Project

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Simulation of strongly correlated quantum many-body systems with tensor network and Monte Carlo algorithms

Applicant Corboz Philippe
Number 136863
Funding scheme Ambizione
Research institution Institute for Theoretical Physics University of Amsterdam
Institution of higher education ETH Zurich - ETHZ
Main discipline Condensed Matter Physics
Start/End 01.10.2011 - 30.04.2014
Approved amount 385'010.00
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All Disciplines (3)

Discipline
Condensed Matter Physics
Other disciplines of Physics
Theoretical Physics

Keywords (7)

Tensor network algorithms; Strongly correlated quantum many-body systems; High-temperature superconductivity; Spin liquids; Monte Carlo methods; Hubbard model; Frustrated spin systems

Lay Summary (English)

Lead
Lay summary
One of the major goals in condensed matter physics is understanding the emergent properties  of a very large number of strongly interacting quantum particles, called strongly correlated quantum many-body systems (QMBS). The interplay between different type of interactions and quantum statistics gives rise to novel, exciting physics such as high-temperature superconductivity, quantum magnetism, the fractional quantum Hall effect, Mott insulators, or topological insulators. The theoretical study of these systems is very challenging, because typically standard analytical approaches fail for these systems, and thus accurate numerical simulations are essential. However, the usually most powerful numerical method, Quantum Monte Carlo, fails for many important models due to the so-called negative sign problem. As a consequence the properties of many models are still controversial, and it is therefore crucial to develop new accurate and efficient numerical tools to study these systems.

In this project I will focus on a new class of simulation techniques for QMBS that have been developed through combining ideas from quantum information theory and condensed matter physics: the so-called tensor network algorithms. The main idea is to efficiently represent quantum many-body states by a product of tensors. First results for the t-J model, an important model in the context of high-temperature superconductivity, show that the tensor network called PEPS (projected entangled-pair state) yields better energies than other variational approaches based on Gutzwiller projected ansatz wave functions (GWF).

To further improve upon these methods I will combine them with fixed-node Monte Carlo (FNMC) which yields the best variational wave function compatible with the nodal structure of an (input) guiding wave function. FNMC has been applied to the t-J model in the past, using GWF as guiding wave functions, which resulted in a considerable improvement of the variational energy. This new FN+PEPS method, which combines PEPS with fixed-node Monte Carlo, will be better than both PEPS and current fixed-node results, and thus define a new state-of-the-art variational method for the study of quantum many-body systems in two dimensions. I will apply this method to several important models in condensed matter physics where accurate studies so far have been severely limited by the sign problem. These simulations will help to shed new light into controversial, open questions such as:

- Do frustrated spin models such as the Heisenberg model on the kagome lattice and the J1 - J2 Heisenberg model on the square/honeycomb lattice give rise to a spin liquid phase? If yes, what is the nature of this phase? Does it exhibit topological order?

- What is the nature of the spin liquid that emerges in the Hubbard model on the honeycomb lattice? What happens if the system is doped?

- Does the t-J model and the Hubbard model reproduce the physics of high-temperature superconductors? Is there formation of stripes or phase separation at finite doping in the physically relevant parameter regime? What is the effect of higher-ranged interactions and hoppings? What is the mechanism leading to superconductivity?
Direct link to Lay Summary Last update: 21.02.2013

Responsible applicant and co-applicants

Employees

Publications

Publication
Crystals of bound States in the magnetization plateaus of the shastry-sutherland model.
Corboz Philippe, Mila Frédéric (2014), Crystals of bound States in the magnetization plateaus of the shastry-sutherland model., in Physical review letters, 112(14), 147203-147203.
Competing states in the SU(3) Heisenberg model on the honeycomb lattice: Plaquette valence-bond crystal versus dimerized color-ordered state
Corboz Philippe, Lajko Miklos, Penc Karlo, Mila Frederic, Laeuchli Andreas M. (2013), Competing states in the SU(3) Heisenberg model on the honeycomb lattice: Plaquette valence-bond crystal versus dimerized color-ordered state, in PHYSICAL REVIEW B, 87(19), 195113.
Competition between three-sublattice order and superfluidity in the quantum three-state Potts model of ultracold bosons and fermions on a square optical lattice
Messio Laura, Corboz Philippe, Mila Frédéric (2013), Competition between three-sublattice order and superfluidity in the quantum three-state Potts model of ultracold bosons and fermions on a square optical lattice, in Physical Review B - Condensed Matter and Materials Physics, 88(15), 155106.
Magnetization of SrCu2(BO3)(2) in Ultrahigh Magnetic Fields up to 118 T
Matsuda Y. H., Abe N., Takeyama S., Kageyama H., Corboz P., Honecker A., Manmana S. R., Foltin G. R., Schmidt K. P., Mila F. (2013), Magnetization of SrCu2(BO3)(2) in Ultrahigh Magnetic Fields up to 118 T, in PHYSICAL REVIEW LETTERS, 111(13), 041013.
Tensor network study of the Shastry-Sutherland model in zero magnetic field
Corboz Philippe, Mila Frederic (2013), Tensor network study of the Shastry-Sutherland model in zero magnetic field, in PHYSICAL REVIEW B, 87(11), 115144.
Comment on "Topological quantum phase transitions of attractive spinless fermions in a honeycomb lattice" by Poletti D. et al.
Corboz Philppe, Capponi Sylvain, Läuchli Andreas, Bauer Bela, Orus Roman (2012), Comment on "Topological quantum phase transitions of attractive spinless fermions in a honeycomb lattice" by Poletti D. et al., in EPL, 98(2), 27005-p1-27005-p2.
Simplex solids in SU(N) Heisenberg models on the kagome and checkerboard lattices
Corboz Philippe, Penc Karlo, Mila Frédéric, Läuchli Andreas M. (2012), Simplex solids in SU(N) Heisenberg models on the kagome and checkerboard lattices, in PHYSICAL REVIEW B, 86(4), 041106-1-041106-5.
Spin-orbital quantum liquid on the honeycomb lattice
Corboz Philippe, Lajko Miklos, Läuchli Andreas, Penc Karlo, Mila Frédéric (2012), Spin-orbital quantum liquid on the honeycomb lattice, in Physical Review X, 2, 041013.

Collaboration

Group / person Country
Types of collaboration
Dr. Roman Orus/MPQ Garching Germany (Europe)
- Publication
Miklos Lajko/Budapest University of Technology and Economics Hungary (Europe)
- Publication
Prof. Matthias Troyer/ETH Switzerland (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
- Research Infrastructure
Prof. Frederic Mila/EPFL Switzerland (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
Prof. Andreas Laeuchli/University of Innsbruck Austria (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
Karlo Penc/Budapest University of Technology and Economics Hungary (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
Sylvain Capponi/University of Toulouse France (Europe)
- Publication
Prof. T. M. Rice/ETH, Switzerland Switzerland (Europe)
- in-depth/constructive exchanges on approaches, methods or results
Bela Bauer/Station Q, Santa Barbara (from Sept 2011 on) United States of America (North America)
- Publication

Scientific events

Active participation

Title Type of contribution Title of article or contribution Date Place Persons involved
XVII. International Conference on Recent Progress in Many-Body Theories (MBT17) Talk given at a conference Simulation of strongly correlated systems in two dimensions with tensor network algorithms 08.09.2013 Rostock, Germany Corboz Philippe;
Theory Seminar Individual talk Tensor network simulations of exotic phases in SU(N) Heisenberg models 12.07.2013 Köln, Germany Corboz Philippe;
Topological Phases in Condensed Matter and Cold Atom Systems: towards quantum computations Talk given at a conference Introduction to tensor network methods 24.06.2013 Cargèse, France Corboz Philippe;
Emergence and Entanglement II Talk given at a conference Spin-orbital quantum liquid on the honeycomb lattice 06.05.2013 Perimeter Institute, Waterloo, Canada Corboz Philippe;
APS March meeting Talk given at a conference Spin-orbital quantum liquid on the honeycomb lattice 18.03.2013 Baltimore, United States of America Corboz Philippe;
Theory Seminar Individual talk Recent progress in the simulation of strongly correlated systems in two dimensions with tensor network algorithms 07.12.2012 ICFO, Castel-del-Fels (Barcelona), Spain Corboz Philippe;
Condensed Matter Theory Seminar Individual talk Tensor network studies of exotic phases in SU(N) Heisenberg models 29.11.2012 LMU, München, Germany Corboz Philippe;
Cooperative Quantum Dynamics and Its Control (CQDC2012) Talk given at a conference Simulation of strongly correlated systems in two dimensions with infinite projected entangled-pair states (iPEPS) 29.10.2012 Jülich, Germany, Germany Corboz Philippe;
Workshop on Mott Physics beyond Heisenberg Talk given at a conference Exotic phases in the symmetric Kugel-Khomskii model in two dimensions 26.06.2012 EPFL, Switzerland Corboz Philippe;
Networking tensor networks: many-body systems and simulations Talk given at a conference Recent progress with infinite projected entangled-pair states (iPEPS) 06.05.2012 Benasque, Spain Corboz Philippe;
DMRG Gathering 2012 Talk given at a conference Simulations of SU(N) Heisenberg models with iPEPS: simplex solid states 04.05.2012 University of Vienna, Austria Corboz Philippe;
Theory Colloquium Individual talk Simulation of strongly correlated systems in two dimensions with tensor network algorithms 26.03.2012 Universität Zürich, Switzerland Corboz Philippe;
Tensor Networks for Quantum Field Theories Talk given at a conference Simulation of Fermionic and Frustrated Systems with 2D Tensor Networks 24.10.2011 Perimeter Intitute for Theoretical Physics, Waterloo, Canada, Canada Corboz Philippe;
Workshop on Quantum Information in Quantum Many-body Physics Talk given at a conference Recent progress in the simulation of strongly correlated systems in two dimensions with tensor network algorithms 17.10.2011 CRM, Université de Montréal, Canada, Canada Corboz Philippe;


Abstract

The simulation of strongly correlated quantum many-body systems (QMBS) is one of the biggest challenges in computational physics. Accurate numerical studies are essential to gain insight into the physics of these systems. However, the most powerful simulation method, Quantum Monte Carlo (QMC), fails for important classes of systems (frustrated and fermionic models) due to the so-called negative sign problem. In order to make substantial progress in the understanding of QMBS, it is crucial to develop new accurate and efficient numerical tools for the cases where QMC fails.In this project I will focus on a new class of simulation techniques for QMBS that have been developed through combining ideas from quantum information theory and condensed matter physics: the so-called tensor network algorithms. The main idea is to efficiently represent quantum many-body states by a product of tensors. First results for the t-J model, an important model in the context of high-temperature superconductivity, show that the tensor network called PEPS (projected entangled-pair state) yields better energies than other variational approaches based on Gutzwiller projected ansatz wave functions (GWF).To further improve upon these methods I will combine them with fixed-node Monte Carlo (FNMC) which yields the best variational wave function compatible with the nodal structure of an (input) guiding wave function. FNMC has been applied to the t-J model in the past, using GWF as guiding wave functions, which resulted in a considerable improvement of the variational energy.This new FN+PEPS method, which combines PEPS with fixed-node Monte Carlo, will be better than both PEPS and current fixed-node results, and thus define a new state-of-the-art variational method for the study of quantum many-body systems in two dimensions. This method will also be a milestone in high-performance computing, since the algorithm requires highly-efficient C++ code, parallelized to many CPUs.I will apply this method to several important models in condensed matter physics where accurate studies so far have been severely limited by the sign problem. These simulations will help to shed new light into controversial, open questions such as:• Do frustrated spin models such as the Heisenberg model on the kagome lattice and the J1 - J2 Heisenberg model on the square/honeycomb lattice give rise to a spin liquid phase? If yes, what is the nature of this phase? Does it exhibit topological order?• What is the nature of the spin liquid that emerges in the Hubbard model on the honeycomb lattice? What happens if the system is doped?• Does the t-J model and the Hubbard model reproduce the physics of high- temperature superconductors? Is there formation of stripes or phase separation at finite doping in the physically relevant parameter regime? What is the effect of higher-ranged interactions and hoppings? What is the mechanism leading to superconductivity?
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