Two-sites quantum island in the quasi-ballistic regime

Quantum Hall edge channels can be combined with metallic regions to fractionalize electrons and form correlated impurity models. We study a minimal device, that has been experimentally achieved quite recently, with two floating islands connected to three edge channels via quantum point contacts in the integer quantum Hall regime. At high transparency of the quantum point contacts, we establish a mapping to the boundary sine-Gordon model and thereby reveal the nature of the quantum critical point. We deduce from this mapping universal expressions for the conductance and noise, in agreement with the experimental findings, and discuss the competition between Kondo-like screening of each individual island and the cooperative transfer of electrons between them. We further predict that the device operated at finite voltage bias produces fractional charges $e^* =e/3$ and propose a generalization to $N$ islands with the fractional charge $e^* =e/(N+1)$.Comment: 12 pages, 8 figure

Phase diagram of one-dimensional earth-alkaline cold fermionic atoms

The phase diagram of one-dimensional earth-alkaline fermionic atoms and ytterbium 171 atoms is investigated by means of a low-energy approach and density-matrix renormalization group calculations. For incommensurate filling, four gapless phases with a spin gap are found and consist of two superconducting instabilities and two coexisting bond and charge density-waves instabilities. In the half-filled case, seven Mott-insulating phases arise with the emergence of four non-degenerate phases with exotic hidden orderings.Comment: Proceedings of StatPhys 24 satellite conference in Hanoi, 8 pages, 8 figure

Z3\mathbb{Z}_3 parafermion in the double charge-Kondo model

Quantum impurity models with frustrated Kondo interactions can support quantum critical points with fractionalized excitations. Recent experiments [arXiv:2108.12691] on a circuit containing two coupled metal-semiconductor islands exhibit transport signatures of such a critical point. Here we show using bosonization that the double charge-Kondo model describing the device can be mapped in the Toulouse limit to a sine-Gordon model. Its Bethe-ansatz solution shows that a $\mathbb{Z}_3$ parafermion emerges at the critical point, characterized by a fractional $\tfrac{1}{2}\ln(3)$ residual entropy, and scattering fractional charges $e/3$. We also present full numerical renormalization group calculations for the model and show that the predicted behavior of conductance is consistent with experimental results.Comment: 5 pages+, 3 figure

Effect of Hund coupling in the one-dimensional SU(4) Hubbard model

The one-dimensional SU(4) Hubbard model perturbed by Hund coupling is studied, away from half-filling, by means of renormalization group and bosonization methods. A spectral gap is always present in the spin-orbital sector irrespective of the magnitude of the Coulomb repulsion. We further distinguish between two qualitatively different regimes. At small Hund coupling, we find that the symmetry of the system is dynamically enlarged to SU(4) at low energy with the result of {\it coherent} spin-orbital excitations. When the charge sector is not gapped, a superconducting instability is shown to exist. At large Hund coupling, the symmetry is no longer enlarged to SU(4) and the excitations in the spin sector become {\it incoherent}. Furthermore, the superconductivity can be suppressed in favor of the conventional charge density wave state.Comment: 10 pages, 1 figur

The one-dimensional SU(4) Hubbard model : an approach to orbital degeneracy

This thesis is dedicated to the study of orbital degeneracy in one-dimensional strongly correlated electron systems. A simple model is defined which maximally accounts for orbital degeneracy: the SU(4)-symmetric Hubbard model. The zero temperature phase diagram is obtained using analytical methods (bosonization, conformal field theory, renormalization group). Our theoretical predictions are compared to quantum Monte Carlo simulations. In the critical phases, the conformal field theory describing the universality class of the model is identified. In the massive phases, we derive the low energy effective theory, which turns out to be quasi-integrable. This allows for a description of the low lying collective modes. The phase diagram of the model is surprisingly rich, in spite of its simplicity. An interesting feature is the existence of a Mott insulator with no magnetic order at half filling. In the second part of the thesis, realistic physical processes which break the SU(4) symmetry are taken into account. The stability of the phases of the SU(4) Hubbard model under these perturbations is studied. The generic tendency is the appearance of a gaped spin liquid. Exact (non perturbative) discrete symmetries of the phase diagram are revealed. These symmetries connect different spin liquids and allow for a classification of the gaped spin liquid phases for a two-leg spin ladder in the vicinity of the SU(4) symmetric line. Two broad classes of gaped spin liquids are found, one associated with diagonal (charge density wave-like) order, the other supporting a superconducting instability.Cette thèse est consacrée à l'étude de la dégénérescence orbitale dans les systèmes d'électrons fortement corrélés à une dimension. Nous définissons un modèle simplifié, le modèle de Hubbard à symétrie SU(4), qui prend en compte de manière maximale la dégénérescence orbitale. Le diagramme des phases à température nulle est obtenu par des méthodes analytiques (bosonisation, théorie conforme, groupe de renormalisation). Les prédictions théoriques sont confrontées à des simulations numériques par Monte Carlo quantique. Dans les phases critiques, la théorie conforme décrivant la classe d'universalité du modèle est identifiée. Dans les phases massives, nous dérivons la théorie effective, qui s'avère être quasi-intégrable, permettant une description des modes collectifs de basse énergie. Le diagramme des phases obtenu est d'une grande richesse en regard de la simplicité du modèle, une particularité intéressante étant la présence d'une phase de liquide de spin gapé isolante de Mott au voisinage du demi remplissage. Dans la deuxième partie de cette thèse, nous incluons des processus réalistes qui brisent la symétrie SU(4), et étudions la stabilité des phases du modèle de Hubbard SU(4) sous ces perturbations. La tendance générique est à l'apparition d'un liquide de spin gapé. Nous mettons en évidence des symétries discrètes exactes (non perturbatives) du diagramme des phases, qui relient entre elles différentes phases de liquide de spin. Ces symétries autorisent une classification des liquides de spin portés par l'échelle de spin à deux montants au voisinage de la ligne à symétrie SU(4). Deux grandes classes de liquide de spin apparaissent, l'une associée à un ordre diagonal, de type onde de densité de charge, l'autre exhibant une instabilité supraconductrice

Full exact solution of the out-of-equilibrium boundary sine Gordon model

The massless boundary sine-Gordon (SG) model is the only interacting impurity model with a known exact solution out-of-equilibrium, yet existing so far only for integer values of the sine Gordon coupling $\lambda$ [Phys. Rev. Lett. {\bf74}, 3005 (1995)]. We present here a full exact solution for arbitrary rational values of $\lambda$, at arbitrary voltage $V$ and temperature $T$. We use the "string" solutions of the bulk SG model, here regarded as genuine quasiparticles avoiding charge diffusion in momentum space. We carefully present the finite voltage and temperature thermodynamics of this gas of interacting exotic quasiparticles, whose very nature depends on subtle arithmetic properties of the rational SG parameter $\lambda$, and explicitly check that the string representation is thermodynamically complete. By considering a Loschmidt echo, we derive the exact transmission probability of strings on the impurity. We obtain the exact universal scaling function for the electrical current $I(V,T)$. Our results are in excellent agreement with recent experimental out-of-equilibrium data and question the reality of these exotic quasiparticles

Le modèle de Hubbard SU(4) à une dimension (une approche de la dégénérescence orbitale)

PARIS-BIUSJ-Thèses (751052125) / SudocPARIS-BIUSJ-Physique recherche (751052113) / SudocSudocFranceF

Universality at work – the local sine-Gordon model, lattice fermions, and quantum circuits

We review the intriguing many-body physics resulting out of the interplay of a single, local impurity and the two-particle interaction in a one-dimensional Fermi system. Even if the underlying homogeneous correlated system is taken to be metallic, this interplay leads to an emergent quantum phase transition between metallic and insulating states. We show that the zero temperature critical point and the universal low-energy physics associated to it, is realized in two different models, the field theoretical local sine-Gordon model and spinless fermions on a lattice with nearest-neighbor hopping and two-particle interaction, as well as in an experimental setup consisting of a highly tunable quantum circuit. Despite the different high-energy physics of the three systems the universal low-energy scaling curves of the conductance as a function of temperature agree up to a very high precision without any free parameter. Overall this provides a convincing example of how emergent universality in complex systems originating from a common underlying quantum critical point establishes a bridge between different fields of physics. In our case between field theory, quantum many-body theory of correlated Fermi systems, and experimental circuit quantum electrodynamics