arXiv subjects

Julien Vidal

Publications and source records attributed to Julien Vidal.

14 recordsLinked to original sources

arXiv2025

Partition function of the Kitaev quantum double model

We compute the degeneracy of energy levels in the Kitaev quantum double model for any discrete group $G$ on any planar graph forming the skeleton of a closed orientable surface of arbitrary genus. The derivation is based on the fusion rules of the properly identified vertex and plaquette excitations, which are selected among the anyons, i.e., the simple objects of the Drinfeld center $\mathcal{Z}(\mathrm{Vec}_G)$. These degeneracies are given in terms of the corresponding $S$-matrix elements and allow one to obtain the exact finite-temperature partition function of the model, valid for any finite-size system.

cond-mat.str-el↗

arXiv2025

Kitaev model in regular hyperbolic tilings

We study the Kitaev model on regular hyperbolic trivalent tilings. Depending on the length $p$ of the elementary polygons, we examine two distinct tri-colorings of the tiling. Using a recent conjecture on the ground-state flux sector, we compute the phase diagram via exact diagonalizations and derive analytical expressions for the effective Hamiltonians in the isolated-dimer limit which are valid for all values of $p$. Our results interpolate between the Euclidean honeycomb lattice and the trivalent Bethe lattice ($p=\infty$) for which we derive the exact solution of the phase boundaries.

cond-mat.str-el↗

arXiv2024

Kitaev model on Hurwitz hyperbolic tilings: A non-Abelian gapped chiral spin liquid

We study the Kitaev model on the trivalent heptagonal Hurwitz hyperbolic tiling. The presence of odd-length loops in the tiling is responsible for a spontaneous time-reversal symmetry breaking. Interestingly, at the isotropic point, the two degenerate ground states (Kramers pair) are shown to be gapped chiral spin liquids and the elementary excitations are non-Abelian Ising anyons.

cond-mat.str-el↗

arXiv2024

Chiral Gapless Spin Liquid in Hyperbolic Space

We analyze the Kitaev model on the $\{9,3\}$ hyperbolic lattice. The $\{9,3\}$ is formed by a regular tricoordinated tiling of nonagons, where the 3-color coding of bonds according to the inequivalent Kitaev Ising spin couplings yields the natural generalization of the original Kitaev model for Euclidean regular honeycomb tiling. Upon investigation of the bulk spectrum for large finite size droplets, we identify a gapless chiral $\mathbb{Z}_2$ spin liquid state featuring spontaneous time reversal symmetry breaking. Due to its non-commutative translation group structure, such type of hyperbolic spin liquid is conjectured to feature chiral quasiparticles with a potentially non-Abelian Bloch profile.

cond-mat.str-el↗

arXiv2024

Finite-temperature properties of string-net models

We consider a refined version of the string-net model which assigns a different energy cost to each plaquette excitation. Using recent exact calculations of the energy-level degeneracies we compute the partition function of this model and investigate several thermodynamical quantities. In the thermodynamic limit, we show that the partition function is dominated by the contribution of special particles, dubbed pure fluxons, which trivially braid with all other (product of) fluxons. We also analyze the behavior of Wegner-Wilson loops associated to excitations and show that they obey an area law, indicating confinement, for any finite temperature except for pure fluxons that always remain deconfined. Finally, using a recently proposed conjecture, we compute the topological mutual information at finite temperature, which features a nontrivial scaling between system size and temperature, similar to the one-dimensional classical Ising model.

cond-mat.other↗

arXiv2023

Effective models for dense vortex lattices in the Kitaev honeycomb model

We introduce low-energy effective models for dense configurations of vortices in the Kitaev honeycomb model. Specifically, we consider configurations of vortices in which vortex-free plaquettes form triangular lattices against a vortex-full background. Depending on the vortex density, these "dual" configurations belong to either one of two families classified by translation and inversion symmetry. As a function of a time-reversal symmetry breaking term, one family exhibits gapped phases with even Chern numbers separated by extended gapless phases, while the other exhibits gapped phases with even or odd Chern numbers, separated by critical points. We construct an effective model for each family, determine the parameters of these models by fitting the integrated density of states, and reproduce energy spectra and Chern numbers of the Kitaev honeycomb model. We also derive phase diagrams and determine these models' validity.

cond-mat.supr-con↗

arXiv2023

Topological and nontopological degeneracies in generalized string-net models

Generalized string-net models have been recently proposed in order to enlarge the set of possible topological quantum phases emerging from the original string-net construction. In the present work, we do not consider vertex excitations and restrict to plaquette excitations, or fluxons, that satisfy important identities. We explain how to compute the energy-level degeneracies of the generalized string-net Hamiltonian associated to an arbitrary unitary fusion category. In contrast to the degeneracy of the ground state, which is purely topological, that of excited energy levels depends not only on the Drinfeld center of the category, but also on internal multiplicities obtained from the tube algebra defined from the category. For a noncommutative category, these internal multiplicities result in extra nontopological degeneracies. Our results are valid for any trivalent graph and any orientable surface. We illustrate our findings with nontrivial examples.

cond-mat.other↗

arXiv2019

Tensor-network approach to phase transitions in string-net models

We use a recently proposed class of tensor-network states to study phase transitions in string-net models. These states encode the genuine features of the string-net condensate such as, e.g., a nontrivial perimeter law for Wilson loops expectation values, and a natural order parameter detecting the breakdown of the topological phase. In the presence of a string tension, a quantum phase transition occurs between the topological phase and a trivial phase. We benchmark our approach for $\mathbb{Z}_2$ string nets and capture the second-order phase transition which is well known from the exact mapping onto the transverse-field Ising model. More interestingly, for Fibonacci string nets, we obtain first-order transitions in contrast with previous studies but in qualitative agreement with mean-field results.

cond-mat.str-el↗

arXiv2018

Landau levels in quasicrystals

Two-dimensional tight-binding models for quasicrystals made of plaquettes with commensurate areas are considered. Their energy spectrum is computed as a function of an applied perpendicular magnetic field. Landau levels are found to emerge near band edges in the zero-field limit. Their existence is related to an effective zero-field dispersion relation valid in the continuum limit. For quasicrystals studied here, an underlying periodic crystal exists and provides a natural interpretation to this dispersion relation. In addition to the slope (effective mass) of Landau levels, we also study their width as a function of the magnetic flux per plaquette and identify two fundamental broadening mechanisms: (i) tunneling between closed cyclotron orbits and (ii) individual energy displacement of states within a Landau level. Interestingly, the typical broadening of the Landau levels is found to behave algebraically with the magnetic field with a nonuniversal exponent.

cond-mat.dis-nn↗

arXiv2017

Bridging Perturbative Expansions with Tensor Networks

We demonstrate that perturbative expansions for quantum many-body systems can be rephrased in terms of tensor networks, thereby providing a natural framework for interpolating perturbative expansions across a quantum phase transition. This approach leads to classes of tensor-network states parametrized by few parameters with a clear physical meaning, while still providing excellent variational energies. We also demonstrate how to construct perturbative expansions of the entanglement Hamiltonian, whose eigenvalues form the entanglement spectrum, and how the tensor-network approach gives rise to order parameters for topological phase transitions.

cond-mat.str-el↗

arXiv2011

False-positive and False-negative assignments of Topological Insulators in Density-Functional Theory and Hybrids

Density-functional Theory (DFT) approaches have recently been used to judge the topological order of various materials despite its well-known band gap underestimation. Use of the more accurate quasi-particle GW approach reveals here few cases where DFT identifications are false-positive, possibly misguiding experimental searches of materials that are topological insulators (TI) in DFT but not expected to be TI in reality. We also present the case of false-positive due to the incorrect choice of crystal structures and adress the relevancy of such choice of crystal structure with respect to the ground state one and thermodynamical instability with respect to binary competing phases. We conclude that it is then necessary to consider both the correct ground state crystal structure and the correct Hamiltonian in order to predict new TI.

cond-mat.mtrl-sci↗

arXiv2010

Density-based mixing parameter for hybrid functionals

A very popular ab-initio scheme to calculate electronic properties in solids is the use of hybrid functionals in density functional theory (DFT) that mixes a portion of Fock exchange with DFT functionals. In spite of their success, a major problem still remains, related to the use of one single mixing parameter for all materials. Guided by physical arguments that connect the mixing parameter to the dielectric properties of the solid, and ultimately to its band gap, we propose a method to calculate this parameter from the electronic density alone. This method is able to cut significantly the error of traditional hybrid functionals for large and small gap materials, while retaining a good description of structural properties. Moreover, its implementation is simple and leads to a negligible increase of the computational time.

cond-mat.mtrl-sci↗

arXiv2010

Effects of polarization on the band-structure of delafossite transparent conductive oxides

We use hybrid functionals and restricted self-consistent GW, state-of-the-art theoretical approaches for quasiparticle band structures, to study the electronic states of delafossite Cu(Al,In)O$_2$, the first p-type and bipolar transparent conductive oxides. We show that self-consistent GW gives remarkably wider band gaps than all the other approaches used so far. Accounting for polaronic effects in the GW scheme we recover a very nice agreement with experiments. Furthermore, the modifications with respect to the Kohn-Sham bands are strongly k-dependent, which makes questionable the common practice of using a scissor operator. Finally, our results support the view that the low energy structures found in optical experiments, and initially attributed to an indirect transition, are due to intrinsic defects in the samples.

cond-mat.mtrl-sci↗

arXiv1999

Interactions in Quasicrystals

Although the effects of interactions in solid state systems still remains a widely open subject, some limiting cases such as the three dimensional Fermi liquid or the one-dimensional Luttinger liquid are by now well understood when one is dealing with interacting electrons in {\it periodic} crystalline structures. This problem is much more fascinating when periodicity is lacking as it is the case in {\it quasicrystalline} structures. Here, we discuss the influence of the interactions in quasicrystals and show, on a controlled one-dimensional model, that they lead to anomalous transport properties, intermediate between those of an interacting electron gas in a periodic and in a disordered potential.

cond-mat.str-el↗