Quantum Phase Interference in Magnetic Molecular Clusters

The Landau Zener model has recently been used to measure very small tunnel splittings in molecular clusters of Fe8, which at low temperature behaves like a nanomagnet with a spin ground state of S = 10. The observed oscillations of the tunnel splittings as a function of the magnetic field applied along the hard anisotropy axis are due to topological quantum interference of two tunnel paths of opposite windings. Transitions between quantum numbers M = -S and (S - n), with n even or odd, revealed a parity effect which is analogous to the suppression of tunnelling predicted for half integer spins. This observation is the first direct evidence of the topological part of the quantum spin phase (Berry or Haldane phase) in a magnetic system. We show here that the quantum interference can also be measured by ac susceptibility measurements in the thermal activated regime.Comment: 3 pages, 2 figures, conference proceedings of LT22 (Helsinki, Finland, August 4-11, 199

How does a quadratic term in the energy dispersion modify the single-particle Green's function of the Tomonaga-Luttinger model?

We calculate the effect of a quadratic term in the energy dispersion on the low-energy behavior of the Green's function of the spinless Tomonaga-Luttinger model (TLM). Assuming that for small wave-vectors q = k - k_F the fermionic excitation energy relative to the Fermi energy is v_F q + q^2 / (2m), we explicitly calculate the single-particle Green's function for finite but small values of lambda = q_c /(2k_F). Here k_F is the Fermi wave-vector, q_c is the maximal momentum transfered by the interaction, and v_F = k_F / m is the Fermi velocity. Assuming equal forward scattering couplings g_2 = g_4, we find that the dominant effect of the quadratic term in the energy dispersion is a renormalization of the anomalous dimension. In particular, at weak coupling the anomalous dimension is tilde{gamma} = gamma (1 - 2 lambda^2 gamma), where gamma is the anomalous dimension of the TLM. We also show how to treat the change of the chemical potential due to the interactions within the functional bosonization approach in arbitrary dimensions.Comment: 17 pages, 1 figur

Breakdown of Luttinger liquid state in one-dimensional frustrated spinless fermion model

Haldane hypothesis about the universality of Luttinger liquid (LL) behavior in conducting one-dimensional (1D) fermion systems is checked numerically for spinless fermion model with next-nearest-neighbor interactions. It is shown that for large enough interactions the ground state can be gapless (metallic) due to frustrations but not be LL. The exponents of correlation functions for this unusual conducting state are found numerically by finite-size method.Comment: 3 pages, 4 figures, RevTe

The geometry of antiferromagnetic spin chains

We construct spin chains that describe relativistic sigma-models in the continuum limit, using symplectic geometry as a main tool. The target space can be an arbitrary complex flag manifold, and we find universal expressions for the metric and theta-term.Comment: 31 pages, 3 figure

Non-perturbative behavior of the quantum phase transition to a nematic Fermi fluid

We discuss shape (Pomeranchuk) instabilities of the Fermi surface of a two-dimensional Fermi system using bosonization. We consider in detail the quantum critical behavior of the transition of a two dimensional Fermi fluid to a nematic state which breaks spontaneously the rotational invariance of the Fermi liquid. We show that higher dimensional bosonization reproduces the quantum critical behavior expected from the Hertz-Millis analysis, and verify that this theory has dynamic critical exponent $z=3$. Going beyond this framework, we study the behavior of the fermion degrees of freedom directly, and show that at quantum criticality as well as in the the quantum nematic phase (except along a set of measure zero of symmetry-dictated directions) the quasi-particles of the normal Fermi liquid are generally wiped out. Instead, they exhibit short ranged spatial correlations that decay faster than any power-law, with the law $|x|^{-1} \exp(-\textrm{const.} |x|^{1/3})$ and we verify explicitely the vanishing of the fermion residue utilizing this expression. In contrast, the fermion auto-correlation function has the behavior $|t|^{-1} \exp(-{\rm const}. |t|^{-2/3})$. In this regime we also find that, at low frequency, the single-particle fermion density-of-states behaves as $N^*(\omega)=N^*(0)+ B \omega^{2/3} \log\omega +...$, where $N^*(0)$ is larger than the free Fermi value, N(0), and $B$ is a constant. These results confirm the non-Fermi liquid nature of both the quantum critical theory and of the nematic phase.Comment: 20 pages, 2 figures, 1 table; new version with minor changes; new subsection 3C2 added with an explicit calculation of the quasiparticle residue at the nematic transition; minor typos corrected, new references; general beautification of the text and figure

Consequences of a possible adiabatic transition between \nu=1/3 and \nu=1 quantum Hall states in a narrow wire

We consider the possibility of creating an adiabatic transition through a narrow neck, or point contact, between two different quantized Hall states that have the same number of edge modes, such as \nu=1 and \nu=1/3. We apply both the composite fermion and the Luttinger liquid formalism to analyze the transition. We suggest that using such adiabatic junctions one could build a DC step-up transformer, where the output voltage is higher than the input. Difficulties standing in the way of an experimental implementation of the adiabatic junction are addressed.Comment: 4 pages RevTex, includes 2 eps figures, Submitted to Phys. Rev. Let

Exact calculation of the ground-state dynamical spin correlation function of a S=1/2 antiferromagnetic Heisenberg chain with free spinons

We calculate the exact dynamical magnetic structure factor S(Q,E) in the ground state of a one-dimensional S=1/2 antiferromagnet with gapless free S=1/2 spinon excitations, the Haldane-Shastry model with inverse-square exchange, which is in the same low-energy universality class as Bethe's nearest-neighbor exchange model. Only two-spinon excited states contribute, and S(Q,E) is found to be a very simple integral over these states.Comment: 11 pages, LaTeX, RevTeX 3.0, cond-mat/930903

Spin Transport Properties in Heisenberg Antiferromagnetic Spin Chains: Spin Current induced by Twisted Boundary Magnetic Fields

Spin transport properties of the one-dimensional Heisenberg antiferromagnetic spin systems for both $S=1/2$ and S=1 are studied by applying twisted boundary magnetic field. The spin current displays significantly different behavior of the spin transport properties between $S=1/2$ and S=1 cases. For the spin-half case, a London equation for the current and the detection of an alternating electric field are proposed for the linear response regime. The correlation functions reveal the spiral nature of spin configuration for both ground state and the spinon excitations. For the spin-one chain otherwise, a kink is generated in the ground state for the size is larger than the correlation length, leading to an exponential dependence of spin current with respect to the chains length. The midgap state emerges from the degenerate ground state even for small boundary fields.Comment: 4 pages, 5 figure

New Family of Solvable 1D Heisenberg Models

Starting from a Calogero--Sutherland model with hyperbolic interaction confined by an external field with Morse potential we construct a Heisenberg spin chain with exchange interaction $\propto 1/\sinh^2 x$ on a lattice given in terms of the zeroes of Laguerre polynomials. Varying the strength of the Morse potential the Haldane--Shastry and harmonic spin chains are reproduced. The spectrum of the models in this class is found to be that of a classical one-dimensional Ising chain with nonuniform nearest neighbour coupling in a nonuniform magnetic field which allows to study the thermodynamics in the limit of infinite chains.Comment: 8 pp, LaTeX, ITP-UH-07/9

Exact Dynamical Correlation Functions of Calogero-Sutherland Model and One-Dimensional Fractional Statistics

One-dimensional model of non-relativistic particles with inverse-square interaction potential known as Calogero-Sutherland Model (CSM) is shown to possess fractional statistics. Using the theory of Jack symmetric polynomial the exact dynamical density-density correlation function and the one-particle Green's function (hole propagator) at any rational interaction coupling constant $\lambda = p/q$ are obtained and used to show clear evidences of the fractional statistics. Motifs representing the eigenstates of the model are also constructed and used to reveal the fractional {\it exclusion} statistics (in the sense of Haldane's ``Generalized Pauli Exclusion Principle''). This model is also endowed with a natural {\it exchange } statistics (1D analog of 2D braiding statistics) compatible with the {\it exclusion} statistics. (Submitted to PRL on April 18, 1994)Comment: Revtex 11 pages, IASSNS-HEP-94/27 (April 18, 1994