arXiv subjects

J. Richter

Publications and source records attributed to J. Richter.

At least 73 records · Page 4Linked to original sources

arXiv2011

The frustrated Heisenberg antiferromagnet on the honeycomb lattice: A candidate for deconfined quantum criticality

We study the ground-state (gs) phase diagram of the frustrated spin-1/2 $J_{1}$-$J_{2}$-$J_{3}$ antiferromagnet with $J_{2} = J_{3} =κJ_1$ on the honeycomb lattice, using coupled-cluster theory and exact diagonalization methods. We present results for the gs energy, magnetic order parameter, spin-spin correlation function, and plaquette valence-bond crystal (PVBC) susceptibility. We find a Néel antiferromagnetic (AFM) phase for $κ< κ_{c_{1}} \approx 0.47$, a collinear striped AFM phase for $κ> κ_{c_{2}} \approx 0.60$, and a paramagnetic PVBC phase for $κ_{c_{1}} \lesssim κ\lesssim κ_{c_{2}}$. The transition at $κ_{c_{2}}$ appears to be of first-order type, while that at $κ_{c_{1}}$ is continuous. Since the Néel and PVBC phases break different symmetries our results favor the deconfinement scenario for the transition at $κ_{c_{1}}$.

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arXiv2010

Spiral correlations in frustrated one-dimensional spin-1/2 Heisenberg J1-J2-J3 ferromagnets

We use the coupled cluster method for infinite chains complemented by exact diagonalization of finite periodic chains to discuss the influence of a third-neighbor exchange J3 on the ground state of the spin-1/2 Heisenberg chain with ferromagnetic nearest-neighbor interaction J1 and frustrating antiferromagnetic next-nearest-neighbor interaction J2. A third-neighbor exchange J3 might be relevant to describe the magnetic properties of the quasi-one-dimensional edge-shared cuprates, such as LiVCuO4 or LiCu2O2. In particular, we calculate the critical point J2^c as a function of J3, where the ferromagnetic ground state gives way for a ground state with incommensurate spiral correlations. For antiferromagnetic J3 the ferro-spiral transition is always continuous and the critical values J2^c of the classical and the quantum model coincide. On the other hand, for ferromagnetic J3 \lesssim -(0.01...0.02)|J1| the critical value J2^c of the quantum model is smaller than that of the classical model. Moreover, the transition becomes discontinuous, i.e. the model exhibits a quantum tricritical point. We also calculate the height of the jump of the spiral pitch angle at the discontinuous ferro-spiral transition.

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arXiv2010

Comment on "Two-spinon and four-spinon continuum in a frustrated ferromagnetic spin-1/2 chain" by M. Enderle et al

We show that LiVCuO4 should be described by strongly ferromagnetically coupled Heisenberg antiferromagnetic chains (HAC) in sharp contrast with the effective exchange integrals Ji given in Enderle et al., Phys. Rev. Lett. vol. 104, 237207 (2010), and the main issues of that work, namely, (i) LiVCuO4 is well described by two weakly ferromagnetically coupled interpenetrating Heisenberg antiferromagnetic spin-1/2 chains, (ii) the extracted exchange integrals J1, J2 agree with a previous spin-wave description (Enderle et al., Euphys. Lett. vol. 70, 237 (2005)), (iii) the spectral density of inelastic neutron scattering (INS) above 10 meV is ascribed to a 4-spinon continuum. Applying exact diagonalization and DMRG methods to fit their INS and magnetization M(H) data, supported by two independent microscopic methods (5-band Hubbard model and LSDA+U calculations), we demonstrate that LiCuVO4 exhibits strong inchain frustration with alpha =-J2/J1 < 1, i.e. strong coupling of the HAC at odds with (i). An alternative phenomenological set in accord with various experimental results is proposed. In view of the recent possible discovery of quantum-spin nematics and Bose condensation of two-magnon bound states (M. Zhitomirsky et al. arXiv:1003.4096v2 (2010), L. Svistov et al. ibid. 1005.5668v2 (2010)) in LiCuVO4 precise knowledge of the main J-values is of key importance.

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arXiv2010

Coupled frustrated quantum spin-1/2 chains with orbital order in volborthite Cu3V2O7(OH)2(H2O)2

We present a microscopic magnetic model for the spin-liquid candidate volborthite Cu3V2O7(OH)2(H2O)2. The essentials of this DFT-based model are (i) the orbital ordering of Cu(1) 3d 3z2-r2 and Cu(2) 3d 3x2-y2, (ii) three relevant couplings J_ic, J_1 and J_2, (iii) the ferromagnetic nature of J_1 and (iv) frustration governed by the next-nearest-neighbor exchange interaction J_2. Our model implies magnetism of frustrated coupled chains in contrast to the previously proposed anisotropic kagome model. Exact diagonalization studies reveal agreement with experiments.

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arXiv2010

Magnetic properties of the Hubbard model on kagome stripes

We consider the one-orbital $N$-site repulsive Hubbard model on two kagome-like chains, both of which yield a completely dispersionless (flat) one-electron band. Using exact many-electron ground states in the subspaces with $n\le n_{\max}$ ($n_{\max}\propto N$) electrons, we calculate the square of the total spin in the ground state to discuss magnetic properties of the models. We have found that although for $n<n_{\max}$ the ground states contain fully polarized states, there is no finite region of electron densities $n/{\cal{N}} <1$ (${\cal{N}}=N/3$ or ${\cal{N}}=N/5$) where ground-state ferromagnetism survives for ${\cal{N}}\to\infty$.

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arXiv2010

Quasi-1d quantum helimagnets: The fate of multipolar phases

Coupled frustrated spin-1/2 chains in high magnetic fields described within the ferro- antiferromagnetic J1-J2 Heisenberg model are studied by the DMRG, the hard core boson, and the spin wave theory approaches. Multipolar phases related to magnon bound states are destroyed (supported) by weak antiferromagnetic (ferromagnetic) interchain couplings Jic. We show that quantum spin nematics might be found for LiVCuO4 whereas for Li(Na)Cu2O2 it is prevented by a sizeable antiferromagnetic Jic. Also for Li2ZrCuO4 with a small antiferromagnetic Jic expected triatic or quartic phases are unlikely, too. The saturation field is found to be strongly affected even by a relatively small Jic.

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arXiv2010

Thermodynamics of a two-dimensional frustrated spin-1/2 Heisenberg ferromagnet

Using the spin-rotation-invariant Green's function method we calculate the thermodynamic quantities (correlation functions , uniform static spin susceptibility χ, correlation length ξ, and specific heat C_V) of the two-dimensional spin-1/2 J1-J2 Heisenberg ferromagnet for J2 < J2^c \approx 0.44|J1|, where J2^c is the critical frustrating antiferromagnetic next-nearest neighbor coupling at which the ferromagnetic ground state gives way for a ground-state phase with zero magnetization. Examining the low-temperature behavior of χand ξ, in the limit T \to 0 both quantities diverge exponentially, i.e., χ\propto \exp(b/T) and ξ\propto\exp(b/2T), respectively. We find a linear decrease of the coefficient b with increasing frustration according to b=-(π/2)(J1+2J2), i.e., the exponential divergence of χand ξis present up to J2^c. Furthermore, we find an additional low-temperature maximum in the specific heat when approaching the critical point, J2 \to J2^c.

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arXiv2010

Heat capacity uncovers physics of a frustrated spin tube

We report on refined experimental results concerning the low-temperature specific heat of the frustrated spin tube material [(CuCl2tachH)3Cl]Cl2. This substance turns out to be an unusually perfect spin tube system which allows to study the physics of quasi-one dimensional antiferromagnetic structures in rather general terms. An analysis of the specific heat data demonstrates that at low enough temperatures the system exhibits a Tomonaga-Luttinger liquid behavior corresponding to an effective spin-3/2 antiferromagnetic Heisenberg chain with short-range exchange interactions. On the other hand, at somewhat elevated temperatures the composite spin structure of the chain is revealed through a Schottky-type peak in the specific heat located around 2 K. We argue that the dominating contribution to the peak originates from gapped magnon-type excitations related to the internal degrees of freedom of the rung spins.

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arXiv2010

The frustrated spin-1/2 J1-J2 Heisenberg ferromagnet on the square lattice: Exact diagonalization and Coupled-Cluster study

We investigate the ground-state magnetic order of the spin-1/2 J1-J2 Heisenberg model on the square lattice with ferromagnetic nearest-neighbor exchange J1<0 and frustrating antiferromagnetic next-nearest neighbor exchange J2>0. We use the coupled-cluster method to high orders of approximation and Lanczos exact diagonalization of finite lattices of up to N=40 sites in order to calculate the ground-state energy, the spin-spin correlation functions, and the magnetic order parameter. We find that the transition point at which the ferromagnetic ground state disappears is given by J2^{c1}=0.393|J1| (exact diagonalization) and J2^{c1}=0.394|J1| (coupled-cluster method). We compare our results for ferromagnetic J1 with established results for the spin-1/2 J1-J2 Heisenberg model with antiferromagnetic J1. We find that both models (i.e., ferro- and antiferromagnetic J1) behave similarly for large J2, although significant differences between them are observed for J2/|J1| \lesssim 0.6. Although the semiclassical collinear magnetic long-range order breaks down at J2^{c2} \approx 0.6J1 for antiferromagnetic J1, we do not find a similar breakdown of this kind of long-range order until J2 \sim 0.4|J1| for the model with ferromagnetic J1. Unlike the case for antiferromagnetic J1, if an intermediate disordered phase does occur between the phases exhibiting semiclassical collinear stripe order and ferromagnetic order for ferromagnetic J1 then it is likely to be over a very small range below J2 \sim 0.4|J1|.

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arXiv2010

Frustrated spin ladder with alternating spin-1 and spin-1/2 rungs

We study the impact of the diagonal frustrating couplings on the quantum phase diagram of a two-leg ladder composed of alternating spin-1 and spin-1/2 rungs. As the coupling strength is increased the system successively exhibits two gapped paramagnetic phases (a rung-singlet and a Haldane-like non-degenerate states) and two ferrimagnetic phases with different ferromagnetic moments per rung. The first two states are similar to the phases studied in the frustrated spin-1/2 ladder, whereas the magnetic phases appear as a result of the mixed-spin structure of the model. A detailed characterization of these phases is presented using density-matrix renormalization-group calculations, exact diagonalizations of periodic clusters, and an effective Hamiltonian approach inspired by the analysis of numerical data. The present theoretical study was motivated by the recent synthesis of the quasi-one-dimensional ferrimagnetic material Fe$^{II}$Fe$^{III}$ (trans-1,4-cyclohexanedicarboxylate) exhibiting a similar ladder structure.

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arXiv2009

Low-temperature properties of the Hubbard model on highly frustrated one-dimensional lattices

We consider the repulsive Hubbard model on three highly frustrated one-dimensional lattices -- sawtooth chain and two kagomé chains -- with completely dispersionless (flat) lowest single-electron bands. We construct the complete manifold of {\em exact many-electron} ground states at low electron fillings and calculate the degeneracy of these states. As a result, we obtain closed-form expressions for low-temperature thermodynamic quantities around a particular value of the chemical potential $μ_0$. We discuss specific features of thermodynamic quantities of these ground-state ensembles such as residual entropy, an extra low-temperature peak in the specific heat, and the existence of ferromagnetism and paramagnetism. We confirm our analytical results by comparison with exact diagonalization data for finite systems.

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arXiv2009

The spin-1/2 J1-J2 Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N=40 spins

We present numerical exact results for the ground state and the low-lying excitations for the spin-1/2 J1-J2 Heisenberg antiferromagnet on finite square lattices of up to N=40 sites. Using finite-size extrapolation we determine the ground-state energy, the magnetic order parameters, the spin gap, the uniform susceptibility, as well as the spin-wave velocity and the spin stiffness as functions of the frustration parameter J2/J1. In agreement with the generally excepted scenario we find semiclassical magnetically ordered phases for J2 < J2^{c1} and J2 > J2^{c2} separated by a gapful quantum paramagnetic phase. We estimate J2^{c1} \approx 0.35J1 and J2^{c2} \approx 0.66J1.

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arXiv2009

High-Order Coupled Cluster Method Study of Frustrated and Unfrustrated Quantum Magnets in External Magnetic Fields

We apply the coupled cluster method (CCM) in order to study the ground-state properties of the (unfrustrated) square-lattice and (frustrated) triangular-lattice spin-half Heisenberg antiferromagnets in the presence of external magnetic fields. Here we determine and solve the basic CCM equations by using the localised approximation scheme commonly referred to as the `LSUB$m$' approximation scheme and we carry out high-order calculations by using intensive computational methods. We calculate the ground-state energy, the uniform susceptibility, the total (lattice) magnetisation and the local (sublattice) magnetisations as a function of the magnetic field strength. Our results for the lattice magnetisation of the square-lattice case compare well to those results of QMC for all values of the applied external magnetic field. We find a value for magnetic susceptibility of $χ=0.070$ for the square-lattice antiferromagnet, which is also in agreement with the results of other approximate methods (e.g., $χ=0.0669$ via QMC). Our estimate for the range of the extent of the ($M/M_s=$)$\frac 13$ magnetisation plateau for the triangular-lattice antiferromagnet is $1.37< λ< 2.15$, which is in good agreement with results of spin-wave theory ($1.248 < λ< 2.145$) and exact diagonalisations ($1.38 < λ< 2.16$). The CCM value for the in-plane magnetic susceptibility per site is $χ=0.065$, which is below the result of the spin-wave theory (evaluated to order 1/S) of $χ_{SWT}=0.0794$.

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arXiv2009

High-Order Coupled Cluster Method (CCM) Calculations for Quantum Magnets with Valence-Bond Ground States

In this article, we prove that exact representations of dimer and plaquette valence-bond ket ground states for quantum Heisenberg antiferromagnets may be formed via the usual coupled cluster method (CCM) from independent-spin product (e.g. Néel) model states. We show that we are able to provide good results for both the ground-state energy and the sublattice magnetization for dimer and plaquette valence-bond phases within the CCM. As a first example, we investigate the spin-half $J_1$--$J_2$ model for the linear chain, and we show that we are able to reproduce exactly the dimerized ground (ket) state at $J_2/J_1=0.5$. The dimerized phase is stable over a range of values for $J_2/J_1$ around 0.5. We present evidence of symmetry breaking by considering the ket- and bra-state correlation coefficients as a function of $J_2/J_1$. We then consider the Shastry-Sutherland model and demonstrate that the CCM can span the correct ground states in both the Néel and the dimerized phases. Finally, we consider a spin-half system with nearest-neighbor bonds for an underlying lattice corresponding to the magnetic material CaV$_4$O$_9$ (CAVO). We show that we are able to provide excellent results for the ground-state energy in each of the plaquette-ordered, Néel-ordered, and dimerized regimes of this model. The exact plaquette and dimer ground states are reproduced by the CCM ket state in their relevant limits.

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arXiv2009

Ground-state degeneracy and low-temperature thermodynamics of correlated electrons on highly frustrated lattices

Highly frustrated lattices yield a completely flat lowest single-electron band. Remarkably, exact many-body ground states can be constructed for the repulsive Hubbard model and the t-J model by filling this flat band with localized electron states. This construction leads to a macroscopic ground-state degeneracy. We discuss how to compute these ground-state degeneracies for a certain class of models, including in particular the sawtooth chain. Furthermore, we discuss generic consequences for low-temperature thermodynamic properties, like the appearance of a low-temperature peak in the specific heat. Finally, we present complementary numerical results obtained by exact diagonalization.

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arXiv2009

Diamond chains with multiple-spin exchange interactions

We study the phase diagram of a symmetric spin-1/2 Heisenberg diamond chain with additional cyclic four-spin exchange interactions. The presented analysis supplemented by numerical exact-diagonalization results for finite periodic clusters implies a rich phase diagram containing, apart from standard magnetic and spin-liquid phases, two different tetramer-dimer phases as well as an exotic four-fold degenerate dimerized phase. The characteristics of the established spin phases as well as the nature of quantum phase transitions are discussed, as well.

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arXiv2009

Thermodynamics of layered Heisenberg magnets with arbitrary spin

We present a spin-rotation-invariant Green-function theory of long- and short-range order in the ferro- and antiferromagnetic Heisenberg model with arbitrary spin quantum number S on a stacked square lattice. The thermodynamic quantities (Curie temperature T_C, Néel temperature T_N, specific heat C_V, intralayer and interlayer correlation lengths) are calculated, where the effects of the interlayer coupling and the S dependence are explored. In addition, exact diagonalizations on finite two-dimensional (2D) lattices with S>=1 are performed, and a very good agreement between the results of both approaches is found. For the quasi-2D and isotropic 3D magnets, our theory agrees well with available quantum Monte Carlo and high-temperature series-expansion data. Comparing the quasi-2D S=1/2 magnets, we obtain the inequalities T_N>T_C and, for small enough interlayer couplings, T_N<T_C. The results for C_V and the intralayer correlation length are compared to experiments on the quasi-2D antiferromagnets Zn_2VO(PO_4)_2 with S=1/2 and La_2NiO_4 with S=1, respectively.

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arXiv2008

Ground-state phases of the spin-1/2 J_1-J_2 Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment

Using the coupled cluster method for high orders of approximation and complementary exact diagonalization studies we investigate the ground state properties of the spin-1/2 $J_1$--$J_2$ frustrated Heisenberg antiferromagnet on the square lattice. We have calculated the ground-state energy, the magnetic order parameter, the spin stiffness, and several generalized susceptibilities to probe magnetically disordered quantum valence-bond phases. We have found that the quantum critical points for both the Néel and collinear orders are $J_2^{c1}\approx (0.44 \pm 0.01)J_1$ and $J_2^{c2}\approx (0.59 \pm 0.01)J_1$ respectively, which are in good agreement with the results obtained by other approximations. In contrast to the recent study by [Sirker et al. Phys. Rev. B {\bf 73}, 184420 (2006)], our data do not provide evidence for the transition from the Néel to the valence-bond solid state to be first order. Moreover, our results are in favor of the deconfinement scenario for that phase transition. We also discuss the nature of the magnetically disordered quantum phase.

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