Lieb-Robinson Bounds for the Toda Lattice

We establish locality estimates, known as Lieb-Robinson bounds, for the Toda lattice. In contrast to harmonic models, the Lieb-Robinson velocity for these systems do depend on the initial condition. Our results also apply to the entire Toda as well as the Kac-van Moerbeke hierarchy. Under suitable assumptions, our methods also yield a finite velocity for certain perturbations of these systems

A Multi-Dimensional Lieb-Schultz-Mattis Theorem

For a large class of finite-range quantum spin models with half-integer spins, we prove that uniqueness of the ground state implies the existence of a low-lying excited state. For systems of linear size L, of arbitrary finite dimension, we obtain an upper bound on the excitation energy (i.e., the gap above the ground state) of the form (C\log L)/L. This result can be regarded as a multi-dimensional Lieb-Schultz-Mattis theorem and provides a rigorous proof of a recent result by Hastings.Comment: final versio

Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems

We prove Lieb-Robinson bounds for the dynamics of systems with an infinite dimensional Hilbert space and generated by unbounded Hamiltonians. In particular, we consider quantum harmonic and certain anharmonic lattice systems

Exact Antiferromagnetic Ground States of Quantum Spin Chains

We recall a simple class of translation invariant states for an infinite quantum spin chain, which was introduced by L. Accardi. Those states have exponential decay of correlation functions, and a subclass contains the ground states of a certain class of finite range interactions. We consider, in particular, a family of states for integer spin chains, containing as its simplest member the ground state of a spin 1 Heisenberg antiferromagnet recently studied by I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki. For this family we compute explicitly the correlation functions and other properties

Finitely Correlated States on Quantum Spin Chains

We study a construction, which yields a class of translation invariant states on quantum spin chains, characterised by the property that the correlations across any bond can be modelled on a finite dimensional vector space. These states, which are dense in the set of all translation invariant states, can be considered as generalised valence bond states. We develop a complete theory of the ergodic decomposition of such states, including the decomposition into periodic "Néel ordered" states. Ergodic finitely correlated states have exponential decay of correlations. All states considered can be considered as "functions" of states of a special kind, so-called "purely generated states", which are shown to be ground states for suitably chosen interactions. We show that all these states have a spectral gap. Our theory does not require symmetry of the state with respect to a local gauge group, but the isotropic ground states of some one-dimensional antiferromagnets, recently studied by Affleck, Kennedy, Lieb, and Tasaki fall in this class

Valence Bond States on Quantum Spin Chains as Ground States with Spectral Gap

We show that every translation invariant valence bond state on a one-dimensional quantum spin chain arises as the unique ground state of a certain family of finite range interactions. For each interaction in this family we show the existence of a non-zero spectral gap above the ground state energy. A special example of this structure is a state recently studied by Affleck, Lieb, Kennedy, and Tasaki. For the Hamiltonian studied by these authors we can estimate the gap, and prove that it lies between 1/3 and 10/27

Isolated Eigenvalues of the Ferromagnetic Spin-J XXZ Chain with Kink Boundary Conditions

We investigate the low-lying excited states of the spin J ferromagnetic XXZ chain with Ising anisotropy Delta and kink boundary conditions. Since the third component of the total magnetization, M, is conserved, it is meaningful to study the spectrum for each fixed value of M. We prove that for J>= 3/2 the lowest excited eigenvalues are separated by a gap from the rest of the spectrum, uniformly in the length of the chain. In the thermodynamic limit, this means that there are a positive number of excitations above the ground state and below the essential spectrum

Simple Host-Guest Chemistry To Modulate the Process of Concentration and Crystallization of Membrane Proteins by Detergent Capture in a Microfluidic Device

This paper utilizes cyclodextrin-based host-guest chemistry in a microfluidic device to modulate the crystallization of membrane proteins and the process of concentration of membrane protein samples. Methyl-beta-cyclodextrin (MBCD) can efficiently capture a wide variety of detergents commonly used for the stabilization of membrane proteins by sequestering detergent monomers. Reaction Center (RC) from Blastochloris viridis was used here as a model system. In the process of concentrating membrane protein samples, MBCD was shown to break up free detergent micelles and prevent them from being concentrated. The addition of an optimal amount of MBCD to the RC sample captured loosely bound detergent from the protein-detergent complex and improved sample homogeneity, as characterized by dynamic light scattering. Using plug-based microfluidics, RC crystals were grown in the presence of MBCD, giving a different morphology and space group than crystals grown without MBCD. The crystal structure of RC crystallized in the presence of MBCD was consistent with the changes in packing and crystal contacts hypothesized for removal of loosely bound detergent. The incorporation of MBCD into a plug-based microfluidic crystallization method allows efficient use of limited membrane protein sample by reducing the amount of protein required and combining sparse matrix screening and optimization in one experiment. The use of MBCD for detergent capture can be expanded to develop cyclodextrin-derived molecules for fine-tuned detergent capture and thus modulate membrane protein crystallization in an even more controllable way