arXiv subjects

R. R. P. Singh

Publications and source records attributed to R. R. P. Singh.

65 records · Page 4Linked to original sources

arXiv1997

A new paradigm for two-dimensional spin-liquids

Motivated by the geometry of the materials Na_2 Ti_2 As_2 O and Na_2 Ti_2 Sb_2 O, we study a square-lattice Heisenberg antiferromagnet with spins located at the bond-centers. The largest exchange constant J couples neighboring spins in a given row or column. This leads to a mesh of isolated spin-chains running along the X and Y axes. A weaker exchange constant J' couples the nearest-neighbor spins on the lattice. Classically, J' fails to fix the relative spin orientation for different chains and hence the ground state is highly degenerate. Quantum order by disorder effect is studied by spin-wave theory and numerical methods. It is shown that a 4-sublattice order is favored by quantum fluctuations. However, several arguments are presented that suggest that the ground state of the system remains disordered, thus providing us with a paradigm for a two-dimensional spin-liquid.

cond-mat.str-el↗

arXiv1997

Nuclear relaxation in the spin-1/2 antiferromagnetic chain compound Sr_2CuO_3 --- comparison between theories and experiments

The NMR relaxation data on Sr_2CuO_3 [Phys. Rev. Lett. 76, 4612 (1996)] are reexamined and compared with the analytic theory of the dynamic susceptibility in the S=1/2 antiferromagnetic Heisenberg chain including multiplicative logarithmic corrections [Phys. Rev. Lett. 78, 539 (1997); cond-mat/9610015]. Comparisons of the spin-lattice and the gaussian spin-echo decay rates (1/T_1 and 1/T_{2G}) and their ratio all show good quantitative agreement. Our results demonstrate the importance of the logarithmic corrections in the analysis of experimental data for quasi-1D systems and indicate that the dynamics of Sr_2CuO_3 is well described by a S=1/2 one-dimensional Heisenberg model with a nearest neighbor exchange.

cond-mat.str-el↗

arXiv1997

Quantum Monte Carlo in the Interaction Representation --- Application to a Spin-Peierls Model

A quantum Monte Carlo algorithm is constructed starting from the standard perturbation expansion in the interaction representation. The resulting configuration space is strongly related to that of the Stochastic Series Expansion (SSE) method, which is based on a direct power series expansion of exp(-beta*H). Sampling procedures previously developed for the SSE method can therefore be used also in the interaction representation formulation. The new method is first tested on the S=1/2 Heisenberg chain. Then, as an application to a model of great current interest, a Heisenberg chain including phonon degrees of freedom is studied. Einstein phonons are coupled to the spins via a linear modulation of the nearest-neighbor exchange. The simulation algorithm is implemented in the phonon occupation number basis, without Hilbert space truncations, and is exact. Results are presented for the magnetic properties of the system in a wide temperature regime, including the T-->0 limit where the chain undergoes a spin-Peierls transition. Some aspects of the phonon dynamics are also discussed. The results suggest that the effects of dynamic phonons in spin-Peierls compounds such as GeCuO3 and NaV2O5 must be included in order to obtain a correct quantitative description of their magnetic properties, both above and below the dimerization temperature.

cond-mat.str-el↗

arXiv1997

High Temperature Thermodynamics of the Ferromagnetic Kondo-Lattice Model

We present a high temperature series expansion for the ferromagnetic Kondo lattice model in the large coupling limit, which is used to model CMR perovskites. Our results show the expected cross-over to Curie-Weiß behavior at a temperature related to the bandwidth. Estimates for the magnetic transition temperatures are in the experimentally observed range. The compressibility shows that the high temperature charge excitations can be modeled by spinless fermions. The CMR effect itself, however, warrants the inclusion of dynamic effects and cannot be explained by a static calculation.

cond-mat.str-el↗

arXiv1997

Dynamics of the spin-half Heisenberg chain at intermediate temperatures

Combining high-temperature expansions with the recursion method and quantum Monte Carlo simulations with the maximum entropy method, we study the dynamics of the spin-1/2 Heisenberg chain at temperatures above and below the coupling J. By comparing the two sets of calculations, their relative strengths are assessed. At high temperatures, we find that there is a low-frequency peak in the momentum integrated dynamic structure factor, due to diffusive long-wavelength modes. This peak is rapidly suppressed as the temperature is lowered below J. Calculation of the complete dynamic structure factor S(k,w) shows how the spectral features associated with the two-spinon continuum develop at low temperatures. We extract the nuclear spin-lattice relaxation rate 1/T1 from the w-->0 limit, and compare with recent experimental results for Sr2CuO3 and CuGeO3. We also discuss the scaling behavior of the dynamic susceptibility, and of the static structure factor S(k) and the static susceptibility X(k). We confirm the asymptotic low-temperature forms S(pi)~[ln(T)]^(3/2) and X(pi)~T^(-1)[ln(T)]^(1/2), expected from previous theoretical studies.

cond-mat.str-el↗

arXiv1996

Quantum-critical scaling and temperature-dependent logarithmic corrections in the spin-half Heisenberg chain

Low temperature dynamics of the S=1/2 Heisenberg chain is studied via a simple ansatz generalizing the conformal mapping and analytic continuation procedures to correlation functions with multiplicative logarithmic factors. Closed form expressions for the dynamic susceptibility and the NMR relaxation rates 1/T_1 and 1/T_{2G} are obtained, and are argued to improve the agreement with recent experiments. Scaling in q/T and ω/T are violated due to these logarithmic terms. Numerical results show that the logarithmic corrections are very robust. While not yet in the asymptotic low temperature regime, they provide striking qualitative confirmation of the theoretical results.

cond-mat↗

arXiv1996

Convergent expansions for properties of the Heisenberg model for CaV$_4$O$_9$

We have carried out a wide range of calculations for the $S=1/2$ Heisenberg model with nearest- and second-neighbor interactions on a two-dimensional lattice which describes the geometry of the vanadium ions in the spin-gap system CaV$_4$O$_9$. The methods used were convergent high-order perturbation expansions (``Ising'' and ``Plaquette'' expansions at $T=0$, as well as high-temperature expansions) for quantities such as the uniform susceptibility, sublattice magnetization, and triplet elementary excitation spectrum. Comparison with the data for CaV$_4$O$_9$ indicates that its magnetic properties are well described by nearest-neighbor exchange of about 200K in conjunction with second-neighbor exchange of about 100K.

cond-mat↗

arXiv1996

Origin of spin-gap in CaV$_4$O$_9$: effect of frustration and lattice distortion

We study the origin of spin-gap in recently discovered material CaV$_4$O$_9$. We analyze the spin-$1/2$ Heisenberg model on the $1/5$ depleted square lattice with nearest neighbor (nn) and next nearest neighbor (nnn) interactions, in terms of the singlet and triplet states of the 4-spin plaquettes and 2-spin dimers. Phase diagram of the model is obtained within a linear ``spin-wave"-like approximation, and is shown to agree well with the earlier results of QMC simulations for nn interactions. We further propose that the special lattice structure of CaV$_4$O$_9$ naturally leads to lattice distortions, which enhances the spin-gap via a spin-Peierls mechanism.

cond-mat↗

arXiv1995

Spin Dependence of Correlations in Two-Dimensional Quantum Heisenberg Antiferromagnets

We present a series expansion study of spin-S square-lattice Heisenberg antiferromagnets. The numerical data are in excellent agreement with recent neutron scattering measurements. Our key result is that the correlation length for S>1/2 strongly deviates from the exact T->0 (renormalized classical, or RC) scaling prediction for all experimentally and numerically accessible temperatures. We note basic trends with S of the experimental and series expansion correlation length data and propose a scaling crossover scenario to explain them.

cond-mat↗

arXiv1994

Scaling Regimes, Crossovers, and Lattice Corrections in 2D Heisenberg Antiferromagnets

We study scaling behavior in 2D, S=1/2 and S=1 Heisenberg antiferromagnets using the data on full q-dependences of the equal time structure factor and the static susceptibility, calculated through high temperature expansions. We also carry out comparisons with a model of two coupled S=1/2 planes with the interlayer coupling tuned to the T=0 critical point. We separately determine the spin-wave velocity c and mass $m=c/ξ$, in addition to the correlation length, $ξ$, and find that c is temperature dependent; only for $T\alt JS$, it approaches its known T=0 value $c_0$. Despite this temperature dependent spin-wave velocity, full q- and $ω$-dependences of the dynamical susceptibility $χ(\bf q,ω)$ agree with the universal scaling functions computable for the $σ$-model, for temperatures upto $T_0 \sim 0.6c_0/a$. Detailed comparisons show that below $T_0$ the S=1 model is in the renormalized classical (RC) regime, the two plane model is in the quantum critical (QC) regime, and the S=1/2 model exhibits a RC-QC crossover, centered at T=0.55J. In particular, for the S=1/2 model above this crossover and for the two-plane model at all T, the spin-wave mass is in excellent agreement with the universal QC prediction, $m\simeq 1.04\,T$. In contrast, for the S=1/2 model below the RC-QC crossover, and for the S=1 model at all T, the behavior agrees with the known RC expression. For all models nonuniversal behavior occurs above $T\sim 0.6c_0/a$. Our results strongly support the conjecture of Chubukov and Sachdev that the S=1/2 model is close to the T=0 critical point to exhibit QC behavior.

cond-mat↗

arXiv1993

Evidence for Spin-Charge Separation in the Two-Dimensional T-J Model

We have calculated high temperature expansions for the momentum distribution function $n_{\scriptscriptstyle\bf k}$ and the equal time spin and density correlation functions $S({\bf q})$ and $N({\bf q})$ of the two-dimensional $t$-$J$ model. On extrapolation to low temperatures we find that $n_{\scriptscriptstyle\bf k}$ has a step-like feature at ${\bf k}_{\scriptscriptstyle F}$ and $S({\bf q})$ has $2{\bf k}_{\scriptscriptstyle F}$ as a characteristic wavevector, whereas $N({\bf q})$ has $2{\bf k}_{\scriptscriptstyle F}^{\scriptscriptstyle SF}$ as a characteristic wavevector. Here ${\bf k}_{\scriptscriptstyle F}$ and ${\bf k}_{\scriptscriptstyle F}^{\scriptscriptstyle SF}$ are the Fermi wavevectors of the nearest-neighbor square lattice tight-binding and spinless fermion models, respectively. By comparison to the known results for one dimension this suggests spin-charge separation in the two-dimensional $t$-$J$ model.

cond-mat↗