We study TiOCl as an example of an S = 1/2 layered Mott insulator. From our analysis of new susceptibility data, combined with LDA and LDA+U band structure calculations, we conclude that orbital ordering produces quasi-one-dimensional spin chains and that TiOCl is a new example of Heisenberg-chains which undergo a spin-Peierls transition. The energy scale is an order of magnitude larger than that of previously known examples. The effects of non-magnetic Sc impurities are explained using a model of broken finite chains. The discovery of high-T c superconductors has generated a great deal of interest in low-dimensional spin-1/2 materials. Even in the absence of charge degrees of freedom, many questions remain unanswered until today. One of key importance is the question whether a two-dimensional spin system can support unbroken symmetry at zero temperature due to strong quantum fluctuations for S = 1/2 systems. Such a spin liquid state was suggested by Anderson 1 and termed the resonating valence bond (RVB) state . This has motivated us to search for other examples of S = 1/2 layered materials, notably at the beginning of the transition metal series where Ti 3+ is in the d 1 configuration (as opposed to d 9 in the cuprates). From this point of view the layered compound titanium oxihalides TiOX (X=Cl, Br) appear most promising. Indeed, Beynon and Wilson 2 reported in 1993 that the uniform magnetic susceptibility of these materials shows a number of unusual properties. According to them, the susceptibility is almost temperature independent and could not be fitted to the Curie-Weiss law, nor to any one-dimensional model. Moreover, if non-magnetic Sc (d 0 ) impurities were introduced, a large Curie tail corresponding to one spin-1/2 moment per Sc appears. After subtracting this Curie tail, the susceptibility was again found to be temperature independent but substantially reduced compared to the pure material. This effect was particularly striking in TiOCl and led Beynon and Wilson to propose that these materials may be examples of RVB-like states.We have redone the measurement of the susceptibility of TiOCl for both the pure material and in the presence of Sc, and carried out LDA and LDA+U band structure calculations. Our data are not in agreement with that of ref.2, especially for the pure sample. Here, we find that above a temperature of 130K, below which the susceptibility drops abruptly, our data fits well to a nearest neighbor Heisenberg model with an exchange constant of J = 660K. The data for 6% and 10% Sc-doping is in very good agreement with a model based on broken finite linear Heisenberg-chains.In the following we describe the structure of TiOCl and discuss the possibility of 1d spin chains formed by t 2g orbitals. The reasoning here will be justified by band structure calculations, which feature isolated one-dimensional d-bands. We then present our experimental data for the pure and Sc-doped samples and fits to theoretical models. We will argue that all evidence is consistent with a picture based on quasi-...

In this letter we investigate a class of Hamiltonians which, in addition to the usual center-ofmass (CM) momentum conservation, also have center-of-mass position conservation. We find that regardless of the particle statistics, the energy spectrum is at least q-fold degenerate when the filling factor is p/q, where p and q are coprime integers. Interestingly the simplest Hamiltonian respecting this type of symmetry encapsulates two prominent examples of novel states of matter, namely the fractional quantum Hall liquid and the quantum dimer liquid. We discuss the relevance of this class of Hamiltonian to the search for featureless Mott insulators.

A subtle relation between quantum Hall physics and the phenomenon of pairing is unveiled. By use of second quantization, we establish a connection between (i) a broad class of rotationally symmetric two-body interactions within the lowest Landau level and (ii) integrable hyperbolic Richardson-Gaudin-type Hamiltonians that arise in (p x + ip y ) superconductivity. Specifically, we show that general Haldane pseudopotentials (and their sums) can be expressed as a sum of repulsive noncommuting (p x + ip y )-type pairing Hamiltonians. The determination of the spectrum and individual null spaces of each of these noncommuting Richardson-Gaudin-type Hamiltonians is nontrivial yet is Bethe ansatz solvable. For the Laughlin sequence, it is observed that this problem is frustration free and zero-energy ground states lie in the common null space of all of these noncommuting Hamiltonians. This property allows for the use of a new truncated basis of pairing configurations in which to express Laughlin states at general filling factors. We prove separability of arbitrary Haldane pseudopotentials, providing explicit expressions for their second quantized forms, and further show by explicit construction how to exploit the topological equivalence between different geometries (disk, cylinder, and sphere) sharing the same topological genus number, in the second quantized formalism, through similarity transformations. As an application of the second quantized approach, we establish a "squeezing principle" that applies to the zero modes of a general class of Hamiltonians, which includes but is not limited to Haldane pseudopotentials. We also show how one may establish (bounds on) "incompressible filling factors" for those Hamiltonians. By invoking properties of symmetric polynomials, we provide explicit second quantized quasihole generators; the generators that we find directly relate to bosonic chiral edge modes and further make aspects of dimensional reduction in the quantum Hall systems precise.

Giant anomalies are found in the temperature dependence of Raman-active phonons in the quantum magnet TiOCl, suggesting the presence of an extended fluctuation regime. This regime coincides with a pseudogap phase identified in earlier NMR experiments. The observed large, local spin-gap is proposed to origin from coupled spin/lattice fluctuations. Below 100 K, in the long-range crystallographically distorted phase, a dimerized ground state with a smaller, global spin-gap of about 2⌬ spin Ϸ 430 K exists. This transition also marks a dimensionality cross-over of the system.