## LABORATOIRE DE PHYSIQUE THEORIQUE DE LA MATIERE CONDENSEE

### Attention : désormais les séminaires ont lieu tous les lundis à 10h45 en salle  523 du LPTMC - Tour 12-13

Fabien Paillusson

Enseignant-chercheur à l'université de Lincoln en Angleterre

"N!, indistinguishability and entropy: the instructive case of polydisperse systems"

The so-called Gibbs paradox is a paradigmatic narrative illustrating the necessity to account for the N! ways of permuting N identical particles when summing over microstates. Yet, there exist some mixing scenarios for which the expected thermodynamic outcome depends on the interpretation of this combinatorial term one chooses and this is what we wish to investigate in this talk.

In the first part of the talk we will briefly introduce what the Gibbs paradox is about and what is the standard rationale used to justify its resolution. In a second part, we will allow ourself to question from a historical standpoint whether the Gibbs paradox has actually anything to do with Gibbs' work. In so doing, we also aim at shedding a new light with regards to some of the theoretical claims surrounding its resolution. In a third part we will then turn to the statistical thermodynamics of discrete and continuous mixtures and introduce the notion of composition entropy to characterise these systems. This will enable us to address, in a certain sense, a "curiosity" pointed out by Gibbs in a paper published in 1876. Finally, we will finish by proposing a connexion between the results we propose and a recent extension of the Landauer bound regarding the minimum amount of heat to be dissipated to reset one bit of memory.

Le séminaire aura lieu à la bibliothèque du LPTHE et non au LPTMC- Tour 13 4ème étage

Oleg Starykh (University of Utah)

Emergent Ising orders of frustrated magnets

Much of the research in frustrated quantum magnets has focused on the elusive quest for magnetically disordered phases with highly entangled ground states - quantum spin liquids. Somewhat intermediate between these rare states and commonplace magnets are {\em nematic} phases which appear as a result of a two-magnon condensation and are characterized by the presence of a gap for excitations with spin one. As a result, nematic states exhibit no dipolar magnetic order.

In my talk I describe two simple models supporting spin nematic phases. The first of them is provided by the two-magnon instability of the 1/3 magnetization plateau state of the quantum triangular antiferromagnet. I show that the two-magnon instability, which takes place near the end-point of the magnetization plateau, leads to a novel two-dimensional vector chiral phase with alternating spin currents. This interesting state spontaneously breaks inversion symmetry and can be thought of as appearing due to a fluctuation-generated Dzyaloshinskii-Moriya interaction. The second example involves an easy-axis spin-1 antiferromagnet in which transition into nematic state occurs via condensation of spin excitons.

ESSAI

Prof Dr Irene D'Amico FInstP

Information Centre, Market Square
Department of Physics,
University of York,

 "DFT-inspired Methods for Quantum Thermodynamics"

To understand how the increase of disorder in the macroscopic world follows from microscopic order we need to determine the so-called work distribution (which is related to the entropy production) for quantum systems performing suitable cyclic dynamics. This is a crucially difficult task, particularly so when interacting many-particle (or many-spin) systems are considered. Here [1] we study the quantum fluctuations of a many-body system by proposing a new method inspired by density functional theory (DFT). Through this method, we can estimate the transition matrix elements due to the system time-dependent dynamics and obtain an approximation to the work distribution and average work of the driven quantum many-body system. We apply this DFT-inspired approach to obtain the work distribution function of a driven Hubbard dimer using an approximation based on Kohn-Sham states. This model can represent different quantum system, including excitations in coupled quantum dots driven by laser pulses. We compare this new method with the exact result and show under which conditions this approximation is effective.

 [1] "DFT-inspired Methods for Quantum Thermodynamics", M. Herrera, R. M. Serra, and I. D'Amico, submitted (2017) "arXiv:1703.02460"

Satya Majumdar

LPTMS, Orsay

We study a simple model of search where the searcher undergoes normal diffusion, but once in a while resets to its initial starting point stochastically with rate $r$. The effect of a finite resetting rate r turns out to be rather drastic. First, the position of the walker approaches a nonequilibrium stationary state at long times. The approach to the stationary state is accompanied by an interesting `dynamical' phase transition. For searching an immobile target, resetting leads to finite mean search time which, as a function of r, has a minimum at an optimal resetting rate $r^*$. This makes the search process efficient. We then consider various generalizations of this simple resetting model: to Levy flights, to multiple walkers and also to spatially extended system such as fluctuating interfaces.

Benjamin Canals (Institut Néel, Grenoble)

Artificial magnets as model systems : from the fragmentation of magnetization to the square ice model

Complex architectures of nanostructures are routinely elaborated using bottom-up or nanofabrication processes. This technological capability allows scientists to engineer materials with properties that do not exist in nature, but also to manufacture model systems to explore fundamental issues which appeared in condensed matter physics. One- and two-dimensional frustrated arrays of magnetic nanostructures are one class of systems for which theoretical predictions can now be tested and challenged experimentally. These systems have been the subject of intense research in the last few years and have allowed the investigation of a rich physics and fascinating phenomena, such as the exploration of the extensively degenerate ground-state manifolds of spin ice systems, the evidence of new magnetic phases in purely two-dimensional lattices, and the observation of pseudo-excitations involving classical analogues of magnetic charges. This talk aims at providing two examples of two-dimensional artificial magnets which allow to probe the low energy manifolds of two exotic Ising systems.

The first one is related to the seminal 6-vertex model and shows that it is possible to perform a scan through the 6-vertex model phase diagram with an appropriately designed artificial magnet [1]. In particular, the symmetric point of the (Lieb) square ice is recovered, providing with the opportunity to study the signatures of an algebraic Coulomb spin liquid. Because of the experimental procedure used to reach the low energy manifold, quasi-particles are trapped in this disordered manifold, pointing to the need of thermal systems, but also emphasizing that these systems may be well suited to study out of equilibrium relaxation of monopole-(anti)monopole pairs in a near future.

The second one refers to a recent proposal, the fragmentation of magnetisation [2], in an Ising Kagomé model. Here, we show it is possible to observe this intriguing phenomena, which corresponds to the splitting of the local degree of freedom into two channels, one ordering at low effective temperatures, in an AF all-in all-out ordering despite the ferromagnetic nature of the system, the other, building a Coulomb-like low energy manifold, inside which the magnetic equivalent of the Kirchhoff law at each node of the Kagomé lattice is fulfilled [3].

[1] Y. Perrin, B. Canals, N. Rougemaille, Nature 540, 410–413 (2016).
[2] M. E. Brooks-Bartlett, S. T. Banks, L. D. C. Jaubert, A. Harman-Clarke, and P. C. W. Holdsworth, Phys. Rev. X, 4, 011007 (2014).
[3] B. Canals, I. A. Chioar, V.-D. Nguyen, M. Hehn, D. Lacour, F. Montaigne, A. Locatelli, T. O. Mentes, B. S. Burgos and N. Rougemaille, Nat. Comm. 7, 11446 (2016).