Hosted by: Alexei Tsvelik

Accurate account for interactions in theoretical models for strongly correlated many-body systems is the key for understanding real materials and one of the major technical challenges of modern physics. To accept this challenge, new and more effective methods, capable of dealing with interacting systems/models in an approximation-free manner, are required. One of such methods is the field-theoretical Diagrammatic Monte Carlo technique (DiagMC). While a conventional Quantum Monte Carlo samples the configuration space of a given model Hamiltonian, the DiagMC samples the configuration space of the model-specific Feynman diagrams and obtains final results with controlled accuracy by accounting for all the relevant diagrammatic orders. In contrast to conventional QMC, it does not suffer from the fermionic sign problem and can be applied to any system with arbitrary dispersion relation and shape of the interaction potential (both doped and undoped). In the first part of my talk I will introduce the technique, based on its bold-line (skeleton) implementation, and benchmark it against known results for the problem of semimetal-insulator transition in suspended graphene. In the second part I will briefly demonstrate its applications to various strongly-correlated systems/problems (stability of the 2d Dirac liquid state against strong long-range Coulomb interaction; interacting Chern insulators; phonons in metals; 1d chain of hydrogen atoms; uniform electron gas (jellium model), optical conductivity, etc).