## Contact

Swiss National Science Foundation (SNSF)

Wildhainweg 3P.O. Box

CH-3001 Bern

Phone +41 31 308 22 22

English title | Simulation of Correlated Quantum Many Body Systems |
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Applicant | Troyer Matthias |

Number | 140224 |

Funding scheme | Project funding (Div. I-III) |

Research institution | Institut für Theoretische Physik ETH Zürich |

Institution of higher education | ETH Zurich - ETHZ |

Main discipline | Theoretical Physics |

Start/End | 01.04.2012 - 31.03.2015 |

Approved amount | 555'000.00 |

Discipline |
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Theoretical Physics |

Other disciplines of Physics |

condensed matter physics; Monte Carlo simulations; computational physics; computer simulations of quantum systems; fermion sign problem; quantum phase transitions; statistical physics

Lead |
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Lay summary |

Strong interactions between the electrons in some materials cause interesting electronic and magnetic properties that are very hard to understand theoretically. Here progress can be made by using another physical system, gases of ultra cold atoms, to mimic the properties of electrons in a solid. Such ultra cold gases are a much simpler and cleaner system than electrons in a complicated material and thus provide an ideal testing ground for new numerical methods to study interacting quantum systems. The goal of the current project is to apply methods designed for the simulation of electrons in solids to the simulation of these ultra cold gases, to then improve these methods by comparing them to controlled experiments on, and to finally apply the improved methods again to electrons. |

Direct link to Lay Summary | Last update: 21.02.2013 |

Name | Institute |
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Publication |
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Superfluidity and density order in a bilayer extended Hubbard model |

Fermionic quantum critical point of spinless fermions on a honeycomb lattice |

Ferromagnetism of a Repulsive Atomic Fermi Gas in an Optical Lattice: A Quantum Monte Carlo Study |

Interaction effects on topological phase transitions via numerically exact quantum Monte Carlo calculations |

Nonlocal quantum fluctuations and fermionic superfluidity in the imbalanced attractive hubbard model |

Renyi Entanglement Entropy of Interacting Fermions Calculated Using the Continuous-Time Quantum Monte Carlo Method |

Seeing Hofstadter's butterfly in atomic Fermi gases |

Thermodynamics and Magnetic Properties of the Anisotropic 3D Hubbard Model |

Thermodynamics and Magnetic Properties of the Anisotropic 3D Hubbard Model |

Topological phase transition in the Hofstadter-Hubbard model |

Double transfer through Dirac points in a tunable honeycomb optical lattice |

Néel temperature and thermodynamics of the half-filled three-dimensional Hubbard model by diagrammatic determinant Monte Carlo |

One-dimensional Bose-Hubbard model far from equilibrium |

Pomeranchuk Cooling of SU(2N) Ultracold Fermions in Optical Lattices |

Proposal for Direct Measurement of Topological Invariants in Optical Lattices |

Proposal for direct measurement of topological invariants in optical lattices |

Quantum magnetic properties of the SU(2N) Hubbard model in the square lattice: A quantum Monte Carlo study |

Supersymmetric multicritical point in a model of lattice fermions |

Topological charge pumping in a one-dimensional optical lattice |

Topological phase transition in a generalized Kane-Mele-Hubbard model: A combined quantum Monte Carlo and Green's function study |

Topological phase transition in a generalized Kane-Mele-Hubbard model: A combined quantum Monte Carlo and Green's function study |

Tree tensor networks and entanglement spectra |

Density functional theory for atomic Fermi gases |

Interaction-induced topological phase transition in the Bernevig-Hughes-Zhang model |

Interaction-induced topological phase transition in the Bernevig-Hughes-Zhang model |

Pole expansion of self-energy and interaction effect for topological insulators |

Pole expansion of self-energy and interaction effect for topological insulators |

Quantum magnetic properties of the SU(2N) Hubbard model in the square lattice: a quantum Monte Carlo study |

Group / person | Country |
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Types of collaboration |
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ETH Zürich | Switzerland (Europe) |

- Publication |

Chinese Academy of Sciences | China (Asia) |

- in-depth/constructive exchanges on approaches, methods or results - Publication - Exchange of personnel |

Profs. N. Prokof'ev andf B. Svistunov, UMass Amherst | United States of America (North America) |

- in-depth/constructive exchanges on approaches, methods or results - Publication |

Title | Type of contribution | Title of article or contribution | Date | Place | Persons involved |
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CECAM Workshop on Computational Many-Body Physics in the Era of Artificial Gauge Fields | Talk given at a conference | Simulation of Hubbard Models in the Era of Synthetic Gauge Field | 08.04.2015 | Munich, Germany | Wang Lei; |

INT Conference | Talk given at a conference | Classical and quantum simulation of quantum systems | 30.03.2015 | Seattle, WA, United States of America | Troyer Matthias; |

Frontiers in Quantum Simulation with Cold Atoms | Poster | Simulation of Hubbard Models in the Era of Synthetic Gauge Field | 23.03.2015 | Seattle, United States of America | Wang Lei; |

Aspen Winter Conference | Talk given at a conference | Adiabatic and non-adiabatic state preparation | 22.03.2015 | Aspen, CO, United States of America | Troyer Matthias; |

APS March Meeting | Talk given at a conference | Fidelity Susceptibility Made Simple | 02.03.2015 | San Antonio, TX, United States of America | Wang Lei; |

Workshop on Quantum Simulations, | Talk given at a conference | Surprises in simulation of quantum phase transitions | 22.02.2015 | Benasque, Spain | Wang Lei; |

Seminar | Individual talk | Simulation of fermionic quantum gases | 22.10.2014 | Toronto, Canada | Troyer Matthias; |

Simons Foundation Meeting on the Many Electron Problem | Talk given at a conference | Competing order in the 2D t-J model | 04.09.2014 | New York, United States of America | Troyer Matthias; |

Numerical and analytical methods for strongly correlated systems | Poster | Renyi entanglement entropy of interacting fermions | 24.08.2014 | Benasque, Spain | Wang Lei; |

Seminar | Individual talk | Spinless fermions on a honeycomb lattice: from quantum criticality to topological superconductors | 08.07.2014 | Würzburg, Germany | Wang Lei; |

KITPC Program on Precision Many-body Physics of Strongly correlated Quantum Matter | Talk given at a conference | Spinless fermions on a honeycomb lattice: from quantum criticality to topological superconductors | 05.05.2014 | Beijing, China | Wang Lei; |

DPG Frühjahrstagung | Talk given at a conference | Quantum Computing and Strongly Correlated Materials | 31.03.2014 | Dresden, Germany | Troyer Matthias; |

Colloquium | Individual talk | Validation of quantum devices | 28.03.2014 | Princeton University, United States of America | Troyer Matthias; |

Seminar | Individual talk | Validation of quantum devices | 19.03.2014 | RIKEN, Tokyo, Japan | Troyer Matthias; |

QIP | Talk given at a conference | Classical simulations of complex quantum systems | 07.02.2014 | Barcelona, Spain | Troyer Matthias; |

QSIT meeting | Talk given at a conference | Quantum annealing and the D-Wave devices | 06.02.2014 | Arosa, Switzerland | Troyer Matthias; |

QSIT winter school | Talk given at a conference | Numerical simulation of quantum many body systems | 03.02.2014 | Arosa, Switzerland | Troyer Matthias; |

Colloquium | Individual talk | Validation of quantum devices | 15.01.2014 | University of Michiga, Ann Arbor, United States of America | Troyer Matthias; |

Conference on quantum computing | Talk given at a conference | Simulating classically-intractable quantum systems on (small) quantum computers | 10.12.2013 | IBM, Yorktown Heights, United States of America | Troyer Matthias; |

Seminar | Individual talk | Numerical simulations of bosons and fermions in 3D optical lattices | 20.11.2013 | Center for Theoretical Sciences, Taiwan | Ma Ping Nang; |

Seminar | Individual talk | Numerical simulations of bosons and fermions in 3D optical lattices | 01.11.2013 | Center for Quantum Technologies, Singapore | Ma Ping Nang; |

Colloquium | Individual talk | Validation of quantum devices | 17.10.2013 | MIT, United States of America | Troyer Matthias; |

Swiss-Japanese meeting | Talk given at a conference | Magnetism in ultracold atomic Fermi gases | 04.10.2013 | EPFL, Switzerland | Troyer Matthias; |

FOR1807 Fall school | Talk given at a conference | Quantum Monte Carlo methods | 30.09.2013 | Würzburg, Germany | Troyer Matthias; |

FOR1807 Fall school | Talk given at a conference | The ALPS project | 30.09.2013 | Würzburg, Germany | Troyer Matthias; |

Theoretical Physics Workshop and Summer School: Models of Modern Physics | Talk given at a conference | Introduction to path integral Monte Carlo | 08.09.2013 | Svit, Slovakia | Imriska Jakub; |

BEC 2013 | Poster | Seeing Hofstadter’s Butterfly in the Atomic Fermi Gases | 07.09.2013 | San Feliu, Spain | Wang Lei; |

BEC 2013 | Talk given at a conference | Quantum annealing from superconducting devices to ultracold atoms | 07.09.2013 | San Feliu, Spain | Troyer Matthias; |

ICQM Seminar | Individual talk | Density functional theory for static and dynamic properties of cold atomic gases | 08.08.2013 | Beijing University, China | Wang Lei; |

Colloquium | Individual talk | Validation of quantum devices | 08.08.2013 | Aspen Center for Physics, United States of America | Troyer Matthias; |

The 7th national conference on cold atom physics and quantum information for young researchers | Talk given at a conference | Topological charge pumping of cold atoms | 27.07.2013 | Anhui, China | Wang Lei; |

Aspen Summer Workshop | Talk given at a conference | Validation of quantum devices | 15.07.2013 | Aspen, CO, USA, United States of America | Troyer Matthias; |

Workshop on quantum Monte Carlo methods | Talk given at a conference | Continuous time quantum Monte Carlo simulations | 04.07.2013 | Seattle, United States of America | Troyer Matthias; |

Topological Phases in Condensed Matter and Cold Atom Systems: towards quantum computations | Talk given at a conference | Topological charge pumping of cold atoms | 24.06.2013 | Cargese, France | Wang Lei; |

Workshop on Software Infrastructure for Reproducibility in Science | Talk given at a conference | Reproducibility in quantum physics | 30.05.2013 | New York, United States of America | Troyer Matthias; |

DARPA OLE Meeting | Talk given at a conference | Topological charge pumping of cold atoms | 29.05.2013 | San Francisco, United States of America | Wang Lei; |

Tensor network algorithms in computational physics and numerical analysis | Talk given at a conference | Real Time Evolution at Finite Temperatures with Operator Space Matrix Product States | 15.05.2013 | ETH Zurich, Switzerland | Pizorn Iztok; |

Quantum optics group seminar | Talk given at a conference | Topological charge pumping of cold atoms | 23.04.2013 | LMU, Germany | Wang Lei; |

QSIT lunch seminar | Individual talk | Topological charge pumping of cold atoms | 02.04.2013 | ETH Zurich, Switzerland | Wang Lei; |

APS March Meeting | Talk given at a conference | Topological charge pumping of cold atoms | 18.03.2013 | Baltimore, United States of America | Wang Lei; |

Finite-temperature non-equilibrium superfluid systems | Talk given at a conference | Simulating dynamics and topological phases of cold fermionic gases | 16.02.2013 | Queenstown, New Zealand | Wang Lei; |

Aspen Winter Conference | Talk given at a conference | Performance of a quantum annealer: experiments on D-Wave One (and Two) | 13.01.2013 | Aspen, CO, USA, United States of America | Troyer Matthias; |

Seminar | Individual talk | Ab-initio simulations of fermionic quantum gases | 08.01.2013 | PSI, Switzerland | Troyer Matthias; |

Workshop on orbital physics in cold atom systems | Talk given at a conference | Topological charge pumping of cold atoms | 05.01.2013 | Beijing, China, China | Wang Lei; |

Colloquium | Individual talk | Beyond classical computing: validating quantum devices | 05.12.2012 | Google, Venice Beach, CA, United States of America | Troyer Matthias; |

DARPA OLE Review Meeting | Talk given at a conference | Passing through Dirac points | 26.11.2012 | Miami, FL, USA, United States of America | Troyer Matthias; |

Colloquium | Individual talk | Excited and Mixed states with Tensor Networks | 16.08.2012 | Instituto de ciencias fisicas, UNAM Cuernavaca, Mexico | Pizorn Iztok; |

The 6th Workshop of Cold Atom and Quantum Information for Young Scholars | Talk given at a conference | Density functional theory for static and dynamic properties of cold atomic gases | 14.08.2012 | Jinhua, China, China | Wang Lei; |

Open many body systems, quantum computing and correlations, classical and quantum. | Individual talk | Entanglement of quasiparticle excited states | 08.08.2012 | UNAM, Cuernavaca, Mexico | Pizorn Iztok; |

Workshop on Quantum Simulations with Ultracold Atom | Poster | Density functional theory for static and dynamic properties of cold atomic gases | 16.07.2012 | Trieste, Italy, Italy | Wang Lei; |

PASC Junior Retreat | Talk given at a conference | Poster | 09.07.2012 | Mannedorf, Switzerland | Wang Lei; |

QSIT Meeting | Talk given at a conference | Density functional theory for static and dynamic properties of cold atomic gases | 17.06.2012 | Ascona, Switzerland, Switzerland | Wang Lei; |

DAMOP Meeting | Talk given at a conference | Quantum Monte Carlo simulations and thermometry in ultracold quantum gases | 04.06.2012 | Anaheim, CA, USA, United States of America | Troyer Matthias; |

Summer school | Talk given at a conference | Quantum Monte Carlo methods | 28.05.2012 | Sherbrooke, QC, Canada, Canada | Troyer Matthias; |

Seminar | Individual talk | Ab-initio simulations of fermionic quantum gases | 16.05.2012 | Columbia University, United States of America | Troyer Matthias; |

Seminar | Individual talk | Ab-initio simulations of fermionic quantum gases | 11.05.2012 | Universität Frankfurt, Germany | Troyer Matthias; |

Communication | Title | Media | Place | Year |
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Talks/events/exhibitions | Validation of quantum devices | International | 2014 |

Number | Title | Start | Funding scheme |
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159411 | Classical and Quantum Simulation of Quantum Many Body Systems | 01.04.2015 | Project funding (Div. I-III) |

124538 | Simulation of Novel Phases in Correlated Quantum Systems | 01.04.2009 | Project funding (Div. I-III) |

In this project we will continue simulations of novel phases and phase transitions in correlated quantum systems, focusing on correlated fermions in two and three dimensions. While the properties of weakly interacting materials are fairly well understood and can be simulated with high accuracy, the calculation of properties of correlated materials remains a big and important challenge. Strong quantum effects give rise to a plethora of fascinating phenomena and new methodological developments are needed for their understanding. Over the past years we have developed new algorithmic approaches, such as continuous time quantum Monte Carlo (QMC) methods for bosonic and fermionic quantum many body problems. These new methods provide performance improvements of many orders of magnitude compared to the previous state of the art methods. Combined with the power of new massively parallel supercomputers they will allow more accurate simulations of fermionic systems. We plan to address three problems. The first are simulations of lattice models such as the Hubbard model and its variants. These appear both as microscopic models for ultracold atomic gases in optical lattices and as effective models for strongly correlated materials. Specific simulations will include the equation of state of ultracold fermionic gases in optical lattices and the calculation of the phase diagram of extended Hubbard models. Combining bosonic and fermionic versions of the dynamical mean field theory we also plan to investigate Bose-Fermi mixtures. A second line of approach is the development of a Kohn-Sham density-functional theory (DFT) for ultracold atomic gases. DFT, based on density functional for the electron gas, is the main workhorse for materials simulation, but it is challenging to derive and test functionals for the strongly correlated regime. With a DFT method for atomic gases we will be able to both solve challenging problems in ultracold atomic gases, for the ground state as well as non-equilibrium dynamics. Potentially more importantly, we will be able to test and improve various approaches for hybrid functionals for the strongly correlated regime much better than in condensed matter materials.As a third line of research, we will perform ab-initio simulations of semiconductor heterostructures to derive realistic device-dependent effective Hamiltonians for the fractional quantum Hall effect, and then solve those models by large-scale exact diagonalization to investigate the potential for exotic non-Abelian quantum Hall states, and the dependence of the occurrence of such states on device parameters.

Swiss National Science Foundation (SNSF)

Wildhainweg 3P.O. Box

CH-3001 Bern

Phone +41 31 308 22 22

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