One-dimensional Antiferromagnetic Heisenberg Model Research Articles

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.

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.

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.

Matrix Product State, Quantum Entanglement, and Criticality in the One-Dimensional Dimerized Antiferromagnetic Heisenberg Model

The matrix product state (MPS) is utilized to investigate the ground state properties and quantum phase transitions (QPTs) of the dimerized antiferromagnetic Heisenberg (DAH) model. The ground state MPS wavefunctions determined by the infinite time-evolving block decimation (iTEBD) algorithm are shown to be very efficient descriptions of DAH model. In the thermodynamic limit, the quantum entanglement, the bond energy, and the nearest-neighbor correlations are calculated. It is revealed that the singular behavior of the bipartite entanglement can detect the QPTs directly. The critical point Jc2 = 1.0 is determined evidently, and the quantum phase transition is argued to belong to the second-order category. At the critical point, logarithmic divergent character of the block entanglement is observed, and the system can be described by a free bosonic field theory.

Synthesis, structure and magnetic properties of the S=1/2, one-dimensional antiferromagnet, Y 5Re 2O 12

Single crystals of Y 5Re 2O 12 have been grown, and the crystal structure has been determined by X-ray diffraction. This compound crystallizes in space group C2/ m with cell dimensions of a=12.4081(10) Å b=5.6604(5) Å, c=7.4951(6) Å, β=107.837(3)°, Z=2. The final refinement led to R1=0.0238, WR2=0.0459 for 1053 observed reflections with F>4 σ( F 0). Edge-sharing ReO 6 octahedra form infinite linear [ReO 2O 4/2] n chains along the b direction with alternating short and long Re–Re distances. Three crystallographically independent yttrium atoms surround O2 to form OY 4 tetrahedra, which share edges and corners in the ab plane to form a two-dimensional Y 5O 4 network which separates the [ReO 2O 4/2] n magnetic chains. This compound is therefore isostructural with the series Ln 5Re 2O 12 Ln=Gd–Lu, which have been known since 1969. The average Re oxidation state is +4.5 in the chains and a reasonable, if qualitative MO scheme results in one unpaired electron per Re dimer. Consistent with this, magnetic susceptibility data can be fitted to the one-dimensional antiferromagnetic Heisenberg model with S=1/2 and parameters J intra/ k=−89(1) K, g=2.15(4) and χ(TIP)=5(1)×10 −4 emu/mol. There is no sign of long-range magnetic order down to 2 K. These results are contrasted with those for the isostructural Y 5Mo 2O 12.

Dynamics of the quantum one-dimensional Heisenberg antiferromagnet with spin S=1 at low temperature

We report low-temperature dynamic properties of the quantum one-dimensional antiferromagnetic Heisenberg model with spin S=1. The dynamic correlation function is calculated using a procedure that combines a projection operator technique proposed by Reiter and a modified spin wave theory proposed by Takahashi. This modified spin wave theory predicts a temperature-dependent gap whose behavior is compared to the behavior obtained experimentally and also from different approaches. Our calculation suggests that the gap has strong effects on the shape of the dynamical correlation function.

Magnetism of a Bilayer Wigner Crystal

Spin exchange interaction in a bilayer Wigner crystal is calculated with a WKB approximation. It is shown that the magnetic properties of a bilayer Wigner crystal are well described by the one-dimensional antiferromagnetic Heisenberg model when the interlayer distance is significantly smaller than the average interparticle distance in each layer.

A uniform and one-dimensional stacking of 2,5-dichlorotetracyanoquinodimethanide molecules in the tetramethylarsonium salt.

In the tetramethylarsonium salt of 2,5-dichloro-7,7,8,8-tetracyanoquinodimethanide [systematic name: tetramethylarsonium 2,2'-(2,5-dichlorocyclohexa-2,5-diene-1,4-diylidene)bis(propanedinitrile)], C(4)H(12)As(+).C(12)H(2)Cl(2)N(4)(-) or [As(CH(3))(4)](C(12)H(2)Cl(2)N(4)), the cation lies disordered about a twofold axis and the radical ion lies about an inversion center forming a uniform [interplanar distance 3.35 (2) A] and one-dimensional stacking without any slip. The electrical conductivity of the single crystal at room temperature was less than 10(-9) S cm(-1), and the temperature dependence of paramagnetic susceptibility obeyed a one-dimensional antiferromagnetic Heisenberg model with a spin-exchange integral of 83 K in the temperature range 1.8-320.0 K.

Purely Organic Magnetism of Pyridyl-Substituted Stable Thioaminyl Radicals

N-[(4-Nitrophenyl)thio]- (1a) and N-[(2,4-dichlorophenyl)thio)]-2,6-diphenyl-4-(3-pyridyl)phenylaminyl (1b), N-[(4-nitrophenyl)thio]- (2a) and N-[(2,4-dichlorophenyl)thio]-4-phenyl-2,6-di(3-pyridyl)phenylaminyl (2b) were generated by PbO2 oxidation of the corresponding precursors and isolated as radical crystals. For 1b X-ray crystallographic analysis was performed. The magnetic susceptibility measurements were carried out for the isolated radicals using a SQUID magnetometer in the temperature range 1.8 − 300 K. The susceptibilities of 1a and 2a were analyzed in terms of a one-dimensional (1D) antiferromagnetic (AFM) regular Heisenberg model with exchange interaction of 2J/k B= −63.4 and −17.8 K, respectively, and that of 1b was interpreted in terms of a 1D AFM alternating Heisenberg model with 2J/k B = −12.8 K and α = 0.91. On the other hand, that of 2b was explained in terms of a 1D ferromagnetic regular Heisenberg model with 2J/k B = 22.4 K.

Metamagnetism of antiferromagneticXXZquantum spin chains

The magnetization process of the one-dimensional antiferromagnetic Heisenberg model with the Ising-like anisotropic exchange interaction is studied by the exact diagonalization technique. It results in the evidence of the first-order spin flop transition with a finite magnetization jump in the N\'eel ordered phase for $S\geq 1$. It implies that the S=1/2 chain is an exceptional case where the metamagnetic transition becomes second-order due to large quantum fluctuations.

Exact results for a linear chain of classical spins with Dzyaloshinski–Morya interaction

We calculate the exact partition function and two-spin correlation functions for the one-dimensional classical anisotropic antiferromagnetic Heisenberg model with antisymmetric Dzyaloshinski–Morya interaction. We present results for the magnetic susceptibilities and the shift in the EPR frequency.

-exponents in the one-dimensional antiferromagnetic Heisenberg model with next-nearest-neighbour coupling

We investigate the critical exponents and associated with the singularities in the longitudinal and transverse structure factors of the one-dimensional antiferromagnetic Heisenberg model with nearest- (-) and next-nearest- (-) neighbour coupling of relative strength and an external field B with magnetization M(B).

Accurate calculation of ground-state energies in an analytic Lanczos expansion

An analysis of a general non-perturbative technique for calculating ground-state properties of extensive lattice many-body systems is presented, in order to extract accurate numerical values characterizing the ground-state spectrum. This technique, the plaquette expansion, employs an expansion about the thermodynamic limit of the coefficients that are generated by the Lanczos process. For the ground-state energy this error analysis, using theorems on the error bounds for the Lanczos method and the truncation in the plaquette expansion, allows for an accurate estimate when the approximation is taken to a given order. As an example we analyse the one-dimensional antiferromagnetic Heisenberg model, and find that the best ground-state energy density is within of the exact value, although the systematic error is . We also find, for this model, systematic improvement with each new order included in the expansion and have not observed any asymptotic tendencies. At equivalent orders of truncation we achieve far better results than for the other moment methods, such as the t-expansion or the connected-moment expansion.

Dynamics of the one-dimensional Heisenberg model and optical absorption of spinons in cuprate antiferromagnetic chains

We use numerical and analytical results to construct a simple ansatz for the energy dynamical correlation function of the one-dimensional antiferromagnetic Heisenberg model. This is applied to compute the phonon-assisted absorption spectra of magnetic excitations (spinons) in quasi-one-dimensional spin-1/2 insulators and shown to reproduce very well recent infrared measurements in ${\mathrm{Sr}}_{2}$ ${\mathrm{CuO}}_{3}$.

The frustrated antiferromagnetic Heisenberg model in the presence of a uniform field

On the basis of a numerical computation of the ground states in the sectors with a given total spin S we study the magnetic properties of the one-dimensional frustrated antiferromagnetic Heisenberg model at zero temperature and at the spin-fluid - dimer phase transition. We find that the magnetization curve M(B) has a quartic-root singularity near saturation, . The longitudinal spin - spin, the dimer - dimer and the transverse spin - spin structure factors develop singularities at the field-dependent momenta and , respectively. The type of each of these singularities depends on the frustration parameter and the magnetization M.

Cu Nuclear Quadrupole Resonance Study of CuGeO3

We have observed the nuclear quadrupole resonance (NQR) of Cu in the spin-Peierls system CuGeO 3 . The NQR signals have been observed at 34.23±0.02 MHz for 63 Cu and 31.66±0.02 MHz for 65 Cu at 4.2 K under zero external field. These signals persist down to 1.3 K with neither line splitting nor broadening due to the internal magnetic field. This fact indicates there is no long-range order of Cu spins. The 63 Cu nuclear spin-lattice relaxation rate 63 (1/ T 1 ) rapidly drops below 15 K which clearly demonstrates an opening of the energy gap in the excitation spectrum. However, no anomaly was detected in the Cu NQR frequency at the transition temperature. It was also found that 63 (1/ T 1 ) above 15 K smoothly extrapolates to a finite value at 0 K. This may suggest the spin dynamics in the paramagnetic state is described in terms of the one-dimensional antiferromagnetic Heisenberg model with S =1/2.

Low-dimensional quantum antiferromagnetic Heisenberg model studied using Wigner-Jordan transformations.

A Wigner-Jordan (WJ) transformation is used to study the one-dimensional (ID) and two-dimensional (2D) quantum antiferromagnetic Heisenberg model. The advantage of using the Wigner-Jordan transformation is that it preserves all spin-commutation relations as well as the spin on-site exclusion principle

Structure and Physical Properties of Two Perchlorate Salts Derived from a Novel Twin Donor. Bis(4′,5′-ethylenedithio-5-methylthiotetrathiafulvalenyl-4-thio)methane

Abstract A twin donor (1) which consists of two BEDT-TTF moieties linked by a methylenedithio bridge was prepared. Two radical salts of ClO4− with the stoichiometry of 1:1 and 2:1 were obtained through electrochemical crystallization. In the salt of 1•ClO4, the donor has a phane-like conformation. A magnetic behavior of the salt was interpreted by the one-dimensional antiferromagnetic Heisenberg model. On the other hand, the donor exist as a twist phane like conformation in the salt of 1•(ClO4)0.5 and the salt is a semiconductor (σrt = 0.1 S cm−1) with an activation energy of 5 × 10−2 eV.