Project

Back to overview

Simulation of Correlated Quantum Many Body Systems

English title Simulation of Correlated Quantum Many Body Systems
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
Show all

All Disciplines (2)

Discipline
Theoretical Physics
Other disciplines of Physics

Keywords (7)

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

Lay Summary (English)

Lead
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

Responsible applicant and co-applicants

Employees

Publications

Publication
Superfluidity and density order in a bilayer extended Hubbard model
Vanhala Tuomas I., Baarsma Jildou E., Heikkinen Miikka O J, Troyer Matthias, Harju Ari, Törmä Päivi (2015), Superfluidity and density order in a bilayer extended Hubbard model, in Physical Review B - Condensed Matter and Materials Physics, 91(14), 144510.
Fermionic quantum critical point of spinless fermions on a honeycomb lattice
Wang Lei, Corboz Philippe, Troyer Matthias (2014), Fermionic quantum critical point of spinless fermions on a honeycomb lattice, in NEW JOURNAL OF PHYSICS, 16, 103008.
Ferromagnetism of a Repulsive Atomic Fermi Gas in an Optical Lattice: A Quantum Monte Carlo Study
Pilati S., Zintchenko I., Troyer M. (2014), Ferromagnetism of a Repulsive Atomic Fermi Gas in an Optical Lattice: A Quantum Monte Carlo Study, in PHYSICAL REVIEW LETTERS, 112(1), 011603.
Interaction effects on topological phase transitions via numerically exact quantum Monte Carlo calculations
Hung Hsiang-Hsuan, Chua Victor, Wang Lei, Fiete Gregory A. (2014), Interaction effects on topological phase transitions via numerically exact quantum Monte Carlo calculations, in PHYSICAL REVIEW B, 89(23), 235104.
Nonlocal quantum fluctuations and fermionic superfluidity in the imbalanced attractive hubbard model
Heikkinen M. O J, Kim D. H., Troyer M., Törmä P. (2014), Nonlocal quantum fluctuations and fermionic superfluidity in the imbalanced attractive hubbard model, in Physical Review Letters, 113(18), 185301.
Renyi Entanglement Entropy of Interacting Fermions Calculated Using the Continuous-Time Quantum Monte Carlo Method
Wang Lei, Troyer Matthias (2014), Renyi Entanglement Entropy of Interacting Fermions Calculated Using the Continuous-Time Quantum Monte Carlo Method, in PHYSICAL REVIEW LETTERS, 113(11), 110401.
Seeing Hofstadter's butterfly in atomic Fermi gases
Wang Lei, Troyer Matthias (2014), Seeing Hofstadter's butterfly in atomic Fermi gases, in PHYSICAL REVIEW A, 89(1), 011603.
Thermodynamics and Magnetic Properties of the Anisotropic 3D Hubbard Model
Imriska Jakub, Iazzi Mauro, Wang Lei, Gull Emanuel, Greif Daniel, Uehlinger Thomas, Jotzu Gregor, Tarruell Leticia, Esslinger Tilman, Troyer Matthias (2014), Thermodynamics and Magnetic Properties of the Anisotropic 3D Hubbard Model, in PHYSICAL REVIEW LETTERS, 112(11), 115301.
Thermodynamics and Magnetic Properties of the Anisotropic 3D Hubbard Model
Imriska Jakub, Iazzi Mauro, Wang Lei, Gull Emanuel, Greif Daniel, Uehlinger Thomas, Jotzu Gregor, Tarruell Leticia, Esslinger Tilman, Troyer Matthias (2014), Thermodynamics and Magnetic Properties of the Anisotropic 3D Hubbard Model, in PHYSICAL REVIEW LETTERS, 112(11), 115301.
Topological phase transition in the Hofstadter-Hubbard model
Wang Lei, Hung Hsiang-Hsuan, Troyer Matthias (2014), Topological phase transition in the Hofstadter-Hubbard model, in PHYSICAL REVIEW B, 90(20), 205111.
Double transfer through Dirac points in a tunable honeycomb optical lattice
Uehlinger Thomas, Greif Daniel, Jotzu Gregor, Tarruell Leticia, Esslinger Tilman, Wang Lei, Troyer Matthias (2013), Double transfer through Dirac points in a tunable honeycomb optical lattice, in EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS, 217(1), 121-133.
Néel temperature and thermodynamics of the half-filled three-dimensional Hubbard model by diagrammatic determinant Monte Carlo
Kozik Evgeny V., Burovski Evgeni A., Scarola Vito W., Troyer Matthias L. (2013), Néel temperature and thermodynamics of the half-filled three-dimensional Hubbard model by diagrammatic determinant Monte Carlo, in Physical Review B - Condensed Matter and Materials Physics, 87(20), 205102.
One-dimensional Bose-Hubbard model far from equilibrium
Pižorn Iztok (2013), One-dimensional Bose-Hubbard model far from equilibrium, in Physical Review A - Atomic, Molecular, and Optical Physics, 88(4), 043635.
Pomeranchuk Cooling of SU(2N) Ultracold Fermions in Optical Lattices
Cai Zi, Hung Hsiang-hsuan, Wang Lei, Zheng Dong, Wu Congjun (2013), Pomeranchuk Cooling of SU(2N) Ultracold Fermions in Optical Lattices, in PHYSICAL REVIEW LETTERS, 110(22), 220401.
Proposal for Direct Measurement of Topological Invariants in Optical Lattices
Wang Lei, Soluyanov Alexey, Troyer Matthias (2013), Proposal for Direct Measurement of Topological Invariants in Optical Lattices, in Physical Review Letters, 110, 166802.
Proposal for direct measurement of topological invariants in optical lattices
Wang Lei, Soluyanov Alexey A., Troyer Matthias L. (2013), Proposal for direct measurement of topological invariants in optical lattices, in Physical Review Letters, 110(16), 166802.
Quantum magnetic properties of the SU(2N) Hubbard model in the square lattice: A quantum Monte Carlo study
Cai Zi, Hung HsiangHsuan, Wang Lei, Wu Congjun (2013), Quantum magnetic properties of the SU(2N) Hubbard model in the square lattice: A quantum Monte Carlo study, in Physical Review B - Condensed Matter and Materials Physics, 88(12), 125108.
Supersymmetric multicritical point in a model of lattice fermions
Bauer Bela, Huijse Liza, Berg Erez A Torres, Troyer Matthias, Schoutens Kareljan (2013), Supersymmetric multicritical point in a model of lattice fermions, in Physical Review B - Condensed Matter and Materials Physics, 87(16), 165145.
Topological charge pumping in a one-dimensional optical lattice
Wang Lei, Troyer Matthias L., Dai Xi (2013), Topological charge pumping in a one-dimensional optical lattice, in Physical Review Letters, 111(2), 026802.
Topological phase transition in a generalized Kane-Mele-Hubbard model: A combined quantum Monte Carlo and Green's function study
Hung Hsiang-Hsuan, Wang Lei, Gu Zheng-Cheng, Fiete Gregory A. (2013), Topological phase transition in a generalized Kane-Mele-Hubbard model: A combined quantum Monte Carlo and Green's function study, in PHYSICAL REVIEW B, 87(12), 121113(R).
Topological phase transition in a generalized Kane-Mele-Hubbard model: A combined quantum Monte Carlo and Green's function study
Hung Hsiang-Hsuan, Wang Lei, Gu Zheng-Cheng, Fiete Gregory A. (2013), Topological phase transition in a generalized Kane-Mele-Hubbard model: A combined quantum Monte Carlo and Green's function study, in PHYSICAL REVIEW B, 87(12), 121113.
Tree tensor networks and entanglement spectra
Pižorn Iztok, Verstraete Frank, Konik Robert M. (2013), Tree tensor networks and entanglement spectra, in Physical Review B - Condensed Matter and Materials Physics, 88(19), 195102.
Density functional theory for atomic Fermi gases
Ma Ping Nang, Pilati Sebastiano, Troyer Matthias, Dai Xi (2012), Density functional theory for atomic Fermi gases, in NATURE PHYSICS, 8(8), 601-605.
Interaction-induced topological phase transition in the Bernevig-Hughes-Zhang model
Wang Lei, Dai Xi, Xie Xincheng (2012), Interaction-induced topological phase transition in the Bernevig-Hughes-Zhang model, in EPL, 98(5), 57001.
Interaction-induced topological phase transition in the Bernevig-Hughes-Zhang model
Wang Lei, Dai Xi, Xie X. C. (2012), Interaction-induced topological phase transition in the Bernevig-Hughes-Zhang model, in EPL, 98(5), 57001.
Pole expansion of self-energy and interaction effect for topological insulators
Wang L, Jiang H, Dai X, Xie XC (2012), Pole expansion of self-energy and interaction effect for topological insulators, in Physical Review B - Condensed Matter and Materials Physics, 85(23), 235135.
Pole expansion of self-energy and interaction effect for topological insulators
Wang Lei, Jiang Hua, Dai Xi, Xie Xincheng (2012), Pole expansion of self-energy and interaction effect for topological insulators, in Physical Review B - Condensed Matter and Materials Physics, 85(23), 235135.
Quantum magnetic properties of the SU(2N) Hubbard model in the square lattice: a quantum Monte Carlo study
Cai Zi, Hung Hsiang-Hsuan, Wang Lei, Wu Congjun (2012), Quantum magnetic properties of the SU(2N) Hubbard model in the square lattice: a quantum Monte Carlo study, in arXiv, 1207.6843.

Collaboration

Group / person Country
Types of collaboration
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

Scientific events

Active participation

Title Type of contribution Title of article or contribution Date Place Persons involved
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 with the public

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

Associated projects

Number Title Start Funding scheme
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)

Abstract

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.
-