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Person# Frédéric Mila

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Courses taught by this person (3)

PHYS-315: Statistical physics I

L'objectif du cours est d'introduire les concepts fondamentaux de la physique statistique.

PHYS-419: Solid state physics III

The aim of this course is to provide an introduction to the theory of a few remarkable phenomena of condensed matter physics ranging from the Quantum Hall effects to superconductivity.

PHYS-726: Introduction to Frustrated Magnetism

To provide an introduction to all aspects of the rapidly evolving field of frustrated magnetism:

- New paradigms: spin liquids, spin ice, topological order, ...
- Basic models and methods
- Experimental realizations

Related research domains (93)

Phase transition

In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is use

Magnetic field

A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a for

Ising model

The Ising model (ˈiːzɪŋ) (or Lenz-Ising model or Ising-Lenz model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical model of ferromagnetism in statistical mechanics. The m

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Natalia Chepiga, Frédéric Mila

We show that including pairing and repulsion into the description of one-dimensional spinless fermions, as in the domain wall theory of commensurate melting or the interacting Kitaev chain, leads, for strong enough repulsion, to a line of critical points in the eight-vertex universality class terminating floating phases with emergent U (1) symmetry. For nearest-neighbor repulsion and pairing, the variation of the critical exponents along the line that can be extracted from Baxter's exact solution of the XYZ chain at J(x) = -J(z) is fully confirmed by extensive density matrix renormalization group (DMRG) simulations of the entire phase diagram, and the qualitative features of the phase diagram are shown to be independent of the precise form of the interactions.

Loïc Jean Pierre Herviou, Frédéric Mila

Motivated by the experimental observation of a quantized 5/2 thermal conductance at filling nu = 5/2, a result incompatible with both the Pfaffian and the anti-Pfaffian states, we have pushed the expansion of the effective Hamiltonian of the 5/2-quantized Hall state to third order in the parameter K = EC/h over bar wc oc 1/./B controlling the Landau-level mixing, where EC is the Coulomb energy and wc is the cyclotron frequency. Exact diagonalizations of this effective Hamiltonian show that the difference in overlap with the Pfaffian state and the anti-Pfaffian state induced at second order is reduced by third-order corrections and disappears around K = 0.4, suggesting that these states are much closer in energy at smaller magnetic field than previously anticipated. Furthermore, we show that in this range of K the finite-size spectrum is typical of a quantum phase transition, with a strong reduction of the energy gap and with level crossings between excited states. These results point to the possibility of a quantum phase transition at smaller magnetic field into a phase with an emergent particle-hole symmetry that would explain the measured 5/2 thermal conductance of the 5/2-quantized Hall state.

Frédéric Mila, Samuel Louis Nyckees

We investigate the classical chiral Ashkin-Teller model on a square lattice with the corner transfer matrix renormalization group algorithm. We show that the melting of the period-4 phase in the presence of a chiral perturbation takes different forms depending on the coefficient of the four-spin term in the Ashkin-Teller model. Close to the clock limit of two decoupled Ising models, the system undergoes a two-step commensurate-incommensurate transition as soon as the chirality is introduced, with an intermediate critical floating phase bounded by a Kosterlitz-Thouless transition at high temperature and a Pokrovsky-Talapov transition at low temperature. By contrast, close to the four-states Potts model, we argue for the existence of a unique commensurate-incommensurate transition that belongs to the chiral universality class, and for the presence of a Lifshitz point where the ordered, disordered, and floating phases meet. Finally, we map the whole phase diagram, which turns out to be in qualitative agreement with the 40-year-old prediction by Huse and Fisher.