Critical Casimir Force between Inhomogeneous Boundaries

To study the critical Casimir force between chemically structured boundaries immersed in a binary mixture at its demixing transition, we consider a strip of Ising spins subject to alternating fixed spin boundary conditions. The system exhibits a boundary induced phase transition as function of the relative amount of up and down boundary spins. This transition is associated with a sign change of the asymptotic force and a diverging correlation length that sets the scale for the crossover between different universal force amplitudes. Using conformal field theory and a mapping to Majorana fermions, we obtain the universal scaling function of this crossover, and the force at short distances.Comment: 5 pages, 3 figure

Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain

In a many-body quantum system, local operators in Heisenberg picture $O(t) = e^{i H t} O e^{-i H t}$ spread as time increases. Recent studies have attempted to find features of that spreading which could distinguish between chaotic and integrable dynamics. The operator entanglement - the entanglement entropy in operator space - is a natural candidate to provide such a distinction. Indeed, while it is believed that the operator entanglement grows linearly with time $t$ in chaotic systems, numerics suggests that it grows only logarithmically in integrable systems. That logarithmic growth has already been established for non-interacting fermions, however progress on interacting integrable systems has proved very difficult. Here, for the first time, a logarithmic upper bound is established rigorously for all local operators in such a system: the `Rule 54' qubit chain, a model of cellular automaton introduced in the 1990s [Bobenko et al., CMP 158, 127 (1993)], recently advertised as the simplest representative of interacting integrable systems. Physically, the logarithmic bound originates from the fact that the dynamics of the models is mapped onto the one of stable quasiparticles that scatter elastically; the possibility of generalizing this scenario to other interacting integrable systems is briefly discussed.Comment: 4+16 pages, 2+6 figures. Substantial rewriting of the presentation. As published in PR

Bulk and boundary critical behaviour of thin and thick domain walls in the two-dimensional Potts model

The geometrical critical behaviour of the two-dimensional Q-state Potts model is usually studied in terms of the Fortuin-Kasteleyn (FK) clusters, or their surrounding loops. In this paper we study a quite different geometrical object: the spin clusters, defined as connected domains where the spin takes a constant value. Unlike the usual loops, the domain walls separating different spin clusters can cross and branch. Moreover, they come in two versions, "thin" or "thick", depending on whether they separate spin clusters of different or identical colours. For these reasons their critical behaviour is different from, and richer than, those of FK clusters. We develop a transfer matrix technique enabling the formulation and numerical study of spin clusters even when Q is not an integer. We further identify geometrically the crossing events which give rise to conformal correlation functions. We study the critical behaviour both in the bulk, and at a boundary with free, fixed, or mixed boundary conditions. This leads to infinite series of fundamental critical exponents, h_{l_1-l_2,2 l_1} in the bulk and h_{1+2(l_1-l_2),1+4 l_1} at the boundary, valid for 0 <= Q <= 4, that describe the insertion of l_1 thin and l_2 thick domain walls. We argue that these exponents imply that the domain walls are `thin' and `thick' also in the continuum limit. A special case of the bulk exponents is derived analytically from a massless scattering approach.Comment: 18 pages, 5 figures, 2 tables. Work based on the invited talk given by Jesper L. Jacobsen at STATPHYS-24 in Cairns, Australia (July 2010). Extended version of arXiv:1008.121

Generalized HydroDynamics on an Atom Chip

The emergence of a special type of fluid-like behavior at large scales in one-dimensional (1d) quantum integrable systems, theoretically predicted in 2016, is established experimentally, by monitoring the time evolution of the in situ density profile of a single 1d cloud of $^{87}{\rm Rb}$ atoms trapped on an atom chip after a quench of the longitudinal trapping potential. The theory can be viewed as a dynamical extension of the thermodynamics of Yang and Yang, and applies to the whole range of repulsion strength and temperature of the gas. The measurements, performed on weakly interacting atomic clouds that lie at the crossover between the quasicondensate and the ideal Bose gas regimes, are in very good agreement with the 2016 theory. This contrasts with the previously existing 'conventional' hydrodynamic approach---that relies on the assumption of local thermal equilibrium---, which is unable to reproduce the experimental data.Comment: v1: 6+11 pages, 4+4 figures. v2: published version, 6+11 pages, 4+6 figure

Conformal boundary conditions in the critical O(n) model and dilute loop models

We study the conformal boundary conditions of the dilute O(n) model in two dimensions. A pair of mutually dual solutions to the boundary Yang-Baxter equations are found. They describe anisotropic special transitions, and can be interpreted in terms of symmetry breaking interactions in the O(n) model. We identify the corresponding boundary condition changing operators, Virasoro characters, and conformally invariant partition functions. We compute the entropies of the conformal boundary states, and organize the flows between the various boundary critical points in a consistent phase diagram. The operators responsible for the various flows are identified. Finally, we discuss the relation to open boundary conditions in the O(n) model, and present new crossing probabilities for Ising domain walls.Comment: 49 pages, 21 figure

Emergence of curved light-cones in a class of inhomogeneous Luttinger liquids

The light-cone spreading of entanglement and correlation is a fundamental and ubiquitous feature of homogeneous extended quantum systems. Here we point out that a class of inhomogenous Luttinger liquids (those with a uniform Luttinger parameter K) at low energy display the universal phenomenon of curved light cones: gapless excitations propagate along the null geodesics of the metric ds(2) = d x(2) - v (x)(2)d t(2), with v (x) being the calculable spatial dependent velocity induced by the inhomogeneity. We confirm our findings with explicit analytic and numerical calculations both in-and out-of-equilibrium for a Tonks-Girardeau gas in a harmonic potential and in lattice systems with artificially tuned hamiltonian density

Conformal field theory for inhomogeneous one-dimensional quantum systems: the example of non-interacting Fermi gases

Conformal field theory (CFT) has been extremely successful in describing large-scale universal effects in one-dimensional (1D) systems at quantum critical points. Unfortunately, its applicability in condensed matter physics has been limited to situations in which the bulk is uniform because CFT describes low-energy excitations around some energy scale, taken to be constant throughout the system. However, in many experimental contexts, such as quantum gases in trapping potentials and in several out-of-equilibrium situations, systems are strongly inhomogeneous. We show here that the powerful CFT methods can be extended to deal with such 1D situations, providing a few concrete examples for non-interacting Fermi gases. The system's inhomogeneity enters the field theory action through parameters that vary with position; in particular, the metric itself varies, resulting in a CFT in curved space. This approach allows us to derive exact formulas for entanglement entropies which were not known by other means

DESCRIPTIONS A GRANDE ECHELLE DU GAZ DE BOSE 1D & CERTAINS AUTRES PROBLEMES EN PHYSIQUE QUANTIQUE EN BASSE DIMENSION

Considerable progress has taken place in recent years in modeling the large-scale dynam- ics of one-dimensional quantum many-body systems that are integrable or nearly inte- grable, thanks to the advent of Generalized Hydrodynamics. In particular, Generalized Hydrodynamics provides a computationally efficient tool for simulating experiments on one-dimensional Bose gases. In this habilitation thesis I review the main results I ob- tained with my co-authors, both on theory developments and on the application to cold atom experiments. I also discuss our recent attempts at describing the effects of quantum fluctuations of out-of-equilibrium quantum gases within that framework.I also present a few results on other topics in low-dimensional quantum many-body physics. These include basic results on ‘operator entanglement’, an indicator of the complexity of quantum operators and of their approximability by Matrix Product Operators in one- dimensional quantum systems, as well as results on two-dimensional chiral topological phases (e.g. quantum Hall states, Chern bands, or p+ip superfluids) from the point of view of their entanglement properties.Des progrès considérables ont eu lieu ces dernières années concernant la modélisation de la dynamique à grande échelle des systèmes quantiques à N corps en une dimension, quand ceux-ci sont intégrables ou presque intégrables, grâce au développement de l'hydrodynamique généralisée. En particulier, la théorie de l’hydrodynamique généralisée fournit un outil efficace pour la modélisation des expériences sur les gaz de Bose quantiques unidimensionnels. Dans cette thése d’habilitation je décris les principaux résultats que j’ai obtenus avec mes co-auteurs, à la fois sur les développements de la théorie et sur son application aux expériences d’atomes froids. Je discute également nos tentatives récentes d’incorporer les effets des fluctuations quantiques dans les gaz quantiques hors équilibre dans ce cadre théorique.Je présente également quelques résultats sur d’autres sujets en physique quantique à N corps en basse dimension. Ceux-ci incluent quelques résultats fondamentaux sur l’ "intrication d’opérateurs", un indicateur de la complexité des opérateurs quantiques et de leur approximabilité par des “Matrix Product Operators” dans les systèmes quantiques en une dimension, ainsi que des résultats sur les phases topologiques chirales en deux dimensions (par exemple les états d’effet Hall, les isolants de Chern ou les superfluides p+ip) du point de vue de leurs propriétés d’intrication

Conditions aux bords dans des theories conformes non unitaires

Our understanding of surface critical phenomena has made the same progress as its bulk counterpart. In particular, in two dimensions, conformally invariant field theories are now extremely powerful tools which are used to describe phase transitions in a non-perturbative way. In this context, the study of surface critical phenomena has produced numerous new exact results, such as boundary critical exponents or correlation functions in several critical models. In this thesis, we are interested in some statistical field theories in two dimensions, with non-local degrees of freedom. For example, polymers in a good solvant are described by such theories. One can try to turn these theories into local ones, but the price to pay is that we get negative or even complex Boltzmann weights: these theories are then non-unitary. We are interested in surface effects, and in finding out which boundary conditions are compatible with conformal invariance in these theories. Our strategy does not involve an axiomatic approach, but rather relies on concrete lattice models which have an interesting scaling limit.La physique des phénomènes de surface a progressé en même temps que les modèles décrivant des transitions de phase dans le volume. A deux dimensions, en particulier, les théories des champs invariantes sous les transformations conformes se sont révélées des outils extrêmement puissants pour décrire de manière non-perturbative les transitions de phase. L'étude des phénomènes de surface dans ce contexte a produit de nombreux résultats exacts tels que des exposants critiques et des fonctions de corrélations dans divers modèles critiques. Dans cette thèse nous nous intéressons à des théories statistiques à deux dimensions dont les degrés de liberté sont non locaux, comme par exemple des polymères en solution. Ces théories peuvent être formulées localement au prix de poids de Boltzmann négatifs ou complexes, elles sont alors non-unitaires. Nous nous intéressons aux effets de surface dans ces théories, et décrivons les différentes conditions au bord qui sont compatibles avec l'invariance conforme. Notre stratégie n'est pas de formuler une approche axiomatique, mais plutôt de partir de modèles concrets sur réseau, et d'étudier leur limite continue

Generalized hydrodynamics in the one-dimensional Bose gas: theory and experiments

International audienceWe review the recent theoretical and experimental progress regarding the generalized hydrodynamics (GHD) behavior of the one-dimensional (1D) Bose gas with contact repulsive interactions, also known as the Lieb–Liniger gas. In the first section, we review the theory of the Lieb–Liniger gas, introducing the key notions of the rapidities and of the rapidity distribution. The latter characterizes the Lieb–Liniger gas after relaxation and is at the heart of GHD. We also present the asymptotic regimes of the Lieb–Liniger gas with their dedicated approximate descriptions. In the second section we enter the core of the subject and review the theoretical results of GHD in 1D Bose gases. The third and fourth sections are dedicated to experimental results obtained in cold atom experiments: the experimental realization of the Lieb–Liniger model is presented in section 3, with a selection of key results for systems at equilibrium, and section 4 presents the experimental tests of the GHD theory. In section 5 we review the effects of atom losses, which, assuming slow loss processes, can be described within the GHD framework. We conclude with a few open questions