Felix Werner (Laboratoire Kastler Brossel, ENS & Collège de France):

Large-order summation of connected Feynman diagrams for strongly correlated fermions

    

A major long-standing goal is to develop generic unbiased methods for many-fermion problems. Conventional Quantum Monte Carlo methods (e.g. auxiliary-field QMC or lattice QCD) generically suffer from the "fermion sign problem": The computational time increases exponentially with the number of fermions. In contrast, expansions of intensive quantities in series of connected Feynman diagrams can be computed directly in the thermodynamic limit. Over the last decade, diagrammatic Monte Carlo algorithms made it possible to reach large expansion orders, and to obtain state-of-the-art results for various models of interacting fermions in 2 and 3 dimensions. The "Connected Determinant" algorithm allows to sum a factorial number of connected diagrams in an exponential time [1], leading to a computational time that increases only polynomially with the precision [2]. The range of applicability of the approach can be considerably enlarged by two ingredients: divergent-series summation methods, and modification of the expansion by changing the starting point and/or using dressed propagators/vertices. An important aspect is to understand the singularities of the function that stands behind the series. I will present illustrative results for the unitary Fermi gas in the normal phase [3,4] and the superconducting phase of the polarized attractive Hubbard model [5]. 

 

[1] Rossi, PRL 119, 045701 (2017)

[2] Rossi, Prokof’ev, Svistunov, Van Houcke, FW, EPL 118, 10004 (2017)

[3] Rossi, Ohgoe, Van Houcke, FW, PRL 121, 130405 (2018)

[4] Rossi, Ohgoe, Kozik, Prokof’ev, Svistunov, Van Houcke, FW, PRL 121, 130406 (2018)

[5] Spada, Rossi, Simkovic, Garioud, Ferrero, Van Houcke, FW, arXiv:2103.12038

In this talk, I discuss local quenches from initial states generated by a single spin-flip in either the true or the false vacuum state of the confining quantum Ising spin chain in the ferromagnetic regime[1]. Contrary to global quenches, where the light-cone behaviour is strongly suppressed, after local quenches a significant light-cone signal propagating with a nonzero velocity emerges besides the expected localised oscillating component. Combining an analytic representation of the initial state with a numerical description of the relevant excitations using the two-fermion approximation, we can construct the spectrum of post-quench excitations and their overlaps with the initial state, identifying the underlying mechanism. For confining quenches built upon the true vacuum, the propagating signal consists of Schrödinger cats of left and right-moving mesons escaping confinement. In contrast, for anti-confining quenches built upon the false vacuum, it is composed of Schrödinger cats of left and right-moving bubbles which escape Wannier-Stark localisation. 

 

[1] A. Krasznai, G. Takács, arXiv:2401.04193 

Topological bands having a vanishing dispersion, commonly referred to as "flat bands," have beed a source of emergent electronic phenomena since the initial discovery of the quantum Hall effect in two-dimensional (2D) electron systems. Recently, flat bands have been identified in 2D van der Waals materials, including graphene-based electron systems. Among these "magic angle" twisted bilayers and rhombohedral graphite, represent particularly accessible and highly tunable platforms for investigating emergent, correlated phenomena, from superconductivity to magnetism. This presentation will provide an overview of the field, incorporating recent findings from my group, and offer a perspective on future research directions.