arXiv subjects

R. Mosseri

Publications and source records attributed to R. Mosseri.

At least 19 recordsLinked to original sources

arXiv2023

Density of states of tight-binding models in the hyperbolic plane

We study the energy spectrum of tight-binding Hamiltonian for regular hyperbolic tilings. More specifically, we compute the density of states using the continued-fraction expansion of the Green function on finite-size systems with more than $10^9$ sites and open boundary conditions. The coefficients of this expansion are found to quickly converge so that the thermodynamical limit can be inferred quite accurately. This density of states is in stark contrast with the prediction stemming from the recently proposed hyperbolic band theory. Thus, we conclude that the fraction of the energy spectrum described by the hyperbolic Bloch-like wave eigenfunctions vanishes in the thermodynamical limit.

cond-mat.str-el↗

arXiv2022

Aharonov-Bohm cages, flat bands, and gap labeling in hyperbolic tilings

Aharonov-Bohm caging is a localization mechanism stemming from the competition between the geometry and the magnetic field. Originally described for a tight-binding model in the dice lattice, this destructive interference phenomenon prevents any wavepacket spreading away from a strictly confined region. Accordingly, for the peculiar values of the field responsible for this effect, the energy spectrum consists of a discrete set of highly degenerate flat bands. In the present work, we show that Aharonov-Bohm cages are also found in an infinite set of hyperbolic dice tilings defined on a negatively curved hyperbolic plane. We detail the construction of these tilings and compute their Hofstadter butterflies by considering periodic boundary conditions on high-genus surfaces. As recently observed for some regular hyperbolic tilings, these butterflies do not manifest the self-similar structure of their Euclidean counterparts but still contain some gaps. We also consider the energy spectrum of hyperbolic kagome tilings (which are the dual of hyperbolic dice tilings), which displays interesting features, such as highly degenerate states arising for some particular values of the magnetic field. For these two families of hyperbolic tilings, we compute the Chern number in the main gaps of the Hofstadter butterfly and propose a gap labeling inspired by the Euclidean case. Finally, we also study the triangular Husimi cactus, which is a limiting case in the family of hyperbolic kagome tilings, and we derive an exact expression for its spectrum versus magnetic flux.

cond-mat.mes-hall↗

arXiv2019

Landau level broadening, hyperuniformity, and discrete scale invariance

We study the energy spectrum of a two-dimensional electron in the presence of both a perpendicular magnetic field and a potential. In the limit where the potential is small compared to the Landau level spacing, we show that the broadening of Landau levels is simply expressed in terms of the structure factor of the potential. For potentials that are either periodic or random, we recover known results. Interestingly, for potentials with a dense Fourier spectrum made of Bragg peaks (as found, e.g., in quasicrystals), we find an algebraic broadening with the magnetic field characterized by the hyperuniformity exponent of the potential. Furthermore, if the potential is self-similar such that its structure factor has a discrete scale invariance, the broadening displays log-periodic oscillations together with an algebraic envelope.

cond-mat.other↗

arXiv2017

Random tilings of high symmetry: II. Boundary conditions and numerical studies

We perform numerical studies including Monte Carlo simulations of high rotational symmetry random tilings. For computational convenience, our tilings obey fixed boundary conditions in regular polygons. Such tilings are put in correspondence with algorithms for sorting lists in computer science. We obtain statistics on path counting and vertex coordination which compare well with predictions of mean-field theory and allow estimation of the configurational entropy, which tends to the value 0.568 per vertex in the limit of continuous symmetry. Tilings with phason strain appear to share the same entropy as unstrained tilings, as predicted by mean-field theory. We consider the thermodynamic limit and argue that the limiting fixed boundary entropy equals the limiting free boundary entropy, although these differ for finite rotational symmetry.

cond-mat.stat-mech↗

arXiv2015

Phase diagram of an extended quantum dimer model on the hexagonal lattice

We introduce a quantum dimer model on the hexagonal lattice that, in addition to the standard three-dimer kinetic and potential terms, includes a competing potential part counting dimer-free hexagons. The zero-temperature phase diagram is studied by means of quantum Monte Carlo simulations, supplemented by variational arguments. It reveals some new crystalline phases and a cascade of transitions with rapidly changing flux (tilt in the height language). We analyze perturbatively the vicinity of the Rokhsar-Kivelson point, showing that this model has the microscopic ingredients needed for the "devil's staircase" scenario [E. Fradkin et al., Phys. Rev. B 69, 224415 (2004)], and is therefore expected to produce fractal variations of the ground-state flux.

cond-mat.str-el↗

arXiv2011

Entanglement in the symmetric sector of $n$ qubits

We discuss the entanglement properties of symmetric states of $n$ qubits. The Majorana representation maps a generic such state into a system of $n$ points on a sphere. Entanglement invariants, either under local unitaries (LU) or stochastic local operations and classical communication (SLOCC), can then be addressed in terms of the relative positions of the Majorana points. In the LU case, an over complete set of invariants can be built from the inner product of the radial vectors pointing to these points; this is detailed for the well documented three-qubits case. In the SLOCC case, cross ratio of related M^bius transformations are shown to play a central role, examplified here for four qubits. Finally, as a side result, we also analyze the manifold of maximally entangled 3 qubit state, both in the symmetric and generic case.

quant-ph↗

arXiv2008

Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections

The spectrum of the Lipkin-Meshkov-Glick model is exactly derived in the thermodynamic limit by means of a spin coherent states formalism. In the first step, a classical analysis allows one to distinguish between four distinct regions in the parameter space according to the nature of the singularities arising in the classical energy surface; these correspond to spectral critical points. The eigenfunctions are then analyzed more precisely in terms of the associated roots of the Majorana polynomial, leading to exact expressions for the density of states in the thermodynamic limit. Finite-size effects are also analyzed, leading in particular to logarithmic corrections near the singularities occuring in the spectrum. Finally, we also compute expectation values of the spin operators in a semi-classical analysis in order to illustrate some subtle effects occuring in one region of the parameter space.

cond-mat.stat-mech↗

arXiv2007

The Thermodynamical Limit of the Lipkin-Meshkov-Glick Model

A method based on the analyzis of the Majorana polynomial roots is introduced to compute the spectrum of the Lipkin-Meshkov-Glick model in the thermodynamical limit. A rich structure made of four qualitatively different regions is revealed in the parameter space whereas the ground state study only distinguishes between two phases.

cond-mat.stat-mech↗

arXiv2006

Adiabatic Computation - A Toy Model

We discuss a toy model for adiabatic quantum computation which displays some phenomenological properties expected in more realistic implementations. This model has two free parameters: the adiabatic evolution parameter $s$ and the $α$ parameter which emulates many-variables constrains in the classical computational problem. The proposed model presents, in the $s-α$ plane, a line of first order quantum phase transition that ends at a second order point. The relation between computation complexity and the occurrence of quantum phase transitions is discussed. We analyze the behavior of the ground and first excited states near the quantum phase transition, the gap and the entanglement content of the ground state.

quant-ph↗

arXiv2005

Random tilings of high symmetry: I. Mean-field theory

We study random tiling models in the limit of high rotational symmetry. In this limit a mean-field theory yields reasonable predictions for the configurational entropy of free boundary rhombus tilings in two dimensions. We base our mean-field theory on an iterative tiling construction inspired by the work of de Bruijn. In addition to the entropy, we consider correlation functions, phason elasticity and the thermodynamic limit. Tilings of dimension other than two are considered briefly.

cond-mat.stat-mech↗

arXiv2004

A formula for the number of tilings of an octagon by rhombi

We propose the first algebraic determinantal formula to enumerate tilings of a centro-symmetric octagon of any size by rhombi. This result uses the Gessel-Viennot technique and generalizes to any octagon a formula given by Elnitsky in a special case.

math.CO↗

arXiv2003

Entanglement in a first order quantum phase transition

The phase diagram of spins 1/2 embedded in a magnetic field mutually interacting antiferromagnetically is determined. Contrary to the ferromagnetic case where a second order quantum phase transition occurs, a first order transition is obtained at zero field. The spectrum is computed for a large number of spins and allows one to study the ground state entanglement properties which displays a jump of its concurrence at the critical point.

cond-mat.str-el↗

arXiv2003

Entanglement in a second order quantum phase transition

We consider a system of mutually interacting spin 1/2 embedded in a transverse magnetic field which undergo a second order quantum phase transition. We analyze the entanglement properties and the spin squeezing of the ground state and show that, contrarily to the one-dimensional case, a cusp-like singularity appears at the critical point $λ_c$, in the thermodynamic limit. We also show that there exists a value $λ_0 \geq λ_c$ above which the ground state is not spin squeezed despite a nonvanishing concurrence.

cond-mat.str-el↗

arXiv2003

Quantum dynamics in high codimension tilings: from quasiperiodicity to disorder

We analyze the spreading of wavepackets in two-dimensional quasiperiodic and random tilings as a function of their codimension, i.e. of their topological complexity. In the quasiperiodic case, we show that the diffusion exponent that characterizes the propagation decreases when the codimension increases and goes to 1/2 in the high codimension limit. By constrast, the exponent for the random tilings is independent of their codimension and also equals 1/2. This shows that, in high codimension, the quasiperiodicity is irrelevant and that the topological disorder leads in every case, to a diffusive regime, at least in the time scale investigated here.

cond-mat.dis-nn↗

arXiv2003

Topological phase for entangled two-qubit states

We present an unambiguous characterization of the rotation group SO(3) biconnectedness topology using two-qubit maximally entangled states. We show how to generate cyclic evolutions of these states, which are in one-to-one correspondence to closed paths in SO(3). The difference between the well known two classes of such paths translates into the gain of a global phase of $π$ for one class and no phase change for the other. We propose a simple quantum optics interference experiment to demonstrate this topological phase shift.

quant-ph↗

arXiv2003

Arctic octahedron in three-dimensional rhombus tilings and related integer solid partitions

Three-dimensional integer partitions provide a convenient representation of codimension-one three-dimensional random rhombus tilings. Calculating the entropy for such a model is a notoriously difficult problem. We apply transition matrix Monte Carlo simulations to evaluate their entropy with high precision. We consider both free- and fixed-boundary tilings. Our results suggest that the ratio of free- and fixed-boundary entropies is $σ_{free}/σ_{fixed}=3/2$, and can be interpreted as the ratio of the volumes of two simple, nested, polyhedra. This finding supports a conjecture by Linde, Moore and Nordahl concerning the ``arctic octahedron phenomenon'' in three-dimensional random tilings.

cond-mat.stat-mech↗

arXiv2002

Quasiperiodic tilings under magnetic field

We study the electronic properties of a two-dimensional quasiperiodic tiling, the isometric generalized Rauzy tiling, embedded in a magnetic field. Its energy spectrum is computed in a tight-binding approach by means of the recursion method. Then, we study the quantum dynamics of wave packets and discuss the influence of the magnetic field on the diffusion and spectral exponents. Finally, we consider a quasiperiodic superconducting wire network with the same geometry and we determine the critical temperature as a function of the magnetic field.

cond-mat.dis-nn↗

arXiv2001

Quantum dynamics in two and three-dimensional quasiperiodic tilings

We investigate the properties of electronic states in two and three-dimensional quasiperiodic structures: the generalized Rauzy tilings. Exact diagonalizations, limited to clusters with a few thousands sites, suggest that eigenstates are critical and more extended at the band edges than at the band center. These trends are clearly confirmed when we compute the spreading of energy-filtered wavepackets, using a new algorithm which allows to treat systems of about one million sites. The present approach to quantum dynamics, which gives also access to the low frequency conductivity, opens new perspectives in the analyzis of two and three-dimensional models.

cond-mat.dis-nn↗