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 generalizing the manifold studied in [1, 2] to the many body case for spin 1, 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.
Ground-state and finite-temperature properties of $S=1/2$ Heisenberg ladders with a ferromagnetic leg, an antiferromagnetic leg, and antiferromagnetic rungs are studied. It is shown that a partial ferrimagnetic phase extends over a wide parameter range in the ground state. The numerical results are supported by an analytical calculation based on a mapping onto the nonlinear $σ$ model and a perturbation calculation from the strong-rung limit. It is shown that the partial ferrimagnetic state is a spontaneously magnetized Tomonaga--Luttinger liquid with incommensurate magnetic correlation, which …
The antiferromagnetic Heisenberg chain is expected to have an extended symmetry, [SU(2)xSU(2)]/Z 2 , in the infrared limit, whose physical interpretation is that the spin and dimer order parameters form the components of a common 4-dimensional vector. Here we numerically in- vestigate this emergent symmetry using quantum Monte Carlo simulations of a modified Heisenberg chain (the J-Q model) in which the logarithmic scaling corrections of the conventional Heisenberg chain can be avoided. We show how the two- and three-point spin and dimer correlation func- tions approach their forms constrained…
Low temperature ballistic spin transport in the S=1/2 antiferromagnetic Heisenberg chain compound SrCuO2
我们报道了自旋S=1/2反铁磁海森堡链材料SrCuO 2的零磁场和纵向磁场μ子自旋弛豫测量结果。我们发现，在弱的外加磁场B中，自旋-晶格弛豫速率服从幂律B^n，其中n=-0.9（3）。该结果对于5 K < T < 300 K是温度无关的。在共形场论和使用Müller的计算，我们得出弹道自旋输运SrCuO 2。
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 $D$.
We study the two-magnon non-resonant Raman scattering in the (pi,pi) and (pi,0) ordered antiferromagnetic phases of a J1x-J1y-J2-Jc Heisenberg model on the tetragonal lattice within the framework of the spin-wave theory. We discuss the effects of various tuning factors to the two-magnon Raman spectra. We find that both the magnetic frustration J2/J1 and the interlayer exchange coupling Jc may significantly affect the spectra in both the B1g and A1g' channels in the (pi,pi) Neel ordered phase. Moreover, we find a splitting of the two-magnon peak in the (pi,0) antiferromagnetic phase. We further…
Traditional spectroscopy, by its very nature, characterizes properties of physical systems in the momentum and frequency domains. The most interesting and potentially practically useful quantum many-body effects however emerge from the deep composition of 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 ant…
Antikink dispersion of the asymmetric $J_1$-$J_2$ sawtooth spin-1/2 anisotropic Heisenberg antiferromagnetic chain has been derived. Value of spin-gap is obtained by estimating the minimum of dispersion relation variationally. The exact doubly-degenerate ground state energy has been derived at the symmetric point, $J_1=J_2$, for the whole anisotropic regime. Analytic form of dispersion relations of three different antikink states is obtained and their validity in the parameter space is discussed. The value of spin-gap, specific heat and susceptibility are estimated numerically by diagonalizing…
We present a spin-rotation-invariant Green-function theory for the dynamic spin susceptibility in the spin-1/2 antiferromagnetic Heisenberg model on a stacked honeycomb lattice. Employing a generalized mean-field approximation for arbitrary temperatures, the thermodynamic quantities (two-spin correlation functions, internal energy, magnetic susceptibility, staggered magnetization, N'eel temperature, correlation length) and the spin-excitation spectrum are calculated by solving a coupled system of self-consistency equations for the correlation functions. The temperature dependence of the magnet…
The Heisenberg model on a face center cubic (fcc) lattice is a typical three-dimensional frustrated spin system expected to have magnetization plateaus and supersolid phases. There are model compounds $A_2$CoTeO$_6$ ($A$ = Ca, Sr, Pb) for the fcc lattice but with lattice distortions. Motivated by the presence of the compounds, we investigate the ground state of the spin-1/2 antiferromagnetic Heisenberg model on a tetragonally distorted fcc lattice in the magnetic field using a large-size cluster mean-field method for the sake of finding new supersolid phases. We find five supersolid phases in …
Spin-1/2 Heisenberg model on kagome lattice is a typical frustrated quantum spin system. A basic structure of kagome lattice is also present in kagome-strip lattice in one dimension, where a similar type of frustration is expected. We thus study the magnetization plateaus of the spin-1/2 Heisenberg model on a kagome-strip chain with three-independent antiferromagnetic exchange interactions by the density-matrix renormalization group method. In a certain range of exchange parameters, we find twelve kinds of magnetization plateaus, nine of which have magnetic structures breaking either translati…
S=1/2 antiferromagnetic Heisenberg chain with staggered fields: Copper pyrimidine and copper benzoate using the density matrix renormalization group for transfer matrices
We present a study of the spin-1/2 Heisenberg chain with alternating ferro- and antiferromagnetic exchange, focusing on the role of the exchange couplings to cover both, dimer and Haldane limit. Employing a complementary combination of perturbation theory and quantum Monte Carlo simulation, we report results for the magnetic susceptibility as well as the dynamic structure factor over a wide range of coupling constants and for different temperatures to extract the spin gap. For a small ferromagnetic coupling, we find good agreement between perturbation theory and quantum Monte Carlo. For arbitr…
We study the finite temperature, low energy, long wave-length spectrum of the dynamic structure factor of the spin-$1/2$ antiferromagnetic Heisenberg chain in the presence of exchange anisotropy and external magnetic fields. Using imaginary-time quantum Monte-Carlo we extract parameters, relevant to characterize a {\it renormalized} Luttinger liquid. For small momentum our results are consistent with a change from propagating spinon density waves to spin diffusion, described by a finite-frequency spin-current relaxation rate. Results for this relaxation rate as well as other Luttinger liquid p…
By using Density Matrix Renormalization Group (DMRG) technique we study the phase diagram of 1D extended anisotropic Heisenberg model with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. We analyze the static correlation functions for the spin operators both in- and out-of-plane and classify the zero-temperature phases by the range of their correlations. On clusters of $64,100,200,300$ sites with open boundary conditions we isolate the boundary effects and make finite-size scaling of our results. Apart from the ferromagnetic phase, we identify two gaple…
Magnetic field effects on two-leg Heisenberg antiferromagnetic ladders: Thermodynamic properties
利用最近发展起来的转移矩阵重整化群方法，研究了磁场中两条腿反铁磁梯的热力学性质。基于不同的磁化行为，我们发现了无序自旋液体，Luttinger液体，自旋极化相和依赖于磁场和温度的经典制度。我们在Luttinger液相区的计算表明，在Cu $_2$（C $_5$ H $_{12}$ N $_2$）$_2$ Cl $_4$ }上观察到的NMR弛豫速率发散和反常比热行为都是由于准一维效应而不是三维有序.
Magnetization plateaus in quantum spin systems emerges in two-dimensional frustrated systems such as kagome lattice. The spin-1/2 antiferromagnetic Heisenberg model on square-kagome lattice is also appropriate for the study of magnetization plateau. Motivated by recent experimental finding of such a square-kagome lattice with nonequivalent three bonds, we investigate the phase diagrams and magnetization plateaus of the lattice by the exact diagonalization method. In addition to previously reported the 1/3 and 2/3 plateaus in the model with two equivalent bonds, we find a new 2/3 plateau whose …
We investigate the Heisenberg model on a decorated square (Fisher) lattice in the presence of first-neighbor $J_{1}$, second-neighbor $J_{2}$, and third-neighbor $J_{3}$ exchange couplings, with antiferromagnetic $J_{1}$. The classical ground-state phase diagram obtained within a Luttinger-Tisza framework is spanned by two antiferromagnetically ordered phases, and an infinitely degenerate antiferromagnetic chain phase. Employing classical Monte Carlo simulations we show that thermal fluctuations fail to lift the degeneracy of the antiferromagnetic chain phase. Interestingly, the spin-wave spec…
Exact asymptotic expressions of the uniform parts of the two-point correlation functions of bilinear spin operators in the Heisenberg antiferromagnetic spin-$\frac{1}{2}$ chain are obtained. Apart from the algebraic decay, the logarithmic contribution is identified, and the numerical prefactor is determined. We also confirm numerically the multiplicative logarithmic correction of the staggered part of the bilinear spin operators $\langle\langle S^{a}_0S^{a}_{1}S^{b}_{r}S^{b}_{r+1} \rangle\rangle=(-1)^rd/(r \ln^{\frac{3}{2}}r) +(3δ_{a,b}-1) \ln^2r /(12 π^4 r^4)$, and estimate the numerical pref…
Magnetism of Cu_6 Ge_6 O_{18}-x H_2 O (x = 0 ~ 6), a compound of the one-dimensional Heisenberg $S = 1/2$ model with competing antiferromagnetic interactions
我们测量了Cu $_6$ Ge $_6$ O $_{18}$ -xH $_2$ O（$x = 0 \sim 6$）的磁化率.反铁磁（AF）转变温度（$T_{\rm N}$）以上的磁化率同意与竞争AF相互作用的一维海森堡$S = 1/2$模型的磁化率。从最近邻和次最近邻AF交换相互作用之间的估计比率，自旋系统可能位于具有无隙和有隙磁激发的自旋系统之间的边界附近。$T_{\rm N}/T_{\rm max}$的值（其中$T_{\rm max}$是磁化率最大时的温度）显示出对$x$的独特依赖性。$x$依赖性可以定性地解释作为$x$的函数的相变和无序的影响考虑。
用浮区法生长了新化合物SrMn $_2$ V $_2$ O $_8$的大单晶。该过渡金属基氧化物与SrNi $_2$ V $_2$ O $_8$同构，由四元空间群$I4_1cd$描述。通过磁化率，磁化强度和比热测量的磁性能进行了研究。标题化合物在有序温度（$T_N$ = 43 K）以上表现为一维磁性体系。磁基态可以描述为一个经典的长程有序反铁磁体，具有弱的各向异性。
Ground-state properties of the spin-1/2 antiferromagnetic Heisenberg model on the triangular lattice: A variational study based on entangled-plaquette states
We obtain the complete phase diagram of the antiferromagnetic $J_{1}$-$J_{2}$ model, $0\leq α= J_2/J1 \leq 1$, within the framework of the $O(N)$ nonlinear sigma model. We find two magnetically ordered phases, one with N\' eel order, for $α\leq 0.4$, and another with collinear order, for $α\geq 0.6$, separated by a nonmagnetic region, for $0.4\leq α\leq 0.6$, where a gapped spin liquid is found. The transition at $α=0.4$ is of the second order while the one at $α=0.6$ is of the first order and the spin gaps cross at $α=0.5$. Our results are exact at $N\rightarrow\infty$ and agree with numerica…
We study the spectrum and the nature of the excitations of an antiferromagnetic (AFM) Heisenberg chain with staggered long range interactions, both numerically using the time-dependent density matrix renormalization group (tDMRG) method and by means of a multi-spinon approximation that qualitatively explains its main features. The unfrustrated long-range nature of the exchange effectively increases the dimensionality of the system and the chain is able to undergo true symmetry breaking and develop long range order, transitioning from a gapless spin liquid to a gapless ordered AFM phase. We cal…
The antiferromagnetic Heisenberg model is considered for spins $s_{i}={1/2}$ located on the vertices of the dodecahedron and the icosahedron, which belong to the point symmetry group $I_{h}$. Taking into account the permutational and spin inversion symmetries of the Hamiltonian results in a drastic reduction of the dimensionality of the problem, leading to full diagonalization for both clusters. There is a strong signature of the frustration present in the systems in the low energy spectrum, where the first excited states are singlets. Frustration also results in a doubly-peaked specific heat …
We show that the best variational ground state of the spin-$\frac{1}{2}$ Kagome antiferromagnetic Heisenberg model with nearest-neighboring exchange coupling(NN-KAFH) is a $Z_{2}$ spin liquid state, rather than the widely believed $U(1)$ Dirac spin liquid state. The spinon excitation in the $Z_{2}$ spin liquid state has a small gap of about $1/40$ of the spinon band width. We find that while the $Z_{2}$ and the $U(1)$ spin liquid state have a large overlap on finite clusters and are thus very close in energy, they host totally different spinon excitation spectrum. The strength of the RVB theor…
