Influence of Trotterization error on single-particle tunneling
le mercredi 03 avril 2024 à 11:00
Séminaire interne LPMMC
Personne à contacter : Denis Basko ()
Lieu : G421
Résumé : Quantum simulation of the single-particle tunneling problem by means of the Suzuki-Trotter approximation (STA) is analyzed. The target system describes a particle hopping across a chain of sites with position-dependent potential profile. The latter is assumed to be smooth and to posses several local minima separated by a potential barrier, arranging a tunneling problem between the localized states in different minima. The conducted analysis confirms the naive criteria of applicability max{T,P} ≪ 1/δt (with T, P being the typical scales of kinetic and potential terms, respectively), while also revealing the structure of error and its actual behavior with system parameters. Notably, in certain cases we find an exponential acceleration of tunneling, while other configurations lead to a complete suppression of the latter. Analysis of the case of large Trotter step is also performed, with the main result being the reconstruction of the low-energy spectrum due to coupling between states with energy difference close to 2π/δt. The connection of the obtained results with the rigorous upper error bounds on the STA error is discussed, with particular emphasis on the reasons for the fact that these rigorous bounds are not always saturated. We also point out that the proposed problem can be directly implemented on existing quantum devices arXiv:2012.00921. The talk is based on the recent paper arXiv:2312.04735.
Amorphous quantum magnets in a two-dimensional Rydberg atom array
le vendredi 12 avril 2024 à 11:00
Séminaire théorie
Personne à contacter : Adolfo Grushin ()
Lieu : G421
Résumé : Amorphous solids, i.e., systems which feature well-defined short-range properties but lack long-range order, constitute an important research topic in condensed matter. While their microscopic structure is known to differ from their crystalline counterpart, there are still many open questions concerning the emergent collective behavior in amorphous materials. This is particularly the case in the quantum regime, where the numerical simulations are extremely challenging. In this talk, we instead propose to explore amorphous quantum magnets with an analog quantum simulator. To this end, we first present an algorithm to generate amorphous quantum magnets, suitable for Rydberg simulators of the Ising model. Subsequently, we use semiclassical approaches to get a preliminary insight of the physics of the model. In particular, we calculate mean-field phase diagrams, and use the linear-spin-wave theory to study localization properties and dynamical structure factors of the excitations. Finally, we outline an experimental proposal based on Rydberg atoms in programmable tweezer arrays, thus opening the road towards the study of amorphous quantum magnets in regimes difficult to simulate classically.
Quantum phase transitions: microscopic scale and Planckian time
le mardi 07 mai 2024 à 14:00
Séminaire nano-électronique quantique
Personne à contacter : Jeremie Viennot ()
Lieu : Salle Rémy Lemaire K223, Institut Néel
Résumé : For more than thirty years, experimental analysis of quantum phase transitions (QPTs) has been
largely focused on finding critical exponents and universality classes of studied systems. This
approach emphasizes scale-invariance of QPTs and ignores the fact that system response also
depends on two non-universal length scales: microscopic “seeding” scale of the correlation
length and the dephasing length. Correcting this deficiency, we have developed a
phenomenological model of QPTs based on conjecture that the dephasing length is set by a
distance travelled by a system-specific semi-classical elementary excitation over the Planckian
time, and that the scaling function assumes the generic exponential form predicted
by the scaling theory of localization (the figure shows some examples). Using this model, we
have quantitatively explained QPTs in eighteen systems including: magnetic-field-driven QPT
in superconducting films, nanowires, La1.92Sr0.08CuO4 and Josephson junction chains; QPT in
Ising and Heisenberg spin chains, the Mott transition in 2d cold atomic gases and moiré
superlattices; and QPT between the states of quantum Hall and other topological insulators. The
model illuminates the universal microscopic nature of many-body gapless state of matter
emerging near QPTs. Surprisingly, the only system deviating from the trend is doped Si : P,
where metal-insulator transition is explained by the non-interaction version of the model. We
anticipate that shifting emphasis from critical exponents to the microscopic parameters of a
phase transition will be a fruitful approach for many systems beyond equilibrium condensed
matter physics.
Ref. :
[1] A. Rogachev, Microscopic scale of quantum phase transition: from doped semiconductors to
spin chains, cold gases and moiré superlattices, arXiv:2309.00749.
[2] A. Rogachev and K. Davenport, Microscopic scale of pair-breaking quantum phase
transitions in superconducting films, nanowires and La1.92Sr0.08CuO4, arXiv:2309.00747.
[3] A. Rogachev, Quantum phase transitions in quantum Hall and other topological systems: role
of the Planckian time, arXiv:2309.00747.