Unbiased sampling of globular lattice proteins in three dimensions

We present a Monte Carlo method that allows efficient and unbiased sampling of Hamiltonian walks on a cubic lattice. Such walks are self-avoiding and visit each lattice site exactly once. They are often used as simple models of globular proteins, upon adding suitable local interactions. Our algorithm can easily be equipped with such interactions, but we study here mainly the flexible homopolymer case where each conformation is generated with uniform probability. We argue that the algorithm is ergodic and has dynamical exponent z=0. We then use it to study polymers of size up to 64^3 = 262144 monomers. Results are presented for the effective interaction between end points, and the interaction with the boundaries of the system

The traveling salesman problem, conformal invariance, and dense polymers

We propose that the statistics of the optimal tour in the planar random Euclidean traveling salesman problem is conformally invariant on large scales. This is exhibited in power-law behavior of the probabilities for the tour to zigzag repeatedly between two regions, and in subleading corrections to the length of the tour. The universality class should be the same as for dense polymers and minimal spanning trees. The conjectures for the length of the tour on a cylinder are tested numerically.Comment: 4 pages. v2: small revisions, improved argument about dimensions d>2. v3: Final version, with a correction to the form of the tour length in a domain, and a new referenc

Continuous Variable Quantum Key Distribution with a Noisy Laser

Existing experimental implementations of continuous-variable quantum key distribution require shot-noise limited operation, achieved with shot-noise limited lasers. However, loosening this requirement on the laser source would allow for cheaper, potentially integrated systems. Here, we implement a theoretically proposed prepare-and-measure continuous-variable protocol and experimentally demonstrate the robustness of it against preparation noise stemming for instance from technical laser noise. Provided that direct reconciliation techniques are used in the post-processing we show that for small distances large amounts of preparation noise can be tolerated in contrast to reverse reconciliation where the key rate quickly drops to zero. Our experiment thereby demonstrates that quantum key distribution with non-shot-noise limited laser diodes might be feasible.Comment: 10 pages, 6 figures. Corrected plots for reverse reconciliatio

Single-Quadrature Continuous-Variable Quantum Key Distribution

Most continuous-variable quantum key distribution schemes are based on the Gaussian modulation of coherent states followed by continuous quadrature detection using homodyne detectors. In all previous schemes, the Gaussian modulation has been carried out in conjugate quadratures thus requiring two independent modulators for their implementations. Here, we propose and experimentally test a largely simplified scheme in which the Gaussian modulation is performed in a single quadrature. The scheme is shown to be asymptotically secure against collective attacks, and considers asymmetric preparation and excess noise. A single-quadrature modulation approach renders the need for a costly amplitude modulator unnecessary, and thus facilitates commercialization of continuous-variable quantum key distribution.Comment: 13 pages, 7 figure

Exact valence bond entanglement entropy and probability distribution in the XXX spin chain and the Potts model

By relating the ground state of Temperley-Lieb hamiltonians to partition functions of 2D statistical mechanics systems on a half plane, and using a boundary Coulomb gas formalism, we obtain in closed form the valence bond entanglement entropy as well as the valence bond probability distribution in these ground states. We find in particular that for the XXX spin chain, the number N_c of valence bonds connecting a subsystem of size L to the outside goes, in the thermodynamic limit, as = (4/pi^2) ln L, disproving a recent conjecture that this should be related with the von Neumann entropy, and thus equal to 1/(3 ln 2) ln L. Our results generalize to the Q-state Potts model.Comment: 4 pages, 2 figure

Extended two-level quantum dissipative system from bosonization of the elliptic spin-1/2 Kondo model

We study the elliptic spin-1/2 Kondo model (spin-1/2 fermions in one dimension with fully anisotropic contact interactions with a magnetic impurity) in the light of mappings to bosonic systems using the fermion-boson correspondence and associated unitary transformations. We show that for fixed fermion number, the bosonic system describes a two-level quantum dissipative system with two noninteracting copies of infinitely-degenerate upper and lower levels. In addition to the standard tunnelling transitions, and the transitions driven by the dissipative coupling, there are also bath-mediated transitions between the upper and lower states which simultaneously effect shifts in the horizontal degeneracy label. We speculate that these systems could provide new examples of continuous time quantum random walks, which are exactly solvable.Comment: 7 pages, 1 figur

The antiferromagnetic transition for the square-lattice Potts model

We solve the antiferromagnetic transition for the Q-state Potts model (defined geometrically for Q generic) on the square lattice. The solution is based on a detailed analysis of the Bethe ansatz equations (which involve staggered source terms) and on extensive numerical diagonalization of transfer matrices. It involves subtle distinctions between the loop/cluster version of the model, and the associated RSOS and (twisted) vertex models. The latter's continuum limit involves two bosons, one which is compact and twisted, and the other which is not, with a total central charge c=2-6/t, for sqrt(Q)=2cos(pi/t). The non-compact boson contributes a continuum component to the spectrum of critical exponents. For Q generic, these properties are shared by the Potts model. For Q a Beraha number [Q = 4 cos^2(pi/n) with n integer] the two-boson theory is truncated and becomes essentially Z\_{n-2} parafermions. Moreover, the vertex model, and, for Q generic, the Potts model, exhibit a first-order critical point on the transition line, i.e., the critical point is also the locus of level crossings where the derivatives of the free energy are discontinuous. In that sense, the thermal exponent of the Potts model is generically nu=1/2. Things are profoundly different for Q a Beraha number, where the transition is second order, with nu=(t-2)/2 determined by the psi\_1 parafermion. As one enters the adjacant Berker-Kadanoff phase, the model flows, for t odd, to a minimal model of CFT with c=1-6/t(t-1), while for t even it becomes massive. This provides a physical realization of a flow conjectured by Fateev and Zamolodchikov in the context of Z\_N integrable perturbations. Finally, we argue that the antiferromagnetic transition occurs as well on other two-dimensional lattices

On the universality of compact polymers

Fully packed loop models on the square and the honeycomb lattice constitute new classes of critical behaviour, distinct from those of the low-temperature O(n) model. A simple symmetry argument suggests that such compact phases are only possible when the underlying lattice is bipartite. Motivated by the hope of identifying further compact universality classes we therefore study the fully packed loop model on the square-octagon lattice. Surprisingly, this model is only critical for loop weights n < 1.88, and its scaling limit coincides with the dense phase of the O(n) model. For n=2 it is exactly equivalent to the selfdual 9-state Potts model. These analytical predictions are confirmed by numerical transfer matrix results. Our conclusions extend to a large class of bipartite decorated lattices.Comment: 13 pages including 4 figure

Role of conformational entropy in force-induced bio-polymer unfolding

A statistical mechanical description of flexible and semi-flexible polymer chains in a poor solvent is developed in the constant force and constant distance ensembles. We predict the existence of many intermediate states at low temperatures stabilized by the force. A unified response to pulling and compressing forces has been obtained in the constant distance ensemble. We show the signature of a cross-over length which increases linearly with the chain length. Below this cross-over length, the critical force of unfolding decreases with temperature, while above, it increases with temperature. For stiff chains, we report for the first time "saw-tooth" like behavior in the force-extension curves which has been seen earlier in the case of protein unfolding.Comment: 4 pages, 5 figures, ReVTeX4 style. Accepted in Phys. Rev. Let