D. L. Huber
The purpose of this note is to connect early work on thermal transport in spin-1/2 Heisenberg chains with uniaxial exchange anisotropy and nearest-neighbor interactions that was based on a moment analysis of the Fourier transform of the energy density correlation function with subsequent studies that make use of thermal current correlation functions.
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An $S=1/2$ triangular-lattice Heisenberg antiferromagnet with next-nearest-neighbor interactions is investigated under a magnetic field by the numerical-diagonalization method. It is known that, in both cases of weak and strong next-nearest-neighbor interactions, this system reveals a magnetization plateau at one-third of the saturated magnetization. We examine the stability of this magnetization plateau when the amplitude of next-nearest-neighbor interactions is varied. We find that a nonplateau region appears between the plateau phases in the cases of weak and strong next-nearest-neighbor in…
The ground state phase diagram is determined for the frustrated classical Heisenberg chain with added nearest-neighbor biquadratic exchange interactions. There appear ferromagnetic, incommensurate-spiral, and up-up-down-down phases; a lock-in transition occurs at the spiral boundary. The model contains an isotropic version of the ANNNI model; it is also closely related to a model proposed for some manganites. The Luttinger-Tisza method is not obviously useful due to the non-linear weak-constraint problem; however the ground state is obtained analytically by the exact cluster method of Lyons an…
A series of symmetry-protected topological(SPT) and trivial spin-gap phases in the spin-1/2 ferromagnetic--antiferromagnetic alternating Heisenberg chain with alternating next-nearest-neighbour interaction are investigated using two kinds of entanglement spectra defined by different divisions of the whole chain. In the case one of the next-nearest-neighbor interaction vanishes, the model reduces to the $Δ$-chain in which a series of spin-gap phases are found in J. Phys. Soc. Jpn. 77, 044707 (2008). From the degeneracy of the entanglement spectra, these phases are identified as the SPT and triv…
The spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain with ferromagnetic next-nearest-neighbour (NNN) interaction is investigated. The ground state is the Haldane phase for weak NNN interaction, and is the ferromagnetic phase for weak antiferromagnetic interaction. We find a series of topologically distinct spin-gap phases with various magnitudes of edge spins for strong NNN interaction. The phase boundaries between these phases are determined on the basis of the DMRG calculation with additional spins that compensate the edge spins. It is found that each of the exact soluti…
We consider the model of strongly-correlated system of electrons described by an extended Falicov-Kimball Hamiltonian where the stability of some axial and diagonal striped phases was proved. Introducing a next-nearest-neighbor hopping, small enough not to destroy the striped structure, we examine rigorously how the presence of the next-nearest-neighbor hopping anisotropy reduces the $π/2$-rotation degeneracy of the diagonal-striped phase. The effect appears to be similar to that in the case of anisotropy of the nearest-neighbor hopping: the stripes are oriented in the direction of the weaker …
We develop a simple technique for calculation of next to nearest neighbor spin-spin and chiral-spin correlation functions in inhomogeneous XXX model. Exact expression of the chiral-spin order parameter as a function of the model parameter, $ω$, is analytically found. Using the same method we also calculate the next to nearest neighbor spin-spin correlation function. In the limit $ω-> 0$ it reproduces the known result for the vacuum expectation value of the next to nearest neighbor spins in the standard Heisenberg spin chain. The technique is simple and can be extended for calculation of next t…
We study the anisotropic Heisenberg (XYZ) spin-1/2 chain placed in a magnetic field pointing along the x-axis. We use bosonization and a renormalization group analysis to show that the model has a non-trivial fixed point at a certain value of the XY anisotropy a and the magnetic field h. Hence, there is a line of critical points in the (a,h) plane on which the system is gapless, even though the Hamiltonian has no continuous symmetry. The quantum critical line corresponds to a spin-flop transition; it separates two gapped phases in one of which the Z_2 symmetry of the Hamiltonian is broken. Our…
Integrable models support elementary excitations with infinite lifetimes. In the spin-1/2 Heisenberg chain these are known as spinons. We consider the stability of spinons when a weak integrability breaking perturbation is added to the Heisenberg chain in a magnetic field. We focus on the case where the perturbation is a next nearest neighbour exchange interaction. We calculate the spinon decay rate in leading order in perturbation theory using methods of integrability and identify the dominant decay channels. The decay rate is found to be small, which indicates that spinons remain well-define…
Absence of local conserved quantity in the Heisenberg model with next-nearest-neighbor interaction
本文严格证明含次近邻相互作用的 Heisenberg 链不存在非平凡局域守恒量，从而确认其不可积，并将 Majumdar–Ghosh 与 Shastry–Sutherland 模型纳入结论。
We investigate the ground-state properties of the spin-half $J_1{-}J_2$ Heisenberg chain with a next-nearest-neighbor spin-Peierls dimerization using conformal field theory and Lanczos exact diagonalizations. In agreement with the results of a recent bosonization analysis by Sarkar and Sen, we find that for small frustration ($J_2/J_1$) the system is in a Luttinger spin-fluid phase, with gapless excitations, and a finite spin-wave velocity. In the regime of strong frustration the ground state is spontaneously dimerized and the bond alternation reduces the triplet gap, leading to a slight enhan…
Using the matrix product formalism, we introduce a two parameter family of exactly solvable $xyz$ spin 1/2 Heisenberg chains in magnetic field (with nearest neighbor interactions) and calculate the ground state and correlation functions in compact form. The ground state has a very interesting property: all the pairs of spins are equally entangled with each other. Therefore it is possible to engineer long-range entanglement in experimentally realizable spin systems on the one hand and study more closely quantum phase transition in such systems on the other.
We have considered the $S=1/2$ antiferromagnetic Heisenberg model in two dimensions, with an additional Ising \nnn interaction. Antiferromagnetic \nnn interactions will lead to frustration, and the system responds with flipping the spins down in the $xy$ plane. For large next nearest neighbour coupling the system will order in a striped phase along the z axis, this phase is reached through a first order transition. We have considered two generalizations of this model, one with random \nnn interactions, and one with an enlarged unit cell, where only half of the atoms have \nnn interactions. In …
We have studied the phase diagram of the one dimensional $S=1/2$ $XXZ$ model with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest neighbor interactions. We have applied the quantum renormalization group (QRG) approach to get the stable fixed points and the running of coupling constants. The second order QRG has been implemented to get the self similar Hamiltonian. This model shows a rich phase diagram which consists of different phases which possess the quantum spin-fluid and dimer phases in addition to the classical Néel and ferromagnetic ones. The border between different p…
The single-particle spectral properties near the Mott transition in the two-dimensional Hubbard model with next-nearest-neighbor hopping are investigated by using cluster perturbation theory. Complicated spectral features of this model are simply interpreted, by considering how the next-nearest-neighbor hopping shifts the spectral weights of the two-dimensional Hubbard model. Various anomalous features observed in hole-doped and electron-doped cuprate high-temperature superconductors are explained in a unified manner as properties near the Mott transition in a two-dimensional system whose spec…
The ground state phase diagram is determined exactly for the frustrated classical Heisenberg model plus nearest-neighbor biquadratic exchange interactions on a 2-dimensional lattice. A square- and a rhombic-symmetry version are considered. There appear ferromagnetic, incommensurate-spiral, "up-up-down-down" (uudd) and canted ferromagnetic states, a non-spiral coplanar state that is an ordered vortex lattice, plus a non-coplanar ordered state (a "conical vortex lattice"). In the rhombic case, which adds biquadratic terms to the Heisenberg model used widely for insulating manganites, the uudd st…
The topologically nontrivial magnetic phase with a $Z_2$-vortex (Z$_2$V) lattice is investigated by simulation in the Kitaev-Heisenberg honeycomb model expanded by considering the second- and third-nearest-neighbor Heisenberg interactions ($J_{H2}$ and $J_{H3}$). On the parameter region of the Z$_2$V phase, a gradual modulation of vortex density is observed, together with a transition from single-Z$_2$V to triple-Z$_2$V state driven by the variation of frustration. Additionally, $Z_2$ vortices are arranged in different manners on the whole honeycomb structure for these two types of Z$_2$V stat…
Motivated by recent experimental progress on triangular lattice heavy-fermion compounds, we investigate possible Lifshitz transitions and the scanning tunnel microscope (STM) spectra of the Kondo-Heisenberg model on the triangular lattice. In the heavy Fermi liquid state, the introduced Heisenberg antiferromagnetic interaction ($J_H$) results in the twice Lifshitz transition at the case of the nearest-neighbour electron hopping but with next-nearest-neighbour hole hopping and the case of the nearest-neighbour hole hopping but with next-nearest-neighbour electron hopping, respectively. Driven b…
The magnetic structure of the double perovskite compound Sr$_2$CuTeO$_6$ was determined from neutron powder diffraction data. This material is magnetically described as an $S\,{=}\,1/2$ quasi-two-dimensional square-lattice Heisenberg model with antiferromagnetic nearest-neighbor and next-nearest-neighbor interactions. Sr$_2$CuTeO$_6$ undergoes a magnetic phase transition at $T_{\rm N}\,{\simeq}\,29\,$ K. The spin structure below $T_{\rm N}$ is Néel antiferromagnetic on the square lattice, which means that the nearest-neighbor interaction ($J_1$) is stronger than the next-nearest-neighbor inter…
We present evidence that crystalline Sr_2Cu(PO_4)_2 is a nearly perfect one-dimensional (1D) spin-1/2 anti-ferromagnetic Heisenberg model (AHM) chain compound with nearest neighbor only exchange. We undertake a broad theoretical study of the magnetic properties of this compound using first principles (LDA, LDA+U calculations), exact diagonalization and Bethe-ansatz methodologies to decompose the individual magnetic contributions, quantify their effect, and fit to experimental data. We calculate that the conditions of one-dimensionality and short-ranged magnetic interactions are sufficiently fu…
We examine effects of the next-nearest-neighbor repulsion on electronic states of a one-dimensional interacting electron system which consists of quarter-filled band and interactions of on-site and nearest-neighbor repulsion. We derive the effective Hamiltonian for the electrons around wave number $\pm \kf$ ($\kf$: Fermi wave number) and apply the renormalization group method to the bosonized Hamiltonian. It is shown that the next-nearest-neighbor repulsion makes $4\kf$-charge ordering unstable and suppresses the spin fluctuation. Further the excitation gaps and spin susceptibility are also ev…
We study the magnetization process of the $S=1$ Heisenberg model on a two-leg ladder with farther neighbor spin-exchange interaction. We consider the interaction that couples up to the next-nearest neighbor rungs and find an exactly solvable regime where the ground states become product states. The next-nearest neighbor interaction tends to stabilize magnetization plateaus at multiples of 1/6. In most of the exactly solvable regime, a single magnetization curve shows two series of plateaus with different periodicities.
We calculate the local Green function for a quantum-mechanical particle with hopping between nearest and next-nearest neighbors on the Bethe lattice, where the on-site energies may alternate on sublattices. For infinite connectivity the renormalized perturbation expansion is carried out by counting all non-self-intersecting paths, leading to an implicit equation for the local Green function. By integrating out branches of the Bethe lattice the same equation is obtained from a path integral approach for the partition function. This also provides the local Green function for finite connectivity.…
The Hubbard Hamiltonian is investigated by means of a variational trial wave function of Gutzwiller's type. The wave function includes nearest - neighbor correlations in an explicit form. To calculate density matrices the method of Kikuchi's pseudoensemble is used. The case of half-filled fermionic band carefully investigated in the limit of a large number of lattice sites. The ground state energy and correlation functions are determined for lattices with z=2,4 and 6 nearest neighbors.
We study spin fluctuations in quarter-filled one-dimensional spin-density-wave systems in presence of short-range Coulomb interactions. By applying a path integral method, the spin-wave velocity is calculated as a function of on-site (U), nearest (V) and next-nearest (V_2) neighbor-site interactions. With increasing V or V_2, the pure spin-density-wave state evolves into a state with coexisting spin- and charge-density waves. The spin-wave velocity is reduced when several density waves coexist in the ground state, and may even vanish at large V. The effect of dimerization along the chain is al…
By using the coupled cluster method, the numerical exact diagonalization method, and the numerical density matrix renormalization group method, we investigated the properties of the one-dimensional Heisenberg chain with alternating antiferromagnetic and ferromagnetic next nearest neighbor interactions. In the classical limit, the ground state is in the collinear Neel state if a<1/2, while for a>1/2, there is an noncollinear canted state. For the quantum case, we found that, although the classical Neel state is absent, the canted state exists if the frustration parameter a exceeds a critical po…
The influence of next-nearest neighbor electron hopping, $t^{\prime}$, on the polaron and bipolaron formation in a square Hubbard-Holstein model is investigated within a variational approach. The results for electron-phonon and electron-electron correlation functions show that a negative value of $t^{\prime}$ induces a strong anisotropy in the lattice distortions favoring the formation of nearest neighbor intersite bipolaron. The role of $t^{\prime}$, electron-phonon and electron-electron interactions is briefly discussed in view of the formation of charged striped domains.
The phase diagram of correlated, disordered electron systems is calculated within dynamical mean-field theory for the Anderson-Falicov-Kimball model with nearest-neighbors and next-nearest-neighbors hopping. The half-filled band is analyzed in terms of the chemical potential of the system using the geometric and arithmetic averages. We also introduce the on-site energies exhibiting a long-range correlated disorder, which generates a system with similar characteristics as the one created by a random independent variable distribution. A decrease in the correlated disorder reduces the extended ph…
Ground-State Phase Diagram of the Effective Model with Antiferromagnetic Nearest-Neighbor and Ferromagnetic Next-Nearest-Neighbor Interactions in 1/1 Periodic Approximants to Icosahedral Quasicrystals
本研究通过枚举磁矩构型，确定二十面体准晶1/1周期近似上含J₁、J₂的有效模型的基态相图，明确了稳定的磁序类型及对应磁空间群，揭示基态性质以解释相关实验观测。
We present first-principle calculation of the on-site and nearest neighbor Coulomb interaction strength of the Ni $d$ orbitals in bulk $LaNiO_{2}$, using the constrained Random Phase Approximation method. The nearest neighbor correlation within Ni-O plane turns out to be more significant when considering the frequency dependent $U(ω)$, which can be as strong as about 25\% of the on-site value at medium and high frequencies. The inter Ni-O plane nearest neighbor correlation is found to be the same strength as that within the Ni-O plane, indicating the material is non-locally correlated also bet…
For two-dimensional lattices in a tight-binding description, the intrinsic spin-orbit coupling, acting as a complex next-nearest-neighbor hopping, opens gaps that exhibit the quantum spin Hall effect. In this paper, we study the effect of a real next-nearest-neighbor hopping term on the band structure of several Dirac systems. In our model, the spin is conserved, which allows us to analyze the spin Chern numbers. We show that in the Lieb, kagome, and T_3 lattices, variation of the amplitude of the real next-nearest-neighbor hopping term drives interesting topological phase transitions. These t…
We propose a possible mechanism of the charge stripe order due to the next-nearest neighbor exchange interaction J' in the two-dimensional t-J model, based on the concept of the phase separation. We also calculate some hole correlation functions of the finite cluster of the model using the numerical diagonalization, to examine the realization of the mechanism. It is also found that the next-nearest neighbor hopping t' suppresses the stripe order induced by the present mechanism for t'<0, while it enhances for t'>0.
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