Beyond mean-field universality in the random solid state

Xing Zhang, Garnet Kin‐Lic Chan

We introduce an extension to the PySCF package, which makes it automatically differentiable. The implementation strategy is discussed, and example applications are presented to demonstrate the automatic differentiation framework for quantum chemistry methodology development. These include orbital optimization, properties, excited-state energies, and derivative couplings, at the mean-field level and beyond, in both molecules and solids. We also discuss some current limitations and directions for future work.

Alexander K. Hartmann, U. Nowak

Volodymyr Turkowski

Renaud Chrétien

Quantum simulation with ultracold atoms gained a lot of traction recently by proposing a framework with a lot of flexibility, versatility and tunability to emulate diverse quantum ef- fects. It indeed provides the ideal playground to study many–body effects in a well–controlled environment and is particularly useful in the domain of quantum coherent transport of waves in random media. The purpose of this thesis is to study several configurations of coher- ent transport within random media with Bose–Einstein condensates and to investigate the interplay between coherence and interaction effects. In particular, we start by numerically studying Aharonov–Bohm oscillations in the transmission of particles across the eponymous rings in a 1D configuration. When exposed to a suitably chosen disorder potential, those rings yield oscillations with double frequency, which are routinely encountered in solid–state physics where they are referred to as Al’tshuler–Aronov–Spivak oscillations, similar in essence to coherent backscattering and weak localisation. We then study the behaviour of those os- cillations in the presence of interaction within Aharonov–Bohm rings and find that in the mean–field regime, they are inverted for finite interaction. Truncated Wigner simulations are then carried out in the same scenario and indicate that the inversion should be observ- able for realistic atomic and experimental parameters with 39 K atoms, although dephasing of the oscillations is observed at strong interaction owing to interaction–induced inelastic scattering. A first–order nonlinear diagrammatic theory is then presented and benchmarks our numerical findings. The question of the inversion prevalence is then investigated in a 2D scenario, following state–of–the–art observations in the literature. It has indeed been nu- merically observed that coherent backscattering is inverted in the mean–field approximation for finite interaction strength. We numerically confirm this observation with our study and extend it beyond the mean–field approximation by applying the truncated Wigner method. These simulations show that the inversion prevails beyond the mean–field regime and should moreover be observable experimentally with 87 Rb atoms for realistic parameters, despite a partial dephasing. This dephasing however completely eclipses interference effects and washes out this signature of antilocalisation for stronger interaction.

Volodymyr Turkowski

Thomas Vojta, Adam Farquhar, Jason Mast

We study the nonequilibrium phase transition in the two-dimensional contact process on a randomly diluted lattice by means of large-scale Monte Carlo simulations for times up to 10;{10} and system sizes up to 8000x8000 sites. Our data provide strong evidence for the transition being controlled by an exotic infinite-randomness critical point with activated (exponential) dynamical scaling. We calculate the critical exponents of the transition and find them to be universal, i.e., independent of disorder strength. The Griffiths region between the clean and the dirty critical points exhibits power-law dynamical scaling with continuously varying exponents. We discuss the generality of our findings and relate them to a broader theory of rare region effects at phase transitions with quenched disorder. Our results are of importance beyond absorbing state transitions because, according to a strong-disorder renormalization group analysis, our transition belongs to the universality class of the two-dimensional random transverse-field Ising model.