Publications de Pierre Marcel Nataf

Edge states and universality class of the critical two-box symmetric SU(3) chain

Frédéric Mila, Samuel Gozel, Pierre Marcel Nataf

We numerically demonstrate that, although it is critical, the two-box symmetric SU(3) chain possesses edge states in the adjoint representation whose excitation energy scales with the number of sites Ns as 1/(Ns log Ns), in close analogy to those found in ...

2021

Time-reversal symmetry breaking Abelian chiral spin liquid in Mott phases of three-component fermions on the triangular lattice

Frédéric Mila, Karlo Penc, Pierre Marcel Nataf, Carolin Boos, Miklos Lajko

We provide numerical evidence in favor of spontaneous chiral symmetry breaking and the concomitant appearance of an Abelian chiral spin liquid for three-component fermions on the triangular lattice described by an SU(3) symmetric Hubbard model with hopping ...

2020

Haldane Gap of the Three-Box Symmetric SU(3) Chain

Frédéric Mila, Samuel Gozel, Pierre Marcel Nataf

Motivated by the recent generalization of the Haldane conjecture to SU(3) chains [Lajko et al., Nucl. Phys. B924, 508 (2017)] according to which a Haldane gap should be present for symmetric representations if the number of boxes in the Young diagram is a ...

2020

Density matrix renormalization group simulations of SU(N) Heisenberg chains using standard Young tableaus: Fundamental representation and comparison with a finite-size Bethe ansatz

Frédéric Mila, Pierre Marcel Nataf

We develop an efficient method to perform density matrix renormalization group simulations of the SU(N) Heisenberg chain with open boundary conditions taking full advantage of the SU(N) symmetry of the problem. This method is an extension of the method pre ...

2018

Exact diagonalization of SU( N ) Heisenberg and Affleck-Kennedy-Lieb-Tasaki chains using the full SU( N ) symmetry

Frédéric Mila, Pierre Marcel Nataf, Kianna Wan

We present a method for the exact diagonalization of the SU(N) Heisenberg interaction Hamiltonian using Young tableaus to work directly in each irreducible representation of the global SU(N) group. This generalized scheme is applicable to chains consisting ...

2017

Linear flavor-wave theory for fully antisymmetric SU( N ) irreducible representations

Frédéric Mila, Karlo Penc, Pierre Marcel Nataf, Francisco Hyunkyu Kim

The extension of the linear flavor-wave theory to fully antisymmetric irreducible representations (irreps) of SU(N) is presented in order to investigate the color order of SU(N) antiferromagnetic Heisenberg models in several two-dimensional geometries. The ...

2017

Generalization of the Haldane conjecture to SU(3) chains

Frédéric Mila, Pierre Marcel Nataf, Miklos Lajko

2017

Plaquette order in the SU(6) Heisenberg model on the honeycomb lattice

Frédéric Mila, Karlo Penc, Pierre Marcel Nataf, Miklos Lajko

We revisit the SU(6) Heisenberg model on the honeycomb lattice, which has been predicted to be a chiral spin liquid by mean-field theory [G. Szirmai et al., Phys. Rev. A 84, 011611(R) (2011)]. Using exact diagonalizations of finite clusters, infinite proje ...

2016

Exact diagonalization of HeisenbergSU(N)chains in the fully symmetric and antisymmetric representations

Frédéric Mila, Pierre Marcel Nataf

Motivated by recent experimental progress in the context of ultracold multicolor fermionic atoms in optical lattices, we have developed a method to exactly diagonalize the Heisenberg SU(N) Hamiltonian with several particles per site living in a fully symme ...

2016

Chiral Spin Liquids in Triangular-LatticeSU(N)Fermionic Mott Insulators with Artificial Gauge Fields

Frédéric Mila, Karlo Penc, Pierre Marcel Nataf, Miklos Lajko

We show that, in the presence of a π/2 artificial gauge field per plaquette, Mott insulating phases of ultracold fermions with SU(N) symmetry and one particle per site generically possess an extended chiral phase with intrinsic topological order characteri ...

2016

Variational Monte Carlo investigation of SU(N) Heisenberg chains

Frédéric Mila, Jérôme Dufour, Pierre Marcel Nataf

Motivated by recent experimental progress in the context of ultracold multicolor fermionic atoms in optical lattices, we have investigated the properties of the SU (N) Heisenberg chain with totally antisymmetric irreducible representations, the effective m ...

2015

Exact Diagonalization of Heisenberg SU(N) Models

Frédéric Mila, Pierre Marcel Nataf

Building on advanced results on permutations, we show that it is possible to construct, for each irreducible representation of SU(N), an orthonormal basis labeled by the set of standard Young tableaux in which the matrix of the Heisenberg SU(N) model (the ...

2014

Heisenberg uncertainty principle as a probe of entanglement entropy: Application to superradiant quantum phase transitions

Pierre Marcel Nataf

Quantum phase transitions are often embodied by the critical behavior of purely quantum quantities such as entanglement or quantum fluctuations. In critical regions, we underline a general scaling relation between the entanglement entropy and one of the mo ...

Amer Physical Soc2012