arXiv subjects

B. Doucot

Publications and source records attributed to B. Doucot.

At least 19 recordsLinked to original sources

arXiv2018

Josephson Ladders as a Model System for 1D Quantum Phase Transitions

We propose a novel platform for the study of quantum phase transitions in one dimension (1D QPT). The system consists of a specially designed chain of asymmetric SQUIDs; each SQUID contains several Josephson junctions with one junction shared between the nearest-neighbor SQUIDs.We develop the theoretical description of the low energy part of the spectrum. In particular, we show that the system exhibits the quantum phase transition of Ising type. In the vicinity of the transition the low energy excitations of the system can be described by Majorana fermions. This allow us to compute the matrix elements of the physical perturbations in the low energy sector. In the microwave experiments with this system, we explored the phase boundaries between the ordered and disordered phases and the critical behavior of the system's low-energy modes close to the transition. Due to the flexible chain design and control of the parameters of individual Josephson junctions, future experiments will be able to address the effects of non-integrability and disorder on the 1D QPT.

cond-mat.str-el↗

arXiv2016

Large and exact quantum degeneracy in a Skyrmion magnet

We identify a large family of ground states of a topological Skyrmion magnet whose classical degeneracy persists to all orders in a semiclassical expansion. This goes along with an exceptional robustness of the concomitant ground state configurations, which are not at all dressed by quantum fluctuations. We trace these twin observations back to a common root: this class of topological ground states saturates a Bogomolny inequality. A similar phenomenology occurs in high-energy physics for some field theories exhibiting supersymmetry. We propose quantum Hall ferromagnets, where these Skyrmions configurations arise naturally as ground states away from integer filling, as the best available laboratory realisations.

cond-mat.str-el↗

arXiv2011

Classical Bethe Ansatz and Normal Forms in the Jaynes-Cummings Model

The Jaynes-Cummings-Gaudin model describes a collection of $n$ spins coupled to an harmonic oscillator. It is known to be integrable, so one can define a moment map which associates to each point in phase-space the list of values of the $n+1$ conserved Hamiltonians. We identify all the critical points of this map and we compute the corresponding quadratic normal forms, using the Lax matrix representation of the model. The normal coordinates are constructed by a procedure which appears as a classical version of the Bethe Ansatz used to solve the quantum model. We show that only elliptic or focus-focus singularities are present in this model, which provides an interesting example of a symplectic toric action with singularities. To explore these, we study in detail the degeneracies of the spectral curves for the $n=1$ and $n=2$ cases. This gives a complete picture for the image of the momentum map (IMM) and the associated bifurcation diagram. For $n=2$ we found in particular some lines of rank 1 which lie, for one part, on the boundary of the IMM, where they behave like an edge separating two faces, and which go, for another part, inside the IMM.

cond-mat.stat-mech↗

arXiv2009

A semiclassical study of the Jaynes-Cummings model

We consider the Jaynes-Cummings model of a single quantum spin $s$ coupled to a harmonic oscillator in a parameter regime where the underlying classical dynamics exhibits an unstable equilibrium point. This state of the model is relevant to the physics of cold atom systems, in non-equilibrium situations obtained by fast sweeping through a Feshbach resonance. We show that in this integrable system with two degrees of freedom, for any initial condition close to the unstable point, the classical dynamics is controlled by a singularity of the focus-focus type. In particular, it displays the expected monodromy, which forbids the existence of global action-angle coordinates. Explicit calculations of the joint spectrum of conserved quantities reveal the monodromy at the quantum level, as a dislocation in the lattice of eigenvalues. We perform a detailed semi-classical analysis of the associated eigenstates. Whereas most of the levels are well described by the usual Bohr-Sommerfeld quantization rules, properly adapted to polar coordinates, we show how these rules are modified in the vicinity of the critical level. The spectral decomposition of the classically unstable state is computed, and is found to be dominated by the critical WKB states. This provides a useful tool to analyze the quantum dynamics starting from this particular state, which exhibits an aperiodic sequence of solitonic pulses with a rather well defined characteristic frequency.

cond-mat.stat-mech↗

arXiv2008

Entanglement Skyrmions in multicomponent quantum Hall systems

We discuss charged topological spin textures in quantum Hall ferromagnets in which the electrons carry a pseudospin as well as the usual spin degree of freedom, as is the case in bilayer GaAs or monolayer graphene samples. We develop a theory which treats spin and pseudospin on a manifestly equal footing, which may also be of help in visualizing the relevant spin textures. We in particular consider the entanglement of spin and pseudospin in the presence of realistic anisotropies. An entanglement operator is introduced which generates families of degenerate Skyrmions with differing entanglement properties. We propose a local characterization of the latter, and touch on the role entangled Skyrmions play in the nuclear relaxation time of quantum Hall ferromagnets.

cond-mat.mes-hall↗

arXiv2006

Electron interactions in graphene in a strong magnetic field

Graphene in the quantum Hall regime exhibits a multi-component structure due to the electronic spin and chirality degrees of freedom. While the applied field breaks the spin symmetry explicitly, we show that the fate of the chirality SU(2) symmetry is more involved: the leading symmetry-breaking terms differ in origin when the Hamiltonian is projected onto the central (n=0) rather than any of the other Landau levels. Our description at the lattice level leads to a Harper equation; in its continuum limit, the ratio of lattice constant a and magnetic length l_B assumes the role of a small control parameter in different guises. The leading symmetry-breaking terms are direct (n=0) and exchange (n different from 0) terms, which are algebraically small in a/l_B. We comment on the Haldane pseudopotentials for graphene, and evaluate the easy-plane anisotropy of the graphene ferromagnet.

cond-mat.mes-hall↗

arXiv2006

Quasiparticle spectrum of the cuprate BiSrCaCuO: Possible connection to the phase diagram

We previously introduced [T. Cren et al., Europhys. Lett. 52, 203 (2000)] an energy-dependant gap function, $Δ(E)$, that fits the unusual shape of the quasiparticle (QP) spectrum for both BiSrCaCuO and YBaCuO. A simple anti-resonance in $Δ(E)$ accounts for the pronounced QP peaks in the density of states, at an energy $Δ_p$, and the dip feature at a higher energy, $E_{dip}$. Here we go a step further : our gap function is consistent with the ($T, p$) phase diagram, where $p$ is the carrier density. For large QP energies ($E >> Δ_p$), the total spectral gap is $Δ(E) \simeq Δ_p + Δ_ϕ$, where $Δ_ϕ$ is tied to the condensation energy. From the available data, a simple $p$-dependance of $Δ_p$ and $Δ_ϕ$ is found, in particular $Δ_ϕ(p) \simeq 2.3 k_B T_c(p)$. These two distinct energy scales of the superconducting state are interpreted by comparing with the normal and pseudogap states. The various forms of the QP density of states, as well as the spectral function $A(k,E)$, are discussed.

cond-mat.supr-con↗

arXiv2005

Quantum wire networks with local Z2 symmetry

For a large class of networks made of connected loops, in the presence of an external magnetic field of half flux quantum per loop, we show the existence of a large local symmetry group, generated by simultaneous flips of the electronic current in all the loops adjacent to a given node. Using an ultra-localized single particle basis adapted to this local Z_2 symmetry, we show that it is preserved by a large class of interaction potentials. As a main physical consequence, the only allowed tunneling processes in such networks are induced by electron-electron interactions and involve a simultaneous hop of two electrons. Using a mean-field picture and then a more systematic renormalization-group treatment, we show that these pair hopping processes do not generate a superconducting instability, but they destroy the Luttinger liquid behavior in the links, giving rise at low energy to a strongly correlated spin-density-wave state.

cond-mat.str-el↗

arXiv2005

Non-Abelian Chern-Simons models with discrete gauge groups on a lattice

We construct the local Hamiltonian description of the Chern-Simons theory with discrete non-Abelian gauge group on a lattice. We show that the theory is fully determined by the phase factors associated with gauge transformations and classify all possible non-equivalent phase factors. We also construct the gauge invariant electric field operators that move fluxons around and create/anihilate them. We compute the resulting braiding properties of the fluxons. We apply our general results to the simplest class of non-Abelian groups, dihedral groups D_n.

cond-mat.supr-con↗

arXiv2005

Exact solution of Z_2 Chern-Simons model on a triangular lattice

We construct the Hamiltonian description of the Chern-Simons theory with Z_n gauge group on a triangular lattice. We show that the Z_2 model can be mapped onto free Majorana fermions and compute the excitation spectrum. In the bulk the spectrum turns out to be gapless but acquires a gap if a magnetic term is added to the Hamiltonian. On a lattice edge one gets additional non-gauge invariant (matter) gapless degrees of freedom whose number grows linearly with the edge length. Therefore, a small hole in the lattice plays the role of a charged particle characterized by a non-trivial projective representation of the gauge group, while a long edge provides a decoherence mechanism for the fluxes. We discuss briefly the implications for the implementations of protected qubits.

cond-mat.stat-mech↗

arXiv2004

Structure of the superconducting state in a fully frustrated wire network with dice lattice geometry

The superconducting state in a fully frustrated wire network with the dice lattice geometry is investigated in the vicinity of the transition temperature. Using Abrikosov's variational procedure, we write the Ginzburg-Landau free energy functional projected on its unstable supspace as an effective model on the triangular lattice of sixfold coordinated sites. For this latter model, we obtain a large class of degenerate equilibrium configurations in one to one correspondence with those previously constructed for the pure XY model on the maximally frustrated dice lattice. The entropy of these states is proportional to the linear size of the system. Finally we show that magnetic interactions between currents provide a degeneracy lifting mechanism.

cond-mat.supr-con↗

arXiv2004

Regular networks of Luttinger liquids

We consider arrays of Luttinger liquids, where each node is described by a unitary scattering matrix. In the limit of small electron-electron interaction, we study the evolution of these scattering matrices as the high-energy single particle states are gradually integrated out. Interestingly, we obtain the same renormalization group equations as those derived by Lal, Rao, and Sen, for a system composed of a single node coupled to several semi-infinite 1D wires. The main difference between the single node geometry and a regular lattice is that in the latter case, the single particle spectrum is organized into periodic energy bands, so that the renormalization procedure has to stop when the last totally occupied band has been eliminated. We therefore predict a strongly renormalized Luttinger liquid behavior for generic filling factors, which should exhibit power-law suppression of the conductivity at low temperatures E_{F}/(k_{F}a) << k_{B}T << E_{F}, where a is the lattice spacing and k_{F}a >> 1. Some fully insulating ground-states are expected only for a discrete set of integer filling factors for the electronic system. A detailed discussion of the scattering matrix flow and its implication for the low energy band structure is given on the example of a square lattice.

cond-mat.mes-hall↗

arXiv2004

Discrete non-Abelian gauge theories in two-dimensional lattices and their realizations in Josephson-junction arrays

We discuss real-space lattice models equivalent to gauge theories with a discrete non-Abelian gauge group. We construct the Hamiltonian formalism which is appropriate for their solid-state physics implementation and outline their basic properties. The unusual physics of these systems is due to local constraints on the degrees of freedom which are variables localized on the links of the lattice. We discuss two types of constraints that become equivalent after a duality transformation for Abelian theories but are qualitatively different for non-Abelian ones. We emphasize highly nontrivial topological properties of the excitations (fluxons and charges) in these non-Abelian discrete lattice gauge theories. We show that an implementation of these models may provide one with the realization of an ideal quantum computer, that is the computer that is protected from the noise and allows a full set of precise manipulations required for quantum computations. We suggest a few designs of the Josephson-junction arrays that provide the experimental implementations of these models and discuss the physical restrictions on the parameters of their junctions.

cond-mat.str-el↗

arXiv2004

Protected Qubits and Chern Simons theories in Josephson Junction Arrays

We present general symmetry arguments that show the appearance of doubly denerate states protected from external perturbations in a wide class of Hamiltonians. We construct the simplest spin Hamiltonian belonging to this class and study its properties both analytically and numerically. We find that this model generally has a number of low energy modes which might destroy the protection in the thermodynamic limit. These modes are qualitatively different from the usual gapless excitations as their number scales as the linear size (instead of volume) of the system. We show that the Hamiltonians with this symmetry can be physically implemented in Josephson junction arrays and that in these arrays one can eliminate the low energy modes with a proper boundary condition. We argue that these arrays provide fault tolerant quantum bits. Further we show that the simplest spin model with this symmetry can be mapped to a very special Z_2 Chern-Simons model on the square lattice. We argue that appearance of the low energy modes and the protected degeneracy is a natural property of lattice Chern-Simons theories. Finally, we discuss a general formalism for the construction of discrete Chern-Simons theories on a lattice.

cond-mat.supr-con↗

arXiv2004

Fluctuations and vortex pattern ordering in fully frustrated XY model with honeycomb lattice

The accidental degeneracy of various ground states in a fully frustrated XY model with a honeycomb lattice is shown to survive even when the free energy of the harmonic fluctuations is taken into account. The reason for that consists in the existence of a hidden gauge symmetry between the Hamiltonians describing the harmonic fluctuations in all these ground states. A particular vortex pattern is selected only when anharmonic fluctuations are taken into account. However, the observation of vortex ordering requires relatively large system size L>>100000.

cond-mat.stat-mech↗

arXiv2003

Weakly interacting electrons and the renormalization group

We present a general method to study weak-coupling instabilities of a large class of interacting electron models in a controlled and unbiased way. Quite generally, the electron gas is unstable towards a superconducting state even in the absence of phonons, since high-energy spin fluctuations create an effective attraction between the quasi-particles. As an example, we show the occurrence of d-wave pairing in the repulsive Hubbard model in two dimensions. In one dimension or if the Fermi surface is nested, there are several competing instabilities. The required renormalization group formalism for this case is presented to lowest (one-loop) order on a most elementary level, connecting the idea of the ``parquet summation'' to the more modern concept of Wilson's effective action. The validity and restrictions of the one-loop approximation are discussed in detail. As a result, three different renormalization group approaches known in the literature are shown to be equivalent within the regime of applicability. We also briefly discuss the open problem of a two-dimensional Fermi system at Van Hove filling without nesting.

cond-mat.str-el↗

arXiv2003

Interaction-induced Fermi surface deformations in quasi one-dimensional electronic systems

We consider serious conceptual problems with the application of standard perturbation theory, in its zero temperature version, to the computation of the dressed Fermi surface for an interacting electronic system. In order to overcome these difficulties, we set up a variational approach which is shown to be equivalent to the renormalized perturbation theory where the dressed Fermi surface is fixed by recursively computed counterterms. The physical picture that emerges is that couplings that are irrelevant tend to deform the Fermi surface in order to become more relevant (irrelevant couplings being those that do not exist at vanishing excitation energy because of kinematical constraints attached to the Fermi surface). These insights are incorporated in a renormalization group approach, which allows for a simple approximate computation of Fermi surface deformation in quasi one-dimensional electronic conductors. We also analyze flow equations for the effective couplings and quasiparticle weights. For systems away from half-filling, the flows show three regimes corresponding to a Luttinger liquid at high energies, a Fermi liquid, and a low-energy incommensurate spin-density wave. At half-filling Umklapp processes allow for a Mott insulator regime where the dressed Fermi surface is flat, implying a confined phase with vanishing effective transverse single-particle coherence. The boundary between the confined and Fermi liquid phases is found to occur for a bare transverse hopping amplitude of the order of the Mott charge gap of a single chain.

cond-mat.str-el↗

arXiv2002

Renormalization group for 2D fermions with a flat Fermi surface

We present a renormalization group analysis of two-dimensional interacting fermion systems with a closed and partially flat Fermi surface. Numerical solutions of the one-loop flow equations show that for a bare local repulsion, the system evolves through three different regimes as the typical energy is lowered: a high-energy transient with a strong competition between particle-particle and particle-hole channels, an intermediate regime with dominant spin density wave correlations, and finally a ``hot spot'' regime exhibiting d-wave superconductivity. We study, mostly by analytical methods, how this flow pattern depends on the number N of Fermi surface patches used in the numerical solution. This clearly indicates that the final regime requires vanishingly small microscopic interactions, for the one-loop approximation to be valid, as N is going to infinity.

cond-mat.str-el↗