Recent developments in quantum Monte Carlo


QMC-RD workshop logo

Location: Rome, Italy
Dates: Oct 21-22, 2021
Organisers: Fabio Affinito, Giovanni Bachelet, Lilia Boeri, David Ceperley, Irene Iacuitto, Gaetano Senatore

With advances in algorithms and growing computing power, quantum Monte Carlo (QMC) methods have become a powerful tool for the description of a variety of quantum fluids and a viable alternative for high-accuracy calculations of the electronic structure of many atoms, molecules and solids. They are, however, at a less mature stage than today’s ready-for-use quantum-chemistry or density-functional packages: while the production of results on a variety of quantum many-body systems has been going on for at least three decades, a significant effort is still devoted to research and development of methods and algorithms, including real-time dynamics, super-accurate optimization strategies for trial wavefunctions and molecular structures, inputs for the density functional theory of van der Waals forces, and eventually neural networks which at least for small molecular systems seem to improve the accuracy of variational quantum Monte Carlo to the point where it outperforms other ab-initio quantum chemistry methods.

QMC-RD workshop group picture, Oct. 21, 2021, Rome, Italy
QMC-RD workshop group picture in front of the Enrico Fermi Research Center of via Panisperna, Rome, Italy, where the workshop was held on October 21-22, 2021.


The workshop intended to offer the QMC community a meeting opportunity to share and disseminate the most recent results both on the research and development of QMC methods, and on the theoretical-numerical investigation of selected physical systems.

Financially supported by Psi-K, Sapienza University of Rome, and CECAM, it was organized, in the occasion of his 60th birthday, by mentors and former students of Saverio Moroni, a sound condensed-matter theorist who has given key contributions to quantum Monte Carlo methods, to their application to a wealth of quantum fluids and chemical systems, and to their dissemination in Europe.

It took place at the Enrico Fermi Research Center, located in via Panisperna 89A, 00184 Rome, the famous building where Enrico Fermi and his group, ”the boys from via Panisperna”, gave crucial contributions to modern physics.


The event gathered, despite limitations still on for the COVID19 pandemic, scientists from thirteen countries all over the world to discuss the status and recent developments in the field of quantum Monte Carlo.  The logistics was kindly provided by the CREF (Centro Ricerche Enrico Fermi) which made available its premises and the technology to permit remote attendance, too.


The workshop spanned two days, organised in three topical sessions: New methods and algorithms (chaired by David Ceperley, University of Illinois at Urbana Champaign), Quantum fluids (chaired by Gaetano Senatore, University of Trieste) and Solid State Physics (chaired Lilia Boeri from the Sapienza University of Rome). Each of the session consisted of a set of 30-minute, each including some time for questions and discussion. All the talks received a good and lively feedback from the audience, including those given from the (few: 5 out of 19) remote invited speakers.


New methods and algorithms (chair: Ceperley)

  • Carleo:  Neural-network quantum states in continuous space
  • Foulkes: Approximating many-electron wave functions using deep neural networks
  • Sorella: The phase diagram of the Hubbard model by Variational Auxiliary-Field QMC
  • Baroni: Stochastic perturbation theory: a prequel to Reptation quantum Monte Carlo
  • Guidoni: Quantum Computing for Correlated Systems
  • Filippi: Variational principles and excited states in quantum Monte Carlo
  • Mitaš: Quantum Monte Carlo and spins: systems with spin-orbit interactions
  • Umrigar: Green’s functions for cross-node and fixed-node diffusion Monte Carlo

Quantum fluids (chair: Senatore)

  • Boninsegni: The (never ending?) search for exotic phases of helium on graphite
  • Holzmann: Quantum fluids: from helium to electrons
  • Fantoni: A quantum Monte Carlo method for nuclear matter
  • Gori-Giorgi: Noncovalent interactions from models for the Møller−Plesset adiabatic connection
  • Vitali: Ground and excited states of Fermi superfluids from QMC calculations
  • Pierleoni: Energy gap closure and metal-insulator transition in solid and fluid hydrogen with pressure
  • Casula: Phase diagram of high-pressure hydrogen including nuclear quantum effects

Solid state physics (chair: Boeri)

  • Grosso: The young Saverio: the years in Pisa
  • Attaccalite: Optical excitations in layered materials: the case of hexagonal boron nitride
  • De Palo: Long-range order in electron-hole bilayer with valley degeneracy
  • Varsano: Evidence of ideal excitonic insulator in MoS2 under pressure

In addition, at the end of the first day, we had a session with six posters contributed by in-person participants.


The talks were spanning a large landscape, from methodological aspects to applications, and that all contributions fueled active discussions within the audience. The public of the workshop was very heterogenous, extending from people with a long, acknowledged expertise in QMC to much younger students and postdocs. Such a mixture, which the social event further enhanced, certainly played an important role in the unquestionable success of the workshop.


As mentioned, this workshop was meant to be a tribute to Saverio Moroni and his role  in the development of quantum Monte Carlo methods. Its development confirmed that a couple generations of scientists have greatly benefitted from his scientific leadership and presently  contribute to this field of research.


This workshop was a good opportunity to gather a community which, for several decades, has been committed to the invention of new statistical and computational approaches to the solution of condensed-matter and physical-chemistry challenges, and to the development of existing ones. In all of their many different flavors, Quantum Monte Carlo methods take enormous benefit from the exploitation of their intrinsically parallel nature. The technological evolution and the availability of large-scale infrastructures has boosted the opportunity tof inventing, testing and improving algorithms based on stochastic methods for the resolution of a large variety of problems. In the context of HPC exploitation, the TREX Center of Excellence was presented during the poster session. It turned out that many of the participants are already involved in it, which clearly witnesses a structured connection between the HPC and the people working on QMC methods. A promising aspect, touched upon during the discussion, was the possibility of monitoring how beneficial, in the medium term, Quantum Computing might be to the topics discussed during this workshop.


Although the core businees of this workshop was a wide variety of continuum and lattice Quantum Monte Carlo methods, some detours on Density Functionals, Materials Science and, as mentioned, Quantum Computing also took place. Such a large view on diverse approaches amounted to a very valuable networking opportunity (much more so being one of the very first on-person international meetings after the COVID19 “isolation”) both for young researchers and more experienced people, to discuss and confront problems and solutions.


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