arXiv subjects

Adrien Bolens

Publications and source records attributed to Adrien Bolens.

5 recordsLinked to original sources

arXiv2020

Reinforcement Learning for Digital Quantum Simulation

Digital quantum simulation is a promising application for quantum computers. Their free programmability provides the potential to simulate the unitary evolution of any many-body Hamiltonian with bounded spectrum by discretizing the time evolution operator through a sequence of elementary quantum gates, typically achieved using Trotterization. A fundamental challenge in this context originates from experimental imperfections for the involved quantum gates, which critically limits the number of attainable gates within a reasonable accuracy and therefore the achievable system sizes and simulation times. In this work, we introduce a reinforcement learning algorithm to systematically build optimized quantum circuits for digital quantum simulation upon imposing a strong constraint on the number of allowed quantum gates. With this we consistently obtain quantum circuits that reproduce physical observables with as little as three entangling gates for long times and large system sizes. As concrete examples we apply our formalism to a long range Ising chain and the lattice Schwinger model. Our method makes larger scale digital quantum simulation possible within the scope of current experimental technology.

quant-ph↗

arXiv2019

Topological states on the breathing kagome lattice

We theoretically study the topological properties of the tight-binding model on the breathing kagome lattice with antisymmetric spin-orbit coupling (SOC) between nearest neighbors. We show that the system hosts nontrivial topological phases even without second-nearest-neighbor hopping, and that the weakly dispersing band of the kagome lattice can become topological. The main results are presented in the form of phase diagrams, where the $\mathbb{Z}_2$ topological index is shown as a function of SOC (intrinsically allowed and Rashba) and lattice trimerization. In addition, exact diagonalization is compared with effective low-energy theories around the high-symmetry points. We find that the weakly dispersing band has a very robust topological property associated with it. Moreover, the Rashba SOC can produce a topological phase rather than hinder it, in contrast to the honeycomb lattice. Finally, we consider the case of a fully spin polarized (ferromagnetic) system, breaking time-reversal symmetry. We find a phase diagram that includes systems with finite Chern numbers. In this case too, the weakly dispersing band is topologically robust to trimerization.

cond-mat.mes-hall↗

arXiv2018

Theory of electronic magnetoelectric coupling in $d^5$ Mott insulators

Motivated by recent terahertz (THz) spectroscopy measurements in $α$-RuCl$_3$, we develop a theory for magnetoelectric (ME) effects in Mott insulators of $d^5$ transition metal ions in an octahedral crystal field. For $4d$ and $5d$ compounds, the relatively wide-spread orbitals favor charge fluctuations of localized electrons to neighboring ions and a significant ME effect from electronic mechanisms is expected. From a three-orbital Hubbard model with strong spin-orbit coupling, we derive the mechanisms for the electric polarization originating from virtual hopping of the localized holes carrying the spins. We consider the electric polarization generated by pairs of spin operators on nearest neighbor bonds with either an edge-sharing geometry (i.e., two ligands are shared) or a corner-sharing geometry (i.e., one ligand is shared). The allowed couplings are first derived using a symmetry approach. Then, we explicitly calculate the coupling constants and evaluate the effective polarization operator in the ground state manifold using perturbation theory and exact diagonalization. The results are relevant when considering the THz optical conductivity of magnetic systems such as some perovskite iridates or Kitaev materials. In particular, they help explain the recent THz optical measurements of $α$-RuCl$_{3}$ for which the electric-dipole-induced contribution has been shown to be strong.

cond-mat.str-el↗

arXiv2018

Mechanism for subgap optical conductivity in honeycomb Kitaev materials

Motivated by recent terahertz absorption measurements in $α$-RuCl$_3$, we develop a theory for the electromagnetic absorption of materials described by the Kitaev model on the honeycomb lattice. We derive a mechanism for the polarization operator at second order in the nearest-neighbor hopping Hamiltonian. Using the exact results of the Kitaev honeycomb model, we then calculate the polarization dynamical correlation function corresponding to electric dipole transitions, in addition to the spin dynamical correlation function corresponding to magnetic dipole transitions.

cond-mat.str-el↗

arXiv2017

Synergetic effect of spin-orbit coupling and Zeeman splitting on the optical conductivity in the one-dimensional Hubbard model

We study how the synergetic effect of spin-orbit coupling (SOC) and Zeeman splitting (ZS) affects the optical conductivity in the one-dimensional Hubbard model using the Kubo formula. We focus on two phenomena: (1) the electric dipole spin resonance (EDSR) in the metallic regime and (2) the optical conductivity in the Mott-insulating phase above the optical gap. In both cases, we calculate qualitatively the effects of SOC and ZS and how they depend on the relative angle between the SOC vector and the magnetic field direction. First, we investigate the spin resonance without electron correlation (the Hubbard parameter $U=0$). Although, neither SOC nor ZS causes any resonance by itself in the optical conductivity, the EDSR becomes possible when both of them exist. The resulting contribution to the optical conductivity is analyzed analytically. The effect of $U$ on the spin resonance is also studied with a numerical method. It is found that at half-filling, the resonance is first enhanced for small $U$ and then suppressed when the optical gap is large enough. In the strong coupling limit $U \rightarrow \infty$ at half-filling, we also refer to the resonance between the lower and upper Hubbard bands appearing at $ω\sim U$, above the optical gap. A large magnetic field tends to suppress the signal while it is recovered thanks to SOC depending on the relative angle of the magnetic field.

cond-mat.str-el↗