arXiv subjects

D. Ihle

Publications and source records attributed to D. Ihle.

At least 37 records · Page 2Linked to original sources

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

Thermodynamics of the frustrated ferromagnetic spin-1/2 Heisenberg chain

We studied the thermodynamics of the one-dimensional J1-J2 spin-1/2 Heisenberg chain for ferromagnetic nearest-neighbor bonds J1 < 0 and frustrating antiferromagnetic next-nearest-neighbor bonds J1 > 0 using full diagonalization of finite rings and a second-order Green-function formalism. Thereby we focus on J2 < |J1|/4 where the ground state is still ferromagnetic, but the frustration influences the thermodynamic properties. We found that their critical indices are not changed by J2. The analysis of the low-temperature behavior of the susceptibility chi leads to the conclusion that this behavior changes from chi \propto T^{-2} at J2 < |J1|/4 to chi \propto T^{-3/2} at the quantum-critical point J2=|J1|/4. Another effect of the frustration is the appearance of an extra low-T maximum in the specific heat C_v(T) for J2 \gtrsim |J1|/8, indicating its strong influence on the low-energy spectrum.

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arXiv2008

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

We calculate the thermodynamic quantities (correlation functions , correlation length xi, spin susceptibility chi, and specific heat C_V) of the frustrated one-dimensional spin-half J2-J2 Heisenberg ferromagnet, i.e. for J2< 0.25|J1|, using a rotation-invariant Green's-function formalism and full diagonalization of finite lattices. We find that the critical indices are not changed by J2, i.e., chi = y_0 T^{-2} and xi = x_0 T^{-1} at T \to 0. However, the coefficients y_0 and x_0 linearly decrease with increasing J2 according to the relations y_0=(1-4J_2/|J_1|)/24 and x_0 =(1-4J_2/|J_1|)/4, i.e., both coefficients vanish at J2=0.25|J1| indicating the zero-temperature phase transition that is accompanied by a change of the low-temperature behavior of chi (xi) from chi \propto T^{-2} (xi \propto T^{-1}) at J2 < 0.25|J1| to chi \propto T^{-3/2} (xi \propto T^{-1/2}) at J2 = 0.25|J1|. In addition, we detect the existence of an additional low-temperature maximum in the specific heat when approaching the critical point at J2=0.25|J1|.

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arXiv2008

Bound state formation and nature of the excitonic insulator phase in the extended Falicov-Kimball model

Motivated by the possibility of pressure-induced exciton condensation in intermediate-valence Tm[Se,Te] compounds we study the Falicov-Kimball model extended by a finite f-hole valence bandwidth. Calculating the Frenkel-type exciton propagator we obtain excitonic bound states above a characteristic value of the local interband Coulomb attraction. Depending on the system parameters coherence between c- and f-states may be established at low temperatures, leading to an excitonic insulator phase. We find strong evidence that the excitonic insulator typifies either a BCS condensate of electron-hole pairs (weak-coupling regime) or a Bose-Einstein condensate (BEC) of preformed excitons (strong-coupling regime), which points towards a BCS-BEC transition scenario as Coulomb correlations increase.

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arXiv2008

Thermodynamics of Heisenberg ferromagnets with arbitrary spin in a magnetic field

The thermodynamic properties (magnetization, magnetic susceptibility, transverse and longitudinal correlation lengths, specific heat) of one- and two-dimensional ferromagnets with arbitrary spin S in a magnetic field are investigated by a second-order Green-function theory. In addition, quantum Monte Carlo simulations for S= 1/2 and S=1 are performed using the stochastic series expansion method. A good agreement between the results of both approaches is found. The field dependence of the position of the maximum in the temperature dependence of the susceptibility fits well to a power law at low fields and to a linear increase at high fields. The maximum height decreases according to a power law in the whole field region. The longitudinal correlation length may show an anomalous temperature dependence: a minimum followed by a maximum with increasing temperature. Considering the specific heat in one dimension and at low magnetic fields, two maxima in its temperature dependence for both the S= 1/2 and S = 1 ferromagnets are found. For S>1 only one maximum occurs, as in the two-dimensional ferromagnets. Relating the theory to experiments on the S= 1/2 quasi-one-dimensional copper salt TMCuC [(CH_3)_4NCuCl_3], a fit to the magnetization as a function of the magnetic field yields the value of the exchange energy which is used to make predictions for the occurrence of two maxima in the temperature dependence of the specific heat.

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arXiv2006

Quantum $J_1$--$J_2$ antiferromagnet on the stacked square lattice: Influence of the interlayer coupling on the ground-state magnetic ordering

Using the coupled-cluster method (CCM) and the rotation-invariant Green's function method (RGM), we study the influence of the interlayer coupling $J_\perp$ on the magnetic ordering in the ground state of the spin-1/2 $J_1$-$J_2$ frustrated Heisenberg antiferromagnet ($J_1$-$J_2$ model) on the stacked square lattice. In agreement with known results for the $J_1$-$J_2$ model on the strictly two-dimensional square lattice ($J_\perp=0$) we find that the phases with magnetic long-range order at small $J_2< J_{c_1}$ and large $J_2> J_{c_2}$ are separated by a magnetically disordered (quantum paramagnetic) ground-state phase. Increasing the interlayer coupling $J_\perp>0$ the parameter region of this phase decreases, and, finally, the quantum paramagnetic phase disappears for quite small $J_\perp \sim 0.2 ... 0.3 J_1$.

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arXiv2006

Green's function theory of quasi-two-dimensional spin-half Heisenberg ferromagnets: stacked square versus stacked kagomé lattice

We consider the thermodynamic properties of the quasi-two-dimensional spin-half Heisenberg ferromagnet on the stacked square and the stacked kagomé lattices by using the spin-rotation-invariant Green's function method. We calculate the critical temperature $T_C$, the uniform static susceptibility $χ$, the correlation lengths $ξ_ν$ and the magnetization $M$ and investigate the short-range order above $T_C$. We find that $T_C$ and $M$ at $T>0$ are smaller for the stacked kagomé lattice which we attribute to frustration effects becoming relevant at finite temperatures.

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arXiv2006

Thermodynamics of S>=1 ferromagnetic Heisenberg chains with uniaxial single-ion anisotropy

The thermodynamic properties of S>=1 ferromagnetic chains with an easy-axis single-ion anisotropy are investigated at arbitrary temperatures by both a Green-function approach, based on a decoupling of three-spin operator products, and by exact diagonalizations of chains with up to N=12 sites using periodic boundary conditions. A good agreement between the results of both approaches is found. For the S=1 chain, the temperature dependence of the specific heat reveals two maxima, if the ratio of the anisotropy energy D and the exchange energy J exceeds a characteristic value, D/J >7.4, and only one maximum for D/J <7.4. This is in contrast to previous exact diagonalization data for comparably small chains (N <= 7) using open boundary conditions. Comparing the theory with experiments on di-bromo Ni complexes the fit to the specific heat yields concrete values for D and J which are used to make predictions for the temperature dependences of the spin-wave spectrum, the correlation length, and the transverse magnetic susceptibility.

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arXiv2005

Absence of long-range order in a spin-half Heisenberg antiferromagnet on the stacked kagome lattice

We study the ground state of a spin-half Heisenberg antiferromagnet on the stacked kagome lattice by using a spin-rotation-invariant Green's-function method. Since the pure two-dimensional kagome antiferromagnet is most likely a magnetically disordered quantum spin liquid, we investigate the question whether the coupling of kagome layers in a stacked three-dimensional system may lead to a magnetically ordered ground state. We present spin-spin correlation functions and correlation lengths. For comparison we apply also linear spin wave theory. Our results provide strong evidence that the system remains short-range ordered independent of the sign and the strength of the interlayer coupling.

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arXiv2004

Green's-function theory of the Heisenberg ferromagnet in a magnetic field

We present a second-order Green's-function theory of the one- and two-dimensional S=1/2 ferromagnet in a magnetic field based on a decoupling of three-spin operator products, where vertex parameters are introduced and determined by exact relations. The transverse and longitudinal spin correlation functions and thermodynamic properties (magnetization, isothermal magnetic susceptibility, specific heat) are calculated self-consistently at arbitrary temperatures and fields. In addition, exact diagonalizations on finite lattices and, in the one-dimensional case, exact calculations by the Bethe-ansatz method for the quantum transfer matrix are performed. A good agreement of the Green's-function theory with the exact data, with recent quantum Monte Carlo results, and with the spin polarization of a $ν=1$ quantum Hall ferromagnet is obtained. The field dependences of the position and height of the maximum in the temperature dependence of the susceptibility are found to fit well to power laws, which are critically analyzed in relation to the recently discussed behavior in Landau's theory. As revealed by the spin correlation functions and the specific heat at low fields, our theory provides an improved description of magnetic short-range order as compared with the random phase approximation. In one dimension and at very low fields, two maxima in the temperature dependence of the specific heat are found. The Bethe-ansatz data for the field dependences of the position and height of the low-temperature maximum are described by power laws. At higher fields in one and two dimensions, the temperature of the specific heat maximum linearly increases with the field.

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arXiv2001

Magnetic order in the quasi-two-dimensional easy-plane XXZ model

A Green's-function theory of antiferromagnetic short-range and long-range order (LRO) in the $S=1/2$ quasi-two-dimensional easy-plane XXZ model is presented. As the main new result, {\it two} phase transitions due to the combined influence of spatial and spin anisotropy are found, where below the higher and lower Néel temperature there occurs LRO in the transverse and in both the transverse and longitudinal spin correlators, respectively. Comparing the theory with neutron-scattering data for the correlation length of $\rm La_2CuO_4$, a very good agreement in the whole temperature dependence is obtained. Moreover, for $\rm La_2CuO_4$, $\rm Sr_2CuO_2Cl_2$, and $\rm Ca_{0.85}Sr_{0.15}CuO_2$ the second phase with longitudinal LRO is predicted to appear far below room temperature.

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arXiv2000

Spin correlation functions and susceptibilities in the easy-plane XXZ chain

We present a Green's-function theory of magnetic short-range order in the $S=1/2$ easy-plane XXZ chain based on the projection method for the dynamic spin susceptibility and a decoupling of three-spin operator products introducing vertex parameters. The longitudinal and transverse static susceptibilities and two-point correlation functions of arbitrary range are calculated self-consistently for all wavenumbers, temperatures, and anisotropy parameters $ -1\leq Δ\leq 1$. In the easy-plane ferromagnetic region $(Δ< 0)$, the longitudinal correlators of spins at distance $n$ change sign at a finite temperature $T_0(n,Δ)$, in reasonable agreement with recent data obtained by finite-chain diagonalizations. The temperature dependence of the uniform static susceptibilities exhibits a maximum which is explained as an effect of magnetic short-range order which decreases with increasing temperature.

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arXiv2000

Quantum to classical crossover in the 2D easy-plane XXZ model

Ground-state and thermodynamical properties of the spin-1/2 two-dimensional easy-plane XXZ model are investigated by both a Green's-function approach and by Lanczos diagonalizations on lattices with up to 36 sites. We calculate the spatial and temperature dependences of various spin correlation functions, as well as the wave-vector dependence of the spin susceptibility for all anisotropy parameters $Δ$. In the easy--plane ferromagnetic region $(-1< Δ< 0)$, the longitudinal correlators of spins at distance $r$ change sign at a finite temperature $T_0(Δ, {\bf r})$. This transition, observed in the 2D case for the first time, can be interpreted as a quantum to classical crossover.

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arXiv2000

Theory of magnetic order in the three-dimensional spatially anisotropic Heisenberg model

A spin-rotation-invariant Green's-function theory of long-range and short-range order (SRO) in the $S=1/2$ antiferromagnetic Heisenberg model with spatially anisotropic couplings on a simple cubic lattice is presented. The staggered magnetization, the two-spin correlation functions, the correlation leng spin-rotation-invariant Green's-function theory of long-range and short-range order (SRO) in the $S=1/2$ antiferromagnetic Heisenberg model with spatially anisotropic couplings on a simple cubic lattice is presented. The staggered magnetization, the two-spin correlation functions, the correlation lengths, and the static spin susceptibility are calculated self-consistently over the whole temperature region, where the effects of spatial anisotropy are explored. As compared with previous spin-wave approaches, the Néel temperature is reduced by the improved description of SRO. The maximum in the temperature dependence of the uniform static susceptibility is shifted with anisotropy and is ascribed to the decrease of SRO with increasing temperature. Comparing the theory with experimental data for the magnetization and correlation length of La$_2$CuO$_4$, a good agreement in the temperature dependences is obtained.

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arXiv1999

Spin correlation functions and Néel order in the 2D Heisenberg model: Effects of spatial anisotropy

The ground-state properties of the square-lattice spin-1/2 Heisenberg antiferromagnet with spatially anisotropic couplings are investigated by Green's-function projection approaches. The staggered magnetization and the two-spin correlators are calculated; the competition between magnetic long- and short-range order is discussed in comparison with experiments on $\rm Sr_2[Ca_2]CuO_3$.

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arXiv1999

Magnetic Order-Disorder Transition in the Two-Dimensional Spatially Anisotropic Heisenberg Model at Zero Temperature

The ground-state properties of the spin-1/2 antiferromagnetic Heisenberg model with spatially anisotropic couplings on a square lattice are investigated by a spin-rotation-invariant Green's-function approach and by Lanczos diagonalizations on lattices up to 36 sites supplemented by finite-size scaling. We focus on the anisotropy-driven transition from the Néel state to a paramagnetic state with antiferromagnetic short-range order and on the spatial dependence of spin correlation functions. Our principal result is that a rather sharp crossover in the magnetic behavior occurs at the coupling ratio $R_0\simeq 0.2$ ($R=J_y/J_x$).

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arXiv1996

Magnetic properties of the 2D t-t'-Hubbard model

The two-dimensional (2D) t-t'-Hubbard model is studied within the slave-boson (SB) theory. At half-filling, a paramagnetic to antiferromagnetic phase transition of first order at a finite critical interaction strength U_c(t'/t) is found. The dependences on U/t and t'/t of the sublattice magnetization and of the local magnetic moment are calculated. Our results reasonably agree with recent (Projector) Quantum Monte Carlo data. The SB ground-state phase diagram reveals a t'-induced electron-hole asymmetry, and, depending on the ratio t'/t, the antiferromagnetic or ferromagnetic phases are stable down to U=0 at a critical hole doping.

cond-mat↗

arXiv1996

Theory of magnetic short-range order for itinerant electron systems

On the basis of the one--band t-t'-Hubbard model a self-consistent renormalization theory of magnetic short--range order (SRO) in the paramagnetic phase is presented combining the four-field slave-boson functional-integral scheme with the cluster variational method. Contrary to previous SRO approaches the SRO is incorporated at the saddle-point and pair-approximation levels. A detailed numerical evaluation of the theory is performed at zero temperature, where both the hole- and electron-doped cases as well as band-structure effects are studied. The ground--state phase diagram shows the suppression of magnetic long-range order in favour of a paramagnetic phase with antiferromagnetic SRO in a wide doping region. In this phase the uniform static spin susceptibility increases upon doping up to the transition to the Pauli paraphase. Comparing the theory with experiments on high--T_c cuprates a good agreement is found.

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