic chain with exchange and single-ion anisotropies in an external magnetic field by using the infinite time-evolving block decimation algorithm to compute the ground-state fidelity per lattice site. We detect all phase boundaries solely by computing the ground-state fidelity per lattice site, with the prescription that a phase transition point is attributed to a pinch point on the ground-state fidelity surface. Furthermore, the results indicate that a magnetization plateau corresponds to a fidelity plateau on the ground-state fidelity surface, thus offering an alternative route for investigating the magnetization processes of quantum many-body spin systems. We characterize all phases by using the local-order parameter, the spin correlation, the momentum distribution of the spin correlation structure factor, and mutual information as a function of the lattice distance. The commensurate and incommensurate phases are distinguished by the mutual information. In addition, the central charges at criticalities are identified by performing a finite-entanglement scaling analysis. The results show that all phase transitions between spin liquids and magnetization plateaus belong to the Pokrovsky-Talapov universality class.

Excitation Spectra and Edge Singularities in the One-Dimensional Anisotropic Heisenberg Model for Δ = cos(π/n), n = 3,4,5

The T=0 excitation spectra of the antiferromagnetic (J&gt;0) anisotropic Heisenberg chain of spins 1/2 are studied using the Bethe Ansatz equations for Δ=cos(π/n), n=3,4 and 5. The number of unknown functions is n−1 for Δ=cos(π/n) and can be solved numerically for a finite external field. The low-energy excitations form a Luttinger liquid parametrized by a conformal field theory with conformal charge of c=1. For higher energy excitations, the spectral functions display deviations from the Luttinger behavior arising from the curvature in the dispersion. Adding a corrective term of the form of a mobile impurity coupled to the Luttinger liquid modes corrects this difference. The “impurity” is an irrelevant operator, which if treated non-perturbatively, yields the threshold singularities in the one-spinwave particle and hole Green’s function correctly.

Unambiguous Experimental Verification of Linear-in-Temperature Spinon Thermal Conductivity in an Antiferromagnetic Heisenberg Chain.

The everlasting interest in spin chains is mostly rooted in the fact that they generally allow for comparisons between theory and experiment with remarkable accuracy, especially for exactly solvable models. A notable example is the spin-1/2 antiferromagnetic Heisenberg chain (AFHC), which can be well described by the Tomonaga-Luttinger liquid theory and exhibits fractionalized spinon excitations with distinct thermodynamic and spectroscopic experimental signatures consistent with theoretical predictions. A missing piece, however, is the lack of a comprehensive understanding of the spinon heat transport in AFHC systems, due to difficulties in its experimental evaluation against the backdrop of other heat carriers and complex scattering processes. Here we address this situation by performing ultralow-temperature thermal conductivity measurements on a nearly ideal spin-1/2 AFHC system copper benzoate Cu(C_{6}H_{5}COO)_{2}·3H_{2}O, whose field-dependent spin excitation gap enables a reliable extraction of the spinon thermal conductivity κ_{s} at zero field. κ_{s} was found to exhibit a linear temperature dependence κ_{s}∼T at low temperatures, with κ_{s}/T as large as 1.70 mW cm^{-1} K^{-2}, followed by a precipitate decline below ∼0.3 K. The observed κ_{s}∼T clarifies the discrepancies between various spin chain systems and serves as a benchmark for one-dimensional spinon heat transport in the low-temperature limit. The abrupt loss of κ_{s} with no corresponding anomaly in the specific heat is discussed in the context of many-body localization.

Quantum wake dynamics in Heisenberg antiferromagnetic chains

Traditional spectroscopy, by its very nature, characterizes physical system properties in the momentum and frequency domains. However, the most interesting and potentially practically useful quantum many-body effects emerge from local, short-time correlations. Here, using inelastic neutron scattering and methods of integrability, we experimentally observe and theoretically describe a local, coherent, long-lived, quasiperiodically oscillating magnetic state emerging out of the distillation of propagating excitations following a local quantum quench in a Heisenberg antiferromagnetic chain. This “quantum wake” displays similarities to Floquet states, discrete time crystals and nonlinear Luttinger liquids. We also show how this technique reveals the non-commutativity of spin operators, and is thus a model-agnostic measure of a magnetic system’s “quantumness.”

Structure and Magnetism of an Ideal One-Dimensional Chain Antiferromagnet [C2NH8]3[Fe(SO4)3] with a Large Spin of S = 5/2

Isolated large-spin Heisenberg antiferromagnetic uniform chain is quite rare. Here, we have successfully synthesized an ideal one-dimensional (1D) S = 5/2 linear-chain antiferromagnet [C2NH8]3[Fe(SO4)3], which crystallizes in a trigonal lattice with the space group R3c. A broad maximum at Tmax = 18 K is observed in the magnetic susceptibility curve. Notably, no long-range magnetic ordering is observed down to 2 K even if the material has a large Curie-Weiss temperature of θCW = -25.5 K. High-field magnetization at 2 K shows a linear increase until saturation at 30 T, and a high-field electron spin resonance (ESR) reveals the absence of a zero-field spin gap. The intrachain interaction J and interchain interaction J' are determined. Quite a small ratio of J'/J < 2.5 × 10-3 suggests that [C2NH8]3[Fe(SO4)3] behaves as an ideal 1D uniform linear-chain antiferromagnet, in which the magnetic ordering is prevented by the extremely small interchain interaction and quantum fluctuation even for a classical spin of S = 5/2.

Unraveling higher-order contributions to spin excitations probed using resonant inelastic x-ray scattering

Resonant inelastic x-ray scattering (RIXS) is an evolving tool for investigating the spin dynamics of strongly correlated materials, which complements inelastic neutron scattering. In isotropic spin-$\frac{1}{2}$ Heisenberg antiferromagnetic (HAFM) spin chains, both techniques have observed non-spin-conserving (NSC) excitations confined to the two-spinon phase space. However, a recent O $K$-edge RIXS study of the one-dimensional HAFM ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}$ observed spin-conserving (SC) four-spinon excitations outside the two-spinon phase space. Here, we demonstrate that analogous four-spinon excitations can also be accessed at the Cu ${L}_{3}$ edge in the related material ${\mathrm{SrCuO}}_{2}$. Through detailed modeling, we establish that these excitations appear in both the SC and NSC channels of the Cu ${L}_{3}$ edge, and are only captured by higher-order terms in the ultrashort core-hole lifetime expansion. Since these terms encode information about spin-spin correlations extending beyond nearest neighbors, our results offer different possibilities for studying nonlocal spin correlations in quantum magnets.

Dissipation-Induced Order: The S=1/2 Quantum Spin Chain Coupled to an Ohmic Bath.

We consider an S=1/2 antiferromagnetic quantum Heisenberg chain where each site is coupled to an independent bosonic bath with ohmic dissipation. The coupling to the bath preserves the global SO(3) spin symmetry. Using large-scale, approximation-free quantum MonteCarlo simulations, we show that any finite coupling to the bath suffices to stabilize long-range antiferromagnetic order. This is in stark contrast to the isolated Heisenberg chain where spontaneous breaking of the SO(3) symmetry is forbidden by the Mermin-Wagner theorem. A linear spin-wave theory analysis confirms that the memory of the bath and the concomitant retarded interaction stabilize the order. For the Heisenberg chain, the ohmic bath is a marginal perturbation so that exponentially large system sizes are required to observe long-range order at small couplings. Below this length scale, our numerics is dominated by a crossover regime where spin correlations show different power-law behaviors in space and time. We discuss the experimental relevance of this crossover phenomena.

Adaptive density matrix renormalization group study of the disordered antiferromagnetic spin- 12 Heisenberg chain

Using an adaptive strategy which enables the study of quenched disordered system via the density-matrix renormalization-group method, we compute the various ground-state spin-spin correlation measures of the spin-$\frac{1}{2}$ antiferromagnetic Heisenberg chain with random coupling constants, namely, the mean values of the bulk and of the end-to-end correlations, the typical value of the bulk correlations, and the distribution of the bulk correlations. Our results are in agreement with the predictions of the strong-disorder renormalization-group method. We do not find any hint of logarithmic corrections either in the bulk average correlations, which were recently reported by Shu et al. [Phys. Rev. B 94, 174442 (2016)], or in the end-to-end average correlations. We report the existence of a logarithmic correction on the end-to-end correlations of the clean chain. Finally, we have determined that the distribution of the bulk correlations, when properly rescaled by an associated Lyapunov exponent, is a narrow and universal (disorder-independent) probability function.

Long-range order and quantum criticality in antiferromagnetic chains with long-range staggered interactions.

We study quantum phase transitions in Heisenberg antiferromagnetic chains with a staggered power-law decaying long-range interactions. Employing the density-matrix renormalization group (DMRG) algorithm and the fidelity susceptibility as the criticality measure, we establish more accurate values of quantum critical points than the results obtained from the spin-wave approximation, quantum Monte Carlo, and DMRG in literatures. The deviation is especially evident for strong long-range interactions. We extend isotropic long-range interactions to the anisotropic cases and find that kaleidoscope of quantum phases emerge from the interplay of anisotropy of the long-range exchange interaction and symmetry breaking. We demonstrate nonfrustrating long-range interactions induce the true long-range order in Heisenberg antiferromagnetic chains with a continuous symmetry breaking, lifting the restrictions imposed by the Mermin-Wagner theorem.

Field-Induced Quantum Spin Nematic Liquid Phase in the S=1 Antiferromagnetic Heisenberg Chain with Additional Interactions

The magnetization process of the S = 1 antiferromagnetic chain with the single-ion anisotropy D and the biquadratic interaction is investigated using the numerical diagonalization. Both interactions stabilize the 2-magnon Tomonaga-Luttinger liquid (TLL) phase in the magnetization process. Based on several excitation gaps calculated by the numerical diagonalization, some phase diagrams of the magnetization process are presented. These phase diagrams reveal that the spin nematic dominant TLL phase appears at higher magnetizations for sufficiently large negative D.

Critical Scaling of Entropy and Thermal Drude Weight in Anisotropic Heisenberg Antiferromagnets: A Thermodynamic Quest for Quantum Criticality

Up to now, probing the quantum phase transition (QPT) and quantum critical (QC) phenomena at finite temperatures in one-dimensional (1D) spin systems still lacks an in-depth understanding. Herein, we study the QPT and thermodynamics of 1D spin-1/2 anisotropic Heisenberg antiferromagnetic chains by Green’s function theory. The quantum phase diagram is renormalized by the anisotropy (∆), which manifests a quantum critical point (QCP) hc = 1 + ∆ signaling the transition from gapless Tomonaga–Luttinger liquid (TLL) to gapped ferromagnetic (FM) state, demonstrated by the magnetic entropy and thermal Drude weight. At low temperatures, it is shown that two crossover temperatures fan out a QC regime and capture the QCP via the linear extrapolation to zero temperature. In addition, around QCP, the QC scaling is performed by analyzing the entropy and thermal Drude weight to extract the critical exponents (α, δ, and β) that fulfill the Essamm–Fisher scaling law, which provides a novel thermodynamic means to detect QPT for experiment. Furthermore, scaling hypothesis equations with two rescaled manners are proposed to testify the scaling analysis, for which all the data points fall on a universal curve or two independent branches for the plot against rescaled field or temperature, implying the self-consistency and reliability of the obtained critical exponents.

Effect of Dzyaloshinskii-Moriya Interaction on Heisenberg Antiferromagnetic Spin Chain in the Presence of a Longitudinal Magnetic Field

Using functional integral method for the Heisenberg antiferromagnetic spin chain with the added Dzyaloshinskii-Moriya Interaction in the presence of the longitudinal magnetic field, we find out expression for free energy of the spin chain via spin fluctuations, from which quantities characterize the antiferromagnetic order and phase transition such as staggered and total magnetizations derived. From that, we deduce the significant effect of the Dzyaloshinskii-Moriya interaction on the reduction of the antiferromagnetic order and show that the total magnetization can be deviated from the initial one under the influence of canting of the spins due to a combination of the Dzyaloshinskii-Moriya interaction and the magnetic field. Besides, the remarkable role of the transverse spin fluctuations due to the above factors on the antiferromagnetic behaviours of the spin chain is also indicated.

Dynamical properties of the Haldane chain with bond disorder

By using Lanczos exact diagonalization and quantum Monte Carlo combined with stochastic analytic continuation, we study the dynamical properties of the S = 1 antiferromagnetic Heisenberg chain with different strengths of bond disorder. In the weak disorder region, we find weakly coupled bonds which can induce additional low-energy excitation below the one-magnon mode. As the disorder increases, the average Haldane gap closes at δΔ ∼ 0.5 with more and more low-energy excitations coming out. After the critical disorder strength δc ∼ 1, the system reaches a random-singlet phase with prominent sharp peak at ω = 0 and broad continuum at ω > 0 of the dynamic spin structure factor. In addition, we analyze the distribution of random spin domains and numerically find three kinds of domains hosting effective spin-1/2 quanta or spin-1 sites in between. These “spins” can form the weakly coupled long-range singlets due to quantum fluctuation which contribute to the sharp peak at ω = 0.

A Semiconductive Nature of Bis(dithiolato)nickelate Radical Salt Exhibiting Broadband Photoconduction.

The fractional oxidation state [M(dmit)2] (dmit2- = 2-thioxo-1, 3-dithiole-4, 5-dithiolate) salts have long attracted attention in the molecular metal area owing to high conductivity and even superconductivity. In this study, we achieved a mixed-valence salt (1) of [Ni(dmit)2]0.5- with monovalent 1,3-N,N-dimethyl-imidazolium (DiMIm+) by a solvent evaporation approach under ambient conditions. The mixed valence of [Ni(dmit)2]0.5- has been characterized by an analysis of the IR spectrum and crystal structure. In the crystal structure of 1, two [Ni(dmit)2]0.5- anions overlap in an eclipsed mode to form a [Ni(dmit)2]21- dimer, featuring a radical bearing an S = 1/2 spin; the dimeric radicals stack into a column along the b axis, and the adjacent columns connect together via the lateral-to-lateral S···S contacts along the a axis, and through the head-to-head S···S contacts along the [101] direction. Salt 1 shows the magnetic behavior of an S = 1/2 Heisenberg antiferromagnetic uniform linear chain with J/kB = -47.5(4) K and a semiconducting feature with σ = 2.52 × 10-3 S cm-1 at 293 K, 2.32 × 10-2 S cm-1 at 373 K, and Ea = 0.22 eV, as well as broadband photoconductivity under irradiation of green and white lights. This study suggests the possibility of designing new photoconductors based on the mixed-valence [Ni(dmit)2]0.5- salt.

Ground-state properties of a quantum frustrated spin chain with side spins and arbitrary spin s

The properties of the spin-s frustrated antiferromagnetic Heisenberg chain with side spins are studied by means of the coupled cluster method and the numerical exact diagonalization method. The results of the two methods both manifest that the ground state quantum phase diagram of the model consists of the Néel phase and the canted phase characterized by two pitch angles, irrespective of the value of the spin quantum number s. Although the phenomenon of quantum melting of magnetic long-range order is absent in the model, quantum fluctuation exerts an important influence on the property of the model. In addition to the reduction of magnetization, the nature of the phase transition from the Néel state to the canted state transforms from a classical second-order transition to a quantum first-order transition at any finite value of s. It is observed that the ways one of the two pitch angles evolves with frustration in quantum and classical cases, are qualitatively different in the large frustration parameter region. The location of the critical point and the physical quantities, including the ground state energy per spin and the magnetic order parameter, move toward their classical values in the form of power series in s.