Session P23: Quantum Spin Chains II

Thermal transport of dimerized and frustrated spin-1/2 chains

We present a numerical study of thermal transport in dimerized and frustrated spin-1/2 chains at finite temperatures. Since these models are nonintegrable, the thermal Drude weight scales to zero in the thermodynamic limit. The conductivity at finite frequencies, however, is non-zero and we discuss the scaling with system size as well as the extrapolation to the zero-frequency limit. Results for three cases are presented. First, the dimerized chain is studied in the limit of weakly coupled dimers. In this case, interactions of the elementary triplet excitations are weak, which should allow for an analytical description based on a bond-boson operator representation. Second, we compare the thermal conductivity of the frustrated chain in the massless and the massive regime of this model. Finally, we extract the zero-frequency thermal conductivity of the isotropic two-leg spin ladder and discuss implications for the interpretation of recent experiments for La$_5$Ca$_9$Cu$_{24}$O$_{41}$.   

A systematic method for constructing a spin-singlet basis for quantum antiferromagnets

We present a new method for constructing a complete orthonormal basis for the singlet states of quantum spin-1/2 lattice systems. Our approach can be used for any dimension and an arbitrary lattice symmetry. In this talk the main group- and graph-theoretical steps are explained. The general theory is then applied to the one-dimensional quantum antiferromagnet. Exploiting the symmetries of closed rings, we can drastically reduce the number of basis states for the different eigenstates of the Hamiltonian (in the singlet sector). The method allows to calculate in an efficient way expectation values of any operator.   

Crossed Spin-1/2 Heisenberg Chains as a Quantum Impurity Problem

Using equivalencies between different models we reduce the model of two spin-1/2 Heisenberg chains crossed at one point to the model of free fermions. The spin-spin correlation function is calculated by summing the perturbation series in the interchain interaction. The result reveals a power law decay with a nonuniversal exponent.   

Comparison of Magnetic Field-Modified Electronic Excitations in Ni(II) Compounds

NTDN (Ni[tn]$_2$[NO$_2$]$_2$) can be considered a paramagnetic analog material to the Haldane compounds NENP and NENB (Ni[en]$_2 $NO$_2$ClO$_4$ and Ni[en]$_2$NO$_2$BF$_4$; where en = C$_2$N$_2 $H$_{8}$ and tn = C$_2$N$_3$H$_10$). Except for the different bonding of one NO$_2$ group and the absence or presence of spin chains, NTDN and the Haldane compounds have nearly identical electronic coordination around the Ni$^{2+}$ ions. Here, we report and compare the magnetic field ($H$)-dependent polarized optical transmittance of the three materials in the range 9,000 to 22,000 cm$^{-1}$. The $H$ dependence is manifest in the varying intensities of certain electronic absorptions with applied field. Although all three materials possess similar $H$- sensitive excitations, the details of the $H$ dependence differ with the magnetic ground states. In NTDN, the intensity changes commence at $H$ = 0 and saturate at $\approx$ 10 T, whereas in the Haldane compounds, the onset of changes is at the gap- closing critical field, $H_C$, above which the intensity is linearly modified with field. The mechanism of the $H$- dependence is yet to be clarified and probably depends on the nature of the electronic excitation. Intensity variations with applied field are observed in both Ni$^{2+}$-to-NO$_2^-$ charge transfer transitions and Ni$^{2+}$ $d-d$ spin forbidden excitations.   

Magnetic Chains Assembled with Atomic Precision

We report the first study of small magnetic chains constructed and studied \textit{in-situ} with atomic precision. By positioning Mn atoms one at a time with an STM, we are able to follow the low energy excitation spectrum of the chain as it changes dramatically with length. The low energy spectra of chains built from an odd number of atoms display a spin-flip excitation similar to that of a single Mn atom. In even-length chains the spin flip excitation is absent and is replaced by an excitation at higher energies that splits into three distinct modes in a magnetic field. We interpret these results as direct evidence of the antiferromagnetic coupling of the individual atomic spins. Quantitative comparison of our results with the Heisenberg model allows us to directly obtain the coupling strength J$\sim $6meV between atomic spins and suggests that the total spin of the individual Mn atoms on the surface is 5/2.   

Resonant Quantum Tunneling of spin chains in 3D-magnetically ordered CoTAC

CoTAC is a well know molecular spin chain system which orders in an antiferromagnetic canted state at $4.15\ K$. We show that, below $300\ mK$, the dynamics of the magnetization in the $c$-direction are governed by resonant quantum tunneling of the magnetization. This conclusion is based on a number of experimental observations: the temperature independence of the relaxation of the magnetization, speeding up of the relaxation at a well defined magnetic field value ($1025\ Oe$) and the increase of the magnetization each time this field is crossed during a succession of minor loops. The key to understanding this behavior could be the absence of resonance in zero field. We propose a mechanism to describe this behavior using a simple model of domain wall nucleation which explains many of the unusual experimental observations.   

Extended Valence-Bond Solid Picture for Quasi-One-Dimensional Quantum Magnets

Ground-state gapped phases of quasi-one-dimensional quantum magnets are given an comprehensive interpretation based on an extended valence-bond solid (VBS) picture. We introduce composite spins with the enlarged spin magnitude in the ground state and regard the system as an effective single spin chain that consists of composite spins. The relevance of the composite spins in the ground state is revealed by the effects of dimerization in the spin-spin couplings. In order to characterize the gapped phases, we inspect the configuration of valence bonds by calculating the appropriate order parameters by the quantum Monte Carlo method with the continuous-time loop algorithm. The so-called short-range resonating-valence bond solid state is identified to be an extended VBS state. Dimensional crossover to the two-dimensional systems is also discussed.   

Luttinger sum rules in the 2-channel spin 1 Kondo chain

We present numerical results, using the DMRG method, for the zero-temperature phase diagram of the one-dimensional 2-channel Kondo lattice model, coupled to $S=1$ localized spins. Unlike the previously studied 1-channel $S=1/2$ case, the $S=1$ localized spins in the 2-channel model permit a gapped Haldane state, which stabilizes the weak-coupling (``small'' Fermi surface) paramagnetic phase. We focus on the paramagnetic region approaching half-filling, where the interesting possibility has been recently raised of a non-trivial crossover region where the Fermi wavenumber varies continuously.   

Coupling of Spin and Charge Degrees of Freedom in a Hydrodynamic Two-Fluid Approach

We use a hydrodynamic approach to study correlated quantum one- dimensional systems. One can derive an effective hydrodynamics in the limit of smooth densities and slow velocities. In the limit when gradients of density and velocity can be neglected, one obtains an integrable system. We discuss the origin of this integrability and, as an application, we calculate some non trivial correlation functions. The Hydrodynamic description is a useful tool to study the dynamics of a system. We introduce a two-fluid hydrodynamic description of one-dimensional spin 1/2 fermions with contact interactions. It is known that linearized hydrodynamics (bosonization) exhibits spin-charge separation. In the full {\it non-linear} theory, the spin and charge degrees of freedom are coupled to each other, therefore spin waves carry charge as well. We discuss the dynamics of such system.   

Coupled one-dimensional magnetic systems: the truncated conformal spectrum approach

We develop a combined analytical/numerical technique in order to understand coupled, possibly strongly, one dimensional magnetic systems. The approach trades on exact knowledge of the underlying one dimensional subsystem and the concomitant ability to compute exactly matrix elements of operators coupling the subsystems together. With these matrix elements in hand, the fully coupled system is first truncated and then diagonalized numerically. In this way we obtain both the spectrum and correlation functions of the system. The truncation can be improved upon through a renormalization group procedure. As a test case we consider coupled quantum Ising chains.   

Random antiferromagnetic spin chains with enlarged symmetry

We present the asympotically exact solution of some random antiferromagnetic spin chains with enlarged symmetry groups. Using a generalization of the strong disorder real space renormalization group method, we considered both the isotropic SU(N) and the anisotropic SU(4) chains with totally antisymmetric irreducible representations. In the first case, the system is governed by a universal infinite-randomness fixed point (IRFP), with activated dynamical scaling between energy $\left(\Omega\right)$ and length $\left(L\right)$ scales $\Omega\sim\exp\left(-L^{\psi}\right)$ (with the tunneling exponent $\psi=1/N$), and average correlation function decaying as a power law with exponent $\eta=4/N$. All thermodynamic quantities are universal with exponents depending only on $N$. In the second case, relevant for systems with SU(2)$_{spin}\otimes$SU(2)$_{orbital}$ symmetry, we determined the full phase diagram as a function of the mean anistropy and its variance. All stable fixed points are of the IRFP variety with activated dynamical scaling. The tunneling exponents span a wide range of values and can even be larger than the SU(2) value, $\psi=1/2$.   

Thermodynamics and magnetization process of the frustrated ferromagnetic spin-1/2 chain

We report a study of the thermodynamics and magnetization curve of a $J_1$--$J_2$ spin-1/2 chain with a ferromagnetic nearest neighbor coupling $J_1$ and an antiferromagnetic next-nearest neighbor interaction $J_2$. This model has recently been suggested to describe the properties of different compounds such as LiCuVO$_4$ and Rb$_2$Cu$_2$Mo$_3$O$_{12}$. We present results for both the specific heat and the magnetic susceptibility for the whole parameter range of $J_2/4<|J_1|<0$ obtained by exact diagonalization of up to $N=24$ sites. The specific heat exhibits a two-peak structure for $J_1<0$, originating from, first, the proximity to a ferromagnetic ground state and, second, antiferromagnetic fluctuations at higher energies. Furthermore, the magnetization process at zero temperature is analyzed by means of the density matrix renormalization group technique. Particular emphasis is given to the presence (or rather absence) of magnetization plateaus and a comparison with other theoretical results for the ground-state phase diagram.   

The Magnetic phase diagram of the spin-chain system Ca$_{2+x}$Y$_{2-x}$Cu$_5$O$_{10-\delta}$ : Oxygen hole-doping

Recently, K. Kudo et al.\footnote{K. Kudo, S. Kurogi, and Y.Koike, Physical Review B \textbf{71}, 104413 (2005)} studied the magnetic ground state in the edge-sharing CuO$_2$ chains in the spin- chain system Ca$_{2+x}$Y$_{2-x}$Cu$_5$O$_{10-\delta}$. In that study, the antiferromagnetic transition temperature decreases with increasing \emph{x} and disappears around \emph{x}=1.4 followed by the appearance of a spin-glass phase at \emph{x}=1.5. We propose that the oxygen content should be included in the hole doping effect by $p=1/5(x-2\delta)$ in the spin-chain system. We present x-ray diffraction, magnetic susceptibility, specific heat and iodometric titration measurements\footnote{This work is supported by the Robert A. Welch Foundation grant No.F-1191 and the National Science Foundation grant No. DMR-0210383} which indicate that an oxygen deficiency shifts the magnetic features toward higher \emph{x}. For example, for $x=1$ samples, the single crystals of Ref.1 are equivalent to our oxygen deficient polycrystalline sample with $\delta \approx 0.5$. Such a composition has an only slightly suppressed N\'eel temperature, while for nearly fully oxygenated $x=1$ samples, the antiferromagnetic transition is completely suppressed.\footnote{M. D. Chabot, and J. T. Markert, Physical Review Letters \textbf{86}, 163 (2001)}   

Low temperature magnetization and the excitation spectrum of antiferromagnetic quantum Heisenberg rings

We have performed quantum Monte Carlo calculations to obtain the low temperature magnetization and differential susceptibility for finite, antiferromagnetic Heisenberg rings of intrinsic spins $s = 1/2, 1,3/2,2,5/2,3,7/2$. From these data we have determined the level-crossing fields as well as the dependence of the minimal excitation energies on the total spin quantum number $S$. For large intrinsic spins ($s \geq 3/2$) we find that the data exhibit scaling behavior, approaching the classical limit proportional to $s^{-1.05}$. Since this limit is approached so slowly, even $s=7/2$ spins are distinctly non-classical. We have also found for large $s$ that as the number of spins $N$ increases, the energy gap between the ground state and the first excited state approaches zero proportional to $1/N^\alpha$, where $\alpha \approx 0.76$ for $s=3/2$ and $\alpha \approx 0.84$ for $s=5/2$. Finally, we demonstrate the usefulness of our results by examining the Fe$_{12}$ molecular ring, leading to a new, more accurate estimate of the exchange constant for this system than has been obtained heretofore.   

Magnetic Properties of a Coordination Polymer [Mn$_{3}$[(OH)$_{2}$Na$_{2}$(3-cnba)$_{6}]$_{n}$

Magnetic properties of [Mn$_{3}$(OH)$_{2}$Na$_{2}$(3-cnba)$_{6}$]$_{n}$ (3-Hcnba = 3-cyanobenzoic acid), a newly discovered three-dimensional coordination polymer, were investigated using magnetic susceptibility $M(T)$/$H$ and isothermal magnetization $M(H)$. The crystal structure of [Mn$_{3}$(OH)$_{2}$Na$_{2}$(3-cnba)$_{6}$]$_{n}$ is triclinic with a space group $P$-1. The lattice parameters are $a$ = 6.663 {\AA}, $b$ = 12.971 {\AA}, $c$ = 14.161 {\AA}, \textit{$\alpha $} = 70.13\r{ }, \textit{$\beta $} = 88.43\r{ }, and \textit{$\gamma $} = 76.47\r{ }. The results of $M(T)$/$H$ on powder samples show that the effective moment \textit{$\mu $}$_{eff}$ of Mn$^{2+}$ is 5.88 \textit{$\mu $}$_{B}$ at temperatures above 100 K, close to the expected value for a free Mn$^{2+}$ ion. Below 3 K, [Mn$_{3}$(OH)$_{2}$Na$_{2}$(3-cnba)$_{6}$]$_{n}$ orders antiferromagneticly. A sudden slope change in $M(H)$ measured at is observed at a very small critical field of H$_{c} \quad \approx $ 20 G, suggesting a metamagnetic transition. Above 20 kG, $M(H)$ starts to saturate, reaching a value equivalent to 1.7 \textit{$\mu $}$_{B}$ per Mn$^{2+}$ ion. The magnetic behavior of the complex is interpreted in terms of an effective ferrimagnetic Mn(II) chains in which spin moments are linked by interactions in an AF-F-AF (F = ferromagnetic and AF = antiferromagnetic) sequence in the triangular magnetic repeating unit.