One-dimensional Heisenberg Antiferromagnet Research Articles

Construction of Ideal One-Dimensional Spin Chains by Topochemical Dehydration/Rehydration Route.

One-dimensional (1D) Heisenberg antiferromagnets are of great interest due to their intriguing quantum phenomena. However, the experimental realization of such systems with large spin S remains challenging because even weak interchain interactions induce long-range ordering. In this study, we present an ideal 1D S = 5/2 spin chain antiferromagnet achieved through a multistep topochemical route involving dehydration and rehydration. By desorbing three water molecules from (2,2'-bpy)FeF3(H2O)·2H2O (2,2'-bpy = 2,2'-bipyridyl) at 150 °C and then intercalating two water molecules at room temperature (giving (2,2'-bpy)FeF3·2H2O 1), the initially isolated FeF3ON2 octahedra combine to form corner-sharing FeF4N2 octahedral chains, which are effectively separated by organic and added water molecules. Mössbauer spectroscopy reveals significant dynamical fluctuations down to 2.7 K, despite the presence of strong intrachain interactions. Moreover, results from electron spin resonance (ESR) and heat capacity measurements indicate the absence of long-range order down to 0.5 K. This controlled topochemical dehydration/rehydration approach is further extended to (2,2'-bpy)CrF3·2H2O with S = 3/2 1D chains, thus opening the possibility of obtaining other low-dimensional spin lattices.

Low-temperature thermodynamic properties of the Heisenberg antiferromagnetic chain with two easy-axis single-ion anisotropies

In this paper, the spin wave theory is applied to the one-dimensional Heisenberg antiferromagnet in the coexistence of two different anisotropies [Formula: see text] and [Formula: see text], which are separately the easy-axis single-ion anisotropies for sublattice A and sublattice B of the system. Both the ground-state and low-temperature properties of the system are strongly affected by the competition between these two anisotropies. Two kinds of the competition in terms of the deviation parameter [Formula: see text] are discussed for the uniform anisotropy taking the values of [Formula: see text] and [Formula: see text], respectively. The [Formula: see text]-dependent behaviors (such as the power, exponential and linear laws) are obtained for the total magnetization, the staggered magnetizations, the internal energy, the specific heat and the susceptibility. It is found that at zero-temperature, the interplay between these two anisotropies induces the antiferromagnetic-disorder phase transition in the small anisotropy region with [Formula: see text]. For the selected cases of [Formula: see text], our results for are in agreement with the findings obtained by the existing theories and the quantum Monte Carlo data.

Realization of a bosonic antiferromagnet

Quantum antiferromagnets are of broad interest in condensed matter physics as they provide a platform for studying exotic many-body states including spin liquids and high-temperature superconductors. Here, we report on the creation of a one-dimensional Heisenberg antiferromagnet with ultracold bosons. In a two-component Bose-Hubbard system, we switch the sign of the spin-exchange interaction and realize the isotropic antiferromagnetic Heisenberg model in an extended 70-site chain. Starting from a low-entropy N\'eel-ordered state, we use optimized adiabatic passage to approach the bosonic antiferromagnet. We demonstrate the establishment of antiferromagnetism by probing the evolution of the staggered magnetization and spin correlations of the system. Compared with condensed matter systems, ultracold gases in optical lattices can be microscopically engineered and measured, offering significant advantages for exploring bosonic magnetism and spin dynamics.

Quantum Singular Value Decomposition of Spin Correlation Matrix in One-Dimensional Heisenberg Model

We present singular value decomposition of spin correlation matrix defined from the ground state of one-dimensional antiferromagnetic quantum Heisenberg model. The decomposition creates a data set that coincides with various domain excitations from classical antiferromagnetic state. We determine the scaling relation for the singular values as a function of the domain size. The singular values are closely related to the square of weights of the bases in the ground-state wavefunction. The nature of the singular value decomposition is to precisely estimate the appropriate bases and corresponding weights of the ground-state wavefunction.

Restricted Boltzmann Machines for Quantum States with Non-Abelian or Anyonic Symmetries.

Although artificial neural networks have recently been proven to provide a promising new framework for constructing quantum many-body wave functions, the parametrization of a quantum wave function with non-abelian symmetries in terms of a Boltzmann machine inherently leads to biased results due to the basis dependence. We demonstrate that this problem can be overcome by sampling in the basis of irreducible representations instead of spins, for which the corresponding ansatz respects the non-abelian symmetries of the system. We apply our methodology to find the ground states of the one-dimensional antiferromagnetic Heisenberg (AFH) model with spin-1/2 and spin-1degrees of freedom, and obtain a substantially higher accuracy than when using the s_{z} basis as an input to the neural network. The proposed ansatz can target excited states, which is illustrated by calculating the energy gap of the AFH model. We also generalize the framework to the case of anyonic spin chains.

Haldane Gaps of Large-S Heisenberg Antiferromagnetic Chains and Asymptotic Behavior

The one-dimensional Heisenberg antiferromagnets of large-integer-$S$ spins are studied; their Haldane gaps are estimated by the numerical diagonalization method for $S=5$ and $6$. We successfully obtain a monotonically increasing sequence of finite-size energy difference data corresponding to the Haldane gaps from the huge-scale parallel calculations of diagonalization under the twisted boundary condition and create a monotonically decreasing sequence within the range of system sizes treated in this study from the monotonically increasing sequence. Consequently, the gaps for $S=5$ and $6$ are estimated to be $0.000050 \pm 0.000005$ and $0.0000030 \pm 0.0000005$, respectively. The asymptotic formula of the Haldane gap for $S\rightarrow\infty$ is examined from the new estimates to determine the coefficient in the formula more precisely.

Quantum disordered vector-spin-chirality state in one dimensional Heisenberg model

We study the existence of a chiral spin ordered state in one-dimensional antiferromagnetic Heisenberg models. We prove that when the coupling constants are short-ranged no quantum vector-spin-chirality order appears at zero temperature for integer spin chains.

A variational lower bound on the ground state of a many-body system and the squaring parametrization of density matrices

A variational upper bound on the ground state energy Egs of a quantum system, Egs ⩽ 〈Ψ|H|Ψ〉, is well-known (here H is the Hamiltonian of the system and Ψ is an arbitrary wave function). Much less known are variational lower bounds on the ground state. We consider one such bound which is valid for a many-body translation-invariant lattice system. Such a lattice can be divided into clusters which are identical up to translations. The Hamiltonian of such a system can be written as , where a term Hi is supported on the i’th cluster. The bound reads , where is some wisely chosen set of reduced density matrices of a single cluster. The implementation of this latter variational principle can be hampered by the difficulty of parameterizing the set , which is a necessary prerequisite for a variational procedure. The root cause of this difficulty is the nonlinear positivity constraint ρ > 0 which is to be satisfied by a density matrix. The squaring parametrization of the density matrix, ρ = τ2/trτ2, where τ is an arbitrary (not necessarily positive) Hermitian operator, accounts for positivity automatically. We discuss how the squaring parametrization can be utilized to find variational lower bounds on ground states of translation-invariant many-body systems. As an example, we consider a one-dimensional Heisenberg antiferromagnet.

Revisiting numerical real-space renormalization group for quantum lattice systems

Although substantial progress has been achieved in solving quantum impurity problems, the numerical renormalization group (NRG) method generally performs poorly when applied to quantum lattice systems in a real-space blocking form. The approach was thought to be unpromising for most lattice systems owing to its flaw in dealing with the boundaries of the block. Here the discovery of intrinsic prescriptions to cure interblock interactions is proposed which is able to clear up the boundary obstacle in applying the NRG to quantum lattice systems. While the resulting RG transformation turns out to be strict in the thermodynamic limit, benchmark tests of the algorithm on a one-dimensional Heisenberg antiferromagnet and a two-dimensional tight-binding model demonstrate its numerical efficiency in resolving low-energy spectra for finite lattice systems.

Accuracy of the microcanonical Lanczos method to compute real-frequency dynamical spectral functions of quantum models at finite temperatures.

We examine the accuracy of the microcanonical Lanczos method (MCLM) developed by Long etal. [Phys. Rev. B 68, 235106 (2003)PRBMDO0163-182910.1103/PhysRevB.68.235106] to compute dynamical spectral functions of interacting quantum models at finite temperatures. The MCLM is based on the microcanonical ensemble, which becomes exact in the thermodynamic limit. To apply the microcanonical ensemble at a fixed temperature, one has to find energy eigenstates with the energy eigenvalue corresponding to the internal energy in the canonical ensemble. Here, we propose to use thermal pure quantum state methods by Sugiura and Shimizu [Phys. Rev. Lett. 111, 010401 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.010401] to obtain the internal energy. After obtaining the energy eigenstates using the Lanczos diagonalization method, dynamical quantities are computed via a continued fraction expansion, a standard procedure for Lanczos-based numerical methods. Using one-dimensional antiferromagnetic Heisenberg chains with S=1/2, we demonstrate that the proposed procedure is reasonably accurate, even for relatively small systems.

Interplay between the Dzyaloshinskii-Moriya term and external fields on spin transport in the spin-1/2 one-dimensional antiferromagnet

We study the effect of the uniform Dzyaloshinskii-Moriya interaction (symmetric exchange anisotropy) and arbitrary oriented external magnetic fields on spin conductivity in the spin-1/2 one-dimensional Heisenberg antiferromagnet. The spin conductivity is calculated employing abelian bosonization and the Kubo formalism of transport. We investigate the influence of three competing phases at zero-temperature, (Néel phase, dimerized phase and gapless Luttinger liquid phase) on the AC spin conductivity.

Entanglement in the quantum one-dimensional integer spin S Heisenberg antiferromagnet

We use the modified spin wave theory of Takahashi to study the entanglement entropy in the quantum one-dimensional integer spin Heisenberg antiferromagnet. We calculate the entanglement entropy of this spin system that is well known to be a quantum wire, in the classical limit (N→∞). We obtain a decreasing the entanglement entropy with the temperature and we obtain none change in the entanglement in the point Δ=1 at T=0 where the system presents a quantum phase transition from a gapless phase in the spectrum Δ<1 to a gapped phase Δ≥1.

Thermalization of a dimerized antiferromagnetic spin chain

Thermalization is investigated for the one-dimensional anisotropic antiferromagnetic Heisenberg model with dimerized nearest-neighbor interactions that break integrability. For this purpose the time evolution of local operator expectation values after an interacting quench is calculated directly with the Chebyshev polynomial expansion, and the deviation of the diagonal from the canonical thermal ensemble value is calculated for increasing system size for these operators. The spatial and spin symmetries of the Hamiltonian are taken into account to divide it into symmetry subsectors. The rate of thermalization is found to weaken with the dimerization parameter as the Hamiltonian evolves between two integrable limits, the non-dimerized and the fully dimerized where the chain breaks up into isolated dimers. This conclusion is supported by the distribution of the local operator off-diagonal elements between the eigenstates of the Hamiltonian with respect to their energy difference, which determines the strength of temporal fluctuations. The off-diagonal elements have a low-energy peak for small dimerization which facilitates thermalization, and originates in the reduction of spatial symmetry with respect to the non-dimerized limit. For increasing dimerization their distribution changes and develops a single low-energy maximum that relates to the fully dimerized limit and slows down thermalization.

Thermalization away from integrability and the role of operator off-diagonal elements.

We investigate the rate of thermalization of local operators in the one-dimensional anisotropic antiferromagnetic Heisenberg model with next-nearest neighbor interactions that break integrability. This is done by calculating the scaling of the difference of the diagonal and canonical thermal ensemble values as a function of system size, and by directly calculating the time evolution of the expectation values of the operators with the Chebyshev polynomial expansion. Spatial and spin symmetry is exploited and the Hamiltonian is divided into subsectors according to their symmetry. The rate of thermalization depends on the proximity to the integrable limit. When integrability is weakly broken thermalization is slow, and becomes faster the stronger the next-nearest neighbor interaction is. Three different regimes for the rate of thermalization with respect to the strength of the integrability breaking parameter are identified. These are shown to be directly connected with the relative strength of the low and higher energy difference off-diagonal operator matrix elements in the symmetry eigenbasis of the Hamiltonian. Close to the integrable limit the off-diagonal matrix elements peak at higher energies and high-frequency fluctuations are important and slow down thermalization. Away from the integrable limit a strong low-energy peak gradually develops that takes over the higher frequency fluctuations and leads to quicker thermalization.

Magnetic Properties of Single-Crystals of the S=2 Quasi-1D Heisenberg Antiferromagnet MnCl3(bpy)

Recent theories have revealed topological differences between one-dimensional (1D) Heisenberg antiferromagnets (HAFs) with odd and even integer spins (S). With this renewed interest, we have investigated the low-field magnetic susceptibility, specific heat, and high-field magnetization of single-crystal samples of MnCl3(bpy), bpy=2,2t-bipyridine, which is regarded as an S = 2 quasi-1D HAF. With the magnetic field oriented along the a*, b and c directions, the magnetic susceptibilities possess broad maxima around 100K. When the magnetic field is parallel to the b-axis, a sharp peak at 11K is observed in the magnetic susceptibility, while a smaller feature is detected in the specific heat, indicating a transition to long-range antiferromagnetic order. At 1.7K, the high-field magnetization curve along the c-axis shows a spin-flop transition, while the responses in the other directions show monotonic increases. These experimental findings confirm that MnCl3(bpy) is not an ideal model system to study the S=2 Haldane phase.

Magnetic properties of S= 1/2 J1-J2 one-dimensional magnets, VO(XO4)(2,2'-bpy) (X=S, Mo; bpy = bipyridine)

Magnetic susceptibility, high field magnetization and specific heat of S = 1/2 J1-J2 spin chain compounds VO(XO4)(2,2'-bpy) (X=S, Mo; bpy = bipyridine) are measured. VO(SO4)(2,2'-bpy) is found to be a one-dimensional Heisenberg antiferromagnet with J1/kB = 6.5 K and J2 =0. A ratio j = J2/J1 of VO(MoO4)(2,2'-bpy) is estimated to be about 0.2 with J1/kB = 51 K. Spin gap is not observed in both the compounds, which is consistent with the theoretical prediction.

Haldane State Formed by Oxygen Molecules Encapsulated in Single-Walled Carbon Nanotubes

We report on the results of X-ray diffraction (XRD), magnetic susceptibility, and high-field magnetization measurements of oxygen molecules, which are unique magnetic homonuclear diatomic molecules with spin-1, encapsulated in single-walled carbon nanotubes (SWCNTs) with diameters of about 0.8 nm. Antiferromagnetic interactions between neighboring oxygen molecules are expected in SWCNTs, resulting in the formation of a spin-1 one-dimensional Heisenberg antiferromagnet, known as a Haldane magnet. The XRD pattern can be predicted accurately by considering the expected oxygen molecule alignment. The temperature evolution of the magnetic susceptibility and the high-field magnetization curve are typical of those for a Haldane magnet with spin-1. The results indicate that the Haldane state has been realized in a nanospaced material for the first time. This provides an alternative to the conventional condensed matter approach to forming quantum spin systems.

Negative Renormalization of Spin Excitation Energies — A New Paradigm for Quantum Frustration?

Ono et al. [1] report the large downward renormalization of spin excitation energies relative to the linear spin-wave theory prediction in a frustrated spin-1/2 two-dimensional kagome lattice antiferromagnet. The authors attribute this “negative” renormalization to quantum frustration. This surprising finding is in contrast to the upward renormalization of the excitation energies observed in spin-1/2 one-dimensional Heisenberg antiferromagnet, which has been referred to as the quantum renormalization.

Spin transport of the frustrated integer spin S antiferromagnetic Heisenberg chain

We study the effect of the nearest-neighbor (nn) and next-nearest-neighbor (nnn) interactions on spin transport in the quantum integer spin one-dimensional isotropic antiferromagnetic Heisenberg model. The Kubo formalism of the linear response theory is used to calculate the spin conductivity. We obtain the regular part of the spin conductivity, σreg(ω), as function of the frequency at T=0 and obtain a strong effect of the (nnn) interaction on magnon transport.

High-field multi-frequency ESR in the S=2 heisenberg antiferromagnetic chain compound MnCl3(bpy)

We report the results of high-field multi-frequency electron spin resonance (ESR) experiments on a powder sample of MnCl3 (bpy) (bpy=2, 2′-bipyridine). This compound is one of the rare examples of the spin (S) 2 quasi one-dimensional (1D) Heisenberg antiferromagnets (HAFs), and magnetic properties of tiny single crystal samples were reported previously (G. E. Granroth et al., Phys. Rev. Lett. 77, 1616 (1996).). In our previous paper on this compound (M. Hagiwara et al., J. Phys.: Conf. Ser. 400, 032014 (2012).), we reported, for the S=2 1D HAF, good agreement between experiment and calculation for the temperature dependence of magnetic susceptibility and the high-field magnetization process at 1.3 K. In this work, we have observed some high-frequency resonance modes with zero-field gaps of about 800 GHz that may correspond to antiferromagnetic resonance modes with orthorhombic anisotropy in a long-range-ordered phase that emerged at low temperatures above the critical field at which the energy gap (Haldane gap) closes. The single-ion anisotropy constant D evaluated from the analysis of these ESR modes is larger than that reported previously.