Pierre Pujol

Universality class of the Nishimori point in the 2D +/- J random-bond Ising model.

We study the universality class of the Nishimori point in the 2D +/- J random-bond Ising model by means of the numerical transfer-matrix method. Using the domain-wall free energy, we locate the position of the fixed point along the Nishimori line at the critical concentration value p(c) = 0.1094 +/- 0.0002 and estimate nu = 1.33 +/- 0.03. Then, we obtain the exponents for the moments of the spin-spin correlation functions as well as the value for the central charge c = 0.464 +/- 0.004. The main qualitative result is the fact that percolation is now excluded as a candidate for describing the universality class of this fixed point.

From quantum mechanics to classical statistical physics: Generalized Rokhsar–Kivelson Hamiltonians and the “Stochastic Matrix Form” decomposition

Abstract Quantum Hamiltonians that are fine-tuned to their so-called Rokhsar–Kivelson (RK) points, first presented in the context of quantum dimer models, are defined by their representations in preferred bases in which their ground state wave functions are intimately related to the partition functions of combinatorial problems of classical statistical physics. We show that all the known examples of quantum Hamiltonians, when fine-tuned to their RK points, belong to a larger class of real, symmetric, and irreducible matrices that admit what we dub a Stochastic Matrix Form (SMF) decomposition. Matrices that are SMF decomposable are shown to be in one-to-one correspondence with stochastic classical systems described by a Master equation of the matrix type, hence their name. It then follows that the equilibrium partition function of the stochastic classical system partly controls the zero-temperature quantum phase diagram, while the relaxation rates of the stochastic classical system coincide with the excitation spectrum of the quantum problem. Given a generic quantum Hamiltonian construed as an abstract operator defined on some Hilbert space, we prove that there exists a continuous manifold of bases in which the representation of the quantum Hamiltonian is SMF decomposable, i.e., there is a (continuous) manifold of distinct stochastic classical systems related to the same quantum problem. Finally, we illustrate with three examples of Hamiltonians fine-tuned to their RK points, the triangular quantum dimer model, the quantum eight-vertex model, and the quantum three-coloring model on the honeycomb lattice, how they can be understood within our framework, and how this allows for immediate generalizations, e.g., by adding non-trivial interactions to these models.

From classical to quantum Kagomé antiferromagnet in a magnetic field

We study the magnetic properties of the Kagome antiferromagnet going from the classical limit to the deep quantum regime of spin ½ systems. In all the cases there are special values for the magnetization, 1/3 in particular, in which a singular behavior is observed to occur in both the classical and quantum cases. We show clear evidence for a magnetization plateau for all S, in a wide range of XXZ anisotropies and for the occurrence of quantum order by disorder effects.

Magnetic properties of zig-zag ladders

Abstract:We analyze the phase diagram of a system of spin-1/2 Heisenberg antiferromagnetic chains interacting through a zig-zag coupling, also called zig-zag ladders. Using bosonization techniques we study how a spin-gap or more generally plateaux in magnetization curves arise in different situations. While for coupled XXZchains, one has to deal with a recently discovered chiral perturbation, the coupling term which is present for normal ladders is restored by an external magnetic field, dimerization or the presence of charge carriers. We then proceed with a numerical investigation of the phase diagram of two coupled Heisenberg chains in the presence of a magnetic field. Unusual behaviour is found for ferromagnetic coupled antiferromagnetic chains. Finally, for three (and more) legs one can choose different inequivalent types of coupling between the chains. We find that the three-leg ladder can exhibit a spin-gap and/or non-trivial plateaux in the magnetization curve whose appearance strongly depends on the choice of coupling.

Ice: A strongly correlated proton system

We discuss the problem of proton motion in Hydrogen bond materials with special focus on ice. We show that phenomenological models proposed in the past for the study of ice can be recast in terms of microscopic models in close relationship to the ones used to study the physics of Mott-Hubbard insulators. We discuss the physics of the paramagnetic phase of ice at 1/4 filling (neutral ice) and its mapping to a transverse field Ising model and also to a gauge theory in two and three dimensions. We show that H3O+ and HO- ions can be either in a confined or deconfined phase. We obtain the phase diagram of the problem as a function of temperature T and proton hopping energy t and find that there are two phases: an ordered insulating phase which results from an order-by-disorder mechanism induced by quantum fluctuations, and a disordered incoherent metallic phase (or plasma). We also discuss the problem of decoherence in the proton motion introduced by the lattice vibrations (phonons) and its effect on the phase diagram. Finally, we suggest that the transition from ice-Ih to ice-XI observed experimentally in doped ice is the confining-deconfining transition of our phase diagram.

Quantum kagomé antiferromagnet in a magnetic field: Low-lying nonmagnetic excitations versus valence-bond crystal order

We study the ground state properties of a quantum antiferromagnet on the kagome lattice in the presence of a magnetic field, paying particular attention to the stability of the plateau at magnetization

Modern Theories of Many-Particle Systems in Condensed Matter Physics

1∕3

Strong disorder fixed points in the two-dimensional random-bond Ising model

of saturation and the nature of its ground state. We discuss fluctuations around classical ground states and argue that quantum and classical calculations at the harmonic level do not lead to the same result in contrast to the zero-field case. For spin

Random bond XXZ chains with modulated couplings

S=1∕2

High-Temperature Criticality in Strongly Constrained Quantum Systems

we find a magnetic gap below which an exponential number of nonmagnetic excitations are present. Moreover, such non-magnetic excitations also have a (much smaller) gap above the threefold degenerate ground state. We provide evidence that the ground state has long-range order of valence-bond crystal type with nine spins in the unit cell.