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 antiferromagnetic chain. This "quantum wake" displays similarities to Floquet states, discrete time crystals and nonlinear Luttinger liquids.
We present up to date investigations of the antiferromagnetic Heisenberg icosidodecahedron by means of the Density Matrix Renormalization Group method. We compare our results with modern Correlator Product State as well as Lanczos calculations.
The exact amplitude for the asymptotic correlation function in the S=1/2 Heisenberg antiferromagnetic chain is determined: <S^a_0 S^b_r> goes to (-1)^r delta^{ab}(ln r)^{1/2}/[(2 pi)^{3/2}r]. The behaviour of the correlation functions for small xxz anisotropy and the form of finite-size corrections to the correlation function are also analysed.
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…
We report zero and longitudinal magnetic field muon spin relaxation measurements of the spin S=1/2 antiferromagnetic Heisenberg chain material SrCuO2. We find that in a weak applied magnetic field B the spin-lattice relaxation rate follows a power law B^n with n=-0.9(3). This result is temperature independent for 5K < T < 300 K. Within conformal field theory and using the Müller ansatz we conclude ballistic spin transport in SrCuO2.
Within Dyson-Maleev (DM) transformation and self-consistent mean-field treatment, the Néel order/disorder transition is studied for an antiferromagnetic Heisenberg model which is defined on a square lattice with a nearest neighbour exchange $J_1$ and a next-nearest neighbour exchange $J_2$ along only one of the diagonals. It is found that the Néel order may exist up to $J_2/J_1=0.572$, beyond its classically stable regime. This result qualitatively improves that from linear spin-wave theory based on Holstein-Primakoff transformation.
To check the reliability of the Majorana representation of quantum spin systems, we use it to compute the ground state energy of an antiferromagnetic spin 1/2 chain to one loop order. We find a very small one loop correction of the mean field energy and a discrepancy of >100% compared to the Bethe Ansatz result. We conclude that a careful handling of the gauge degrees of freedom of this representation is crucial to get correct results.
The antiferromagnetic Heisenberg model on icosahedral symmetry $I_{h}$ fullerene clusters exhibits unconventional magnetic properties, despite the lack of anisotropic interactions. At the classical level, and for number of sites $n \leq 720$, the magnetization has two discontinuities in an external magnetic field, except from the dodecahedron where it has three, emphasizing the role of frustration introduced by the pentagons in the unusual magnetic properties. For spin magnitudes $s_{i}={1/2}$ there is a discontinuity of quantum character close to saturation for $n \leq 80$. This common magnet…
Using the density matrix renormalization group (DMRG) technique, we carry out a large scale numerical calculation for the S=2 antiferromagnetic Heisenberg chain. Performing systematic scaling analysis for both the chain length $L$ and the number of optimal states kept in the iterations $m$, the Haldane gap $Δ(2)$ is estimated accurately as $(0.0876\pm0.0013)J$. Our systematic analysis for the S=2 chains not only ends the controversies arising from various DMRG calculations and Monte Carlo simulations, but also sheds light on how to obtain reliable results from the DMRG calculations for other c…
The antiferromagnetic Heisenberg model on a pyrochlore lattice under external magnetic field is studied by classical Monte Carlo simulation. The model includes bilinear and biquadratic interactions; the latter effectively describes the coupling to lattice distortions. The magnetization process shows a half-magnetization plateau at low temperatures, accompanied with strong suppression of the magnetic susceptibility. Temperature dependence of the plateau behavior is clarified. Finite-temperature phase diagram under the magnetic field is determined. The results are compared with recent experiment…
We develop an analytical approach based on a unitary transformation to investigate S=1/2 antiferromagnetic Heisenberg chains coupled to phonons, and find a new quantum phase transition at zero temperature. Although the usual phase transition occurs depending on the strengths of the spin-spin and spin-phonon interactions, the phase transition in the present work is induced by a change in the geometrical structure of the spin-phonon interaction. The magnetic properties of the phase transition can be understood in relation to a phase transition that has already been found in the frustrated J1-J2 …
By explicitly computing wavefunction overlap via exact diagonalization in finite systems, we provide evidence indicating that, in the limit of strong coupling, i.e., $Δ/t \to \infty$, the ground state of the Gutzwiller-projected BCS Hamiltonian (accompanied by proper particle-number projection) is identical to the exact ground state of the 2D antiferromagnetic Heisenberg model on the square lattice. This identity is adiabatically connected to a very high overlap between the ground states of the projected BCS Hamiltonian and the t-J model at moderate doping.
Using Monte Carlo integration methods, we describe the behavior of the exact four-spinon dynamic structure function $S_{4}$ in the antiferromagnetic spin 1/2 Heisenberg quantum spin chain as a function of the neutron energy $ω$ and momentum transfer $k$. We also determine the four-spinon continuum, the extent of the region in the $(k,ω)$ plane outside which $S_{4}$ is identically zero. In each case, the behavior of $S_{4}$ is shown to be consistent with the four-spinon continuum and compared to the one of the exact two-spinon dynamic structure function $S_{2}$. Overall shape similarity is note…
A recently developed numerical method, entanglement perturbation theory (EPT), is used to study the antiferromagnetic Heisenberg spin chains with z-axis anisotropy $λ$ and magnetic field B. To demonstrate the accuracy, we first apply EPT to the isotropic spin-1/2 antiferromagnetic Heisenberg model, and find that EPT successfully reproduces the exact Bethe Ansatz results for the ground state energy, the local magnetization, and the spin correlation functions (Bethe ansatz result is available for the first 7 lattice separations). In particular, EPT confirms for the first time the asymptotic beha…
The magnetic behaviors of a spin-1/2 alternating Heisenberg antiferromagnetic chain in a staggered transverse magnetic field is studied by means of the density-matrix renormalization group method and Jordan-Wigner transformation. Quantum phase transitions of different types are observed in the S=1 Neel and XY-like gapless phases, which result from the competitions between the staggered transverse field and magnetic orders induced by anisotropy and alternating interactions. The results are compared with the mean-field and some exactly resolved results.
We work out the magnetization and susceptibility of Heisenberg- and XXZ-model antiferromagnet spin-1/2 systems in $D$ dimensions under a rigorous constraint of single particle site occupancy. Quantum fluctuations are taken into account up to the first order in a loop expansion beyond the Néel state mean field solution. We discuss the results, their validity in the vicinity of the critical point and compare them with the results obtained by means of a spin wave approach.
Magnetization processes of spin-1/2 Heisenberg ladders are studied using strong-coupling expansions, numerical diagonalization of finite systems and a bosonization approach. We find that the magnetization exhibits plateaux as a function of the applied field at certain rational fractions of the saturation value. Our main focus are ladders with 3 legs where plateaux with magnetization one third of the saturation value are shown to exist.
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…
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…
We have performed electron spin resonance measurements over a wide frequency and magnetic field range on a single crystal of the S=1 quasi-one-dimensional Heisenberg antiferromagnet $\rm Ni(C_5H_{14}N_2)_2N_3(PF_6)$. We observed gapped excitation branches above the critical field ($H_{\rm c}$) where the Haldane gap closes. These branches are analyzed by a phenomenological field-theory using complex-field $ϕ^{4}$ model. A satisfactory agreement between experiment and theory is obtained.
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 …
We extend the nonlinear spin wave theory (NLSWT) for the spin 1/2 antiferromagnetic Heisenberg model on a triangular lattice (TAFHM). This novel NLSWT considers the corrections one order higher in 1/S than the linear spin wave theory (LSWT). It also distinguishes in which circumstance the negative energy excitation, the sign of the breakdown of LSWT, shall be renormalized to be positive both by a boson normal ordering and a self-consistent iteration. We draw a phase diagram by testing the stability of various magnetic orders for different parameters. In particular, the incommensurate configura…
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…
Recent inelastic neutron scattering experiments in CeIn3 and CePd2Si2 single crystals, measured spin wave excitations at low temperatures. These two heavy fermion compounds exhibit antiferromagnetic long-range order, but a strong competition between the Ruderman-Kittel-Kasuya-Yosida(RKKY) interaction and Kondo effect is evidenced by their nearly equal Neel and Kondo temperatures. Our aim is to show how magnons such as measured in the antiferromagnetic phase of these Ce compounds, can be described with a microscopic Heisenberg-Kondo model as introduced by J.R.Iglesias, C.Lacroix and B.Coqblin, …
We consider the spin-1/2 antiferromagnetic Heisenberg chain in a staggered magnetic field describing materials such as copper benzoate and copper pyrimidine dinitrate. Using the density-matrix renormalization group for transfer matrices (TMRG) we calculate the magnetization of these materials at finite temperature and arbitrary magnetic field. These results are in excellent agreement with experimental data, allowing for a determination of the inhomogeneity parameter c of copper benzoate (c = 0.043) and copper pyrimidine dinitrate (c= 0.11). The TMRG approach can be applied to rather low temper…
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 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 …
The manifestations of topological effects in finite antiferromagnetic Heisenberg chains is examined by density matrix renormalization group technique in this paper. We find that difference between integer and half-integer spin chains shows up in ground state energy per site when length of spin chain is longer than $\simξ$, where $ξ\sim\exp(πS)$ is a spin-spin correlation length, for spin magnitude S up to 5/2. For open chains with spin magnitudes $S=5/2$ to S=5, we verify that end states with fractional spin quantum numbers $S'$ exist and are visible even when the chain length is much smaller …
We have proposed the plaquette-singlet solid (PSS) ground state for the spin-1 antiferromagnetic Heisenberg two-leg ladder. Based on the PSS picture, we discuss the correspondence of the PSS state to the valence-bond solid (VBS) state of the ground state of spin-2 chain by introducing an appropriate composite spin picture. When the bond alternation is introduced, there occur quantum phase transitions and each phase can be identified with that in the dimerized spin-2 chain. Furthermore, we argue that the VBS picture of spin-2S chain can be applied to the ground state of spin-S two-leg ladder.
We study the spin-1/2 antiferromagnetic Heisenberg chain in both uniform and (perpendicular) staggered magnetic fields using the density-matrix renormalization-group method. This model has been shown earlier to describe the physics of the copper benzoate materials in magnetic field. In the present work, we extend the study to more general case for a systematic investigation of the field-induced gap and related properties of the spin-1/2 antiferromagnetic Heisenberg chain. In particular, we explore the high magnetic field regime where interesting behaviors in the field-induced gap, magnetizatio…
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…
We study two-dimensional Heisenberg antiferromagnets with additional multi-spin interactions which can drive the system into a valence-bond solid state. For standard SU(2) spins, we consider both four- and six-spin interactions. We find continuous quantum phase transitions with the same critical exponents. Extending the symmetry to SU(N), we also find continuous transitions for N=3 and 4. In addition, we also study quantitatively the cross-over of the order-parameter symmetry from Z4 deep inside the valence-bond-solid phase to U(1) as the phase transition is approached.
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…
Recent inelastic neutron scattering experiments in CeIn$_{3}$ and CePd$_{2}$Si$_{2}$ single crystals measured spin wave excitations at low temperatures. These two heavy fermion compounds exhibit antiferromagnetic long-range order, but a strong competition between the Ruderman-Kittel-Kasuya-Yosida(RKKY) interaction and Kondo effect is evidenced by their nearly equal Néel and Kondo temperatures. Our aim is to show how magnons such as measured in the antiferromagnetic phase of these Ce compounds, can be described with a microscopic Heisenberg-Kondo model introduced by J.R.Iglesias, C.Lacroix and …
Using the recently developed transfer-matrix renormalization group method, we have studied the thermodynamic properties of two-leg antiferromagnetic ladders in the magnetic field. Based on different behavior of magnetization, we found disordered spin liquid, Luttinger liquid, spin-polarized phases and a classical regime depending on magnetic field and temperature. Our calculations in Luttinger liquid regime suggest that both the divergence of the NMR relaxation rate and the anomalous specific heat behavior observed on Cu$_2$(C$_5$H$_{12}$N$_2$)$_2$Cl$_4$}are due to quasi-one-dimensional effect…
We study the field dependence of the antiferromagnetic spin-1/2 Heisenberg model on the square lattice by means of exact diagonalizations. In a first part, we calculate the spin-wave velocity, the spin-stiffness, and the magnetic susceptibility and thus determine the microscopic parameters of the low-energy long-wavelength description. In a second part, we present a comprehensive study of dynamical spin correlation functions for magnetic fields ranging from zero up to saturation. We find that at low fields, magnons are well defined in the whole Brillouin zone, but the dispersion is substantial…
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…
We measured the magnetic susceptibilities of Cu$_6$Ge$_6$O$_{18}$-xH$_2$O ($x = 0 \sim 6$). Susceptibility above the antiferromagnetic (AF) transition temperature ($T_{\rm N}$) agrees with susceptibility of the one-dimensional Heisenberg $S = 1/2$ model with competing AF interactions. From the estimated ratio between nearest-neighbor and next-nearest-neighbor AF exchange interactions, the spin system is probably located near a boundary between spin systems with gapless and gapped magnetic excitation. The value of $T_{\rm N}/T_{\rm max}$, where $T_{\rm max}$ is temperature at which the suscepti…
The ground-state properties of a spin $S=1/2$ tetrameric Heisenberg antiferromagnetic chain with alternating couplings AF$_{1}$-AF$_{2}$-AF$_{1}$% -F (AF and F denote antiferromagnetic and ferromagnetic couplings, respectively) are studied by means of the density matrix renormalization group method. Two plateaux of magnetization $m$ are found at $m=0$ and 1/4% . It is shown that in such a spin-1/2 AF system, there is a gap from the singlet ground state to the triplet excited states in the absence of a magnetic field. The spin-spin correlation function decays exponentially, and the gapped state…
Large single crystals of the new compound SrMn$_2$V$_2$O$_8$ have been grown by the floating-zone method. This transition-metal based oxide is isostructural to SrNi$_2$V$_2$O$_8$, described by the tetragonal space group $I4_1cd$. Magnetic properties were investigated by means of susceptibility, magnetization, and specific heat measurements. The title compound behaves like a one-dimensional magnetic system above the ordering temperature ($T_N$ = 43 K). The magnetic ground state can be described as a classical long-range ordered antiferromagnet with weak anisotropy.
For a class of quasi-one-dimensional clusters, by using exact diagonalization, we study the effect of side spins on the spin-spin correlations on chain. Our calculations show that the side spins added in the same sublattice can effectively strengthen the spin-spin correlations in large distance region and make the change tend to flat. It is exactly proved that periodically adding side spins can set up magnetic long-range orders in the ground state. Also we investigate the effect of the density of side spins on correlation strength. The case that two sublattices have different localized spins i…
We investigate the dynamical properties of the classical antiferromagnetic Heisenberg model on the kagome lattice using a combination of Monte Carlo and molecular dynamics simulations. We find that frustration induces a distribution of timescales in the cooperative paramagnetic regime (i.e. far above the onset of coplanarity), as recently reported experimentally in deuterium jarosite. At lower temperature, when the coplanar correlations are well established, we show that the weath- ervane loop fluctuations control the system relaxation : the time distribution observed at higher temperatures sp…
We study, on the basis of the general entangled-plaquette variational ansatz, the ground-state properties of the spin-1/2 antiferromagnetic Heisenberg model on the triangular lattice. Our numerical estimates are in good agreement with available exact results and comparable, for large system sizes, to those computed via the best alternative numerical approaches, or by means of variational schemes based on specific (i.e., incorporating problem dependent terms) trial wave functions. The extrapolation to the thermodynamic limit of our results for lattices comprising up to N=324 spins yields an upp…
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 have succeeded in synthesizing single crystals of the verdazyl radical beta-2,6-Cl2-V [= beta-3-(2,6-dichlorophenyl)-1,5-diphenylverdazyl]. The ab initio MO calculation indicated the formation of an S = 1/2 Heisenberg antiferromagnetic chain with four-fold magnetic periodicity consisting of three types of exchange interactions.We have successfully explained the magnetic and thermodynamic properties based on the expected spin model by using the quantum Monte Carlo method. Furthermore, we revealed that the alternating and unique Ising ferromagnetic chains become effective in the specific fiel…
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 …
Employing numerical linked-cluster expansions (NLCEs) along with exact diagonalizations of finite clusters with periodic boundary condition, we study the energy, specific heat, entropy, and various susceptibilities of the antiferromagnetic Heisenberg model on the checkerboard lattice. NLCEs, combined with extrapolation techniques, allow us to access temperatures much lower than those accessible to exact diagonalization and other series expansions. We find that the high-temperature peak in specific heat decreases as the frustration increases, consistent with the large amount of unquenched entro…
We study low-energy excitations in antiferromagnetic Heisenberg chains with a staggered field which splits the spectrum into a longitudinal and a transverse branch. Bound states are found to exist inside the field induced gap in both branches. They originate from the edge effects and are inherent to spin-chain materials. The sine-Gordon scaling $h_s^{2/3}|\log h_s|^{1/6}$ ($h_s$: the staggered field) provides an accurate description for the gap and midgap energies in the transverse branch for $S=1/2$ and the midgap energies in both branches for $S=3/2$ over a wide range of magnetic field; howe…
We study the one-dimensional spin-1/2 model with nearest and next-to-nearest-neighbor couplings exposed to a homogeneous magnetic field $h_{3}$ and a dimer field with period $q$ and strength $δ$. The latter generates a magnetization plateau at $M=(1-q/π)/2$, which evolves with strength $δ$ of the perturbation as $δ^ε$, where $ε=ε(h_{3},α)$ is related to the $η$-exponent which describes the critical behavior of the dimer structure factor, if the perturbation is switched of ($δ=0$). We also discuss the appearance of magnetization plateaus in ladder systems with $l$ legs.
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…
Corrections to the asymptotic correlation function in a Heisenberg spin-1/2 antiferromagnetic spin chain are known to vanish slowly (logarithmically) as a function of the distance r or the chain size L. This leads to significant differences with numerical results. We calculate the sub-leading logarithmic corrections to the finite-size correlation function, using renormalization group improved perturbation theory, and compare the result with numerical data.
