## Contact

Swiss National Science Foundation (SNSF)

Wildhainweg 3P.O. Box

CH-3001 Bern

Phone +41 31 308 22 22

English title | Lattice Gauge Theory: Improvement, Extension, and Dualization |
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Applicant | Wiese Uwe-Jens |

Number | 153245 |

Funding scheme | Project funding |

Research institution | Institut für Theoretische Physik Universität Bern |

Institution of higher education | University of Berne - BE |

Main discipline | Theoretical Physics |

Start/End | 01.04.2014 - 31.03.2017 |

Approved amount | 352'936.00 |

improved actions; lattice gauge theory; self-adjoint extensions

Lead |
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Die fundamentalen Wechselwirkungen zwischen den elementaren Bausteinen der Materie werden durch sogenannte Eichtheorien beschrieben. Die starke Wechselwirkung zwischen Quarks und Gluonen, die den Atomkern im Inneren zusammenhaelt, wird durch die Eichtheorie der Quantenchromodynamik (QCD) beschrieben. Die Loesung dieser sehr komplexen Theorie erfordert umfangreiche numerische Berechnungen mit Hilfe der sogenannten Gitterregularisierung. |

Lay summary |

In diesem Projekt sollen einerseits Methoden entwickelt werden, die die Durchfuehrung numerischer Rechnungen im Rahmen der Gitter-QCD erleichtern. Andererseits wird eine alternative Formulierung von Gitter-Eichtheorien, im Rahmen sogenannter Quantenlink-Modelle, untersucht, die es erlaubt, Probleme der Elementarteilchenphysik mit Methoden der Atomphysik und Quantenoptik zu bearbeiten. Zu diesem Zweck sollen ultra-kalte Atome in einem optischen Gitter so manipuliert werden, dass sie sich aehnlich wie Quarks und Gluonen verhalten. Ein Ziel solcher Quantensimulationen besteht darin, Probleme der Quark und Gluon Dynamik, wie z.B. das Innere von Neutronensternen, besser zu verstehen als es mit den Standardmethoden der Gittereichtheorie moeglich ist. In diesem Projekt sollen wichtige theoretische Grundlagen gelegt werden, die die Konstruktion solcher Quantensimulatoren fuer dynamische Eichtheorien erleichtern sollen. |

Direct link to Lay Summary | Last update: 31.03.2014 |

Name | Institute |
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Publication |
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An improved single-plaquette gauge action |

CP(N−1) quantum field theories with alkaline-earth atoms in optical lattices |

Doubled lattice Chern–Simons–Yang–Mills theories with discrete gauge group |

Dynamics of dissipative Bose-Einstein condensation |

Finite-Volume Energy Spectrum, Fractionalized Strings, and Low-Energy Effective Field Theory for the Quantum Dimer Model on the Square Lattice |

Graphical tensor product reduction scheme for the Lie algebras so(5)=sp(2), su(3), and g(2) |

Proposal for the Quantum Simulation of the CP(2) Model on Optical Lattices |

The CP(2) Model at Non-Zero Chemical Potential |

From doubled Chern-Simons-Maxwell lattice gauge theory to extensions of the toric code |

Real-time dynamics of open quantum spin systems driven by dissipative processes |

Real-time simulation of nonequilibrium transport of magnetization in large open quantum spin systems driven by dissipation |

Crystalline Confinement |

Holes Localized on a Skyrmion in a Doped Antiferromagnet on the Honeycomb Lattice: Symmetry Analysis |

Interfaces, Strings, and a Soft Mode in the Square Lattice Quantum Dimer Model |

O(N) Models with Topological Lattice Actions |

Quantum Simulation of Non-Abelian Lattice Gauge Theories |

Real-Time Simulation of Large Open Quantum Spin Systems driven by Dissipation |

Towards Quantum Simulating QCD |

Two-dimensional Lattice Gauge Theories with Superconducting Quantum Circuits |

Group / person | Country |
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Types of collaboration |
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Prof. Christoph Hofmann, Colima University | Mexico (North America) |

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

Prof. Wolfgang Bietenholz, UNAM Mexico City | Mexico (North America) |

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

Dr. Michele Pepe, INFN Milano | Italy (Europe) |

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

Prof. Kieran Holland, University of the Pacific, Stockton | 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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International Workshop on the Sign Problem in QCD and Beyond (SIGN 2017) | Talk given at a conference | Moderator of the Discussion Session and Discussion Leader of the Rump Session | 20.03.2017 | Seattle, United States of America | Wiese Uwe-Jens; |

632. WE-Heraeus-Seminar: Gauge Field Dynamics with Ultracold Gas Systems | Talk given at a conference | Quantum link models for quantum simulation of gauge theories | 12.12.2016 | Bad Honnef, Germany | Wiese Uwe-Jens; |

34th International Symposium on Lattice Field Theory (LATTICE 2016) | Talk given at a conference | The CP(2) Model at Nonzero Chemical Potential | 24.07.2016 | Southampton, Great Britain and Northern Ireland | Evans Wynne; |

Origin of Mass 2016 | Talk given at a conference | Doubled Abelian and non-Abelian Chern-Simons Gauge Theories on the Lattice | 30.05.2016 | Odense, Denmark | Wiese Uwe-Jens; |

Workshop on "Quantum Simulation with Cold Matter and Photons" | Talk given at a conference | Atomic quantum simulation of Abelian and non-Abelian gauge theories | 08.02.2016 | Brüssel, Belgium | Wiese Uwe-Jens; |

SM&FT - The XVI Workshop on Statistical Mechanics and nonperturbative Field Theory | Talk given at a conference | Real-time simulation of large open quantum spin systems driven by dissipation | 09.11.2015 | Bari, Italy | Wiese Uwe-Jens; |

ECT Workshop 'Advances in Diagrammatic Monte Carlo Methods for Quantum Field Theory Calculations in Nuclear-, Particle-, and Condensed Matter Physics' | Talk given at a conference | Real-time simulation of large open quantum spin systems driven by dissipation | 05.10.2015 | Trento, Italy | Wiese Uwe-Jens; |

SIGN 2015 Workshop | Talk given at a conference | Addressing Sign Problems by Quantum Simulation | 29.09.2015 | Debrecen, Hungary | Wiese Uwe-Jens; |

595th Int. WE-Heraeus-Seminar on 'Cold Atoms meet Quantum Field Theory' | Talk given at a conference | Atomic Quantum Simulation of Abelian and non-Abelian Gauge Theories (U.-J. Wiese) From Chern-Simons-Maxwell Lattice Gauge Theory to the Toric Code (N. Vlasii) | 06.07.2015 | Bad Honnef, Germany | Vlasii Nadiia; Wiese Uwe-Jens; |

Understanding Stronly Coupled Systems in High Energy and Condensed Matter Physics | Talk given at a conference | Atomic Quantum Simulation of Abelian and non-Abelian Gauge Theories | 24.05.2015 | Aspen, United States of America | Wiese Uwe-Jens; |

Frontier in Quantum Simulations with Cold Atoms (INT-15-1) | Talk given at a conference | Tutorial, Quantum link models for the quantum simulation of dynamical gauge theories (Wiese), From Chern-Simons-Maxwell Theory on the Lattice to the Toric Code (Vlasii) | 23.03.2015 | Seattle, United States of America | Wiese Uwe-Jens; Vlasii Nadiia; |

Winter School: Intersection between QCD and Condensed Matter (Lectures) | Talk given at a conference | Quantum link models and quantum simulation of gauge theories | 01.03.2015 | Schladming, Austria | Wiese Uwe-Jens; |

Workshop on Quantum Simulations | Talk given at a conference | Atomic Quantum Simulation of Abelian and non-Abelian Gauge Theories | 22.02.2015 | Benasque, Spain | Wiese Uwe-Jens; |

Quantum Critical Matter - from Atoms to Bulk (QCM14) | Poster | Interfaces, Strings and a Soft Mode in the Square Lattice Quantum Dimer Model | 18.08.2014 | Obergurgl, Austria | Widmer Philippe; |

Gordon Research Conference and Quantum Science Gordon Research Seminar | Talk given at a conference | Atomic Quantum Simulation of Abelian and non-Abelian Gauge Theories | 27.07.2014 | Boston, United States of America | Wiese Uwe-Jens; |

Facing Strong Dynamics | Talk given at a conference | Classical and Quantum Simulation of Gauge Theories | 02.06.2014 | Liselund Castle, Denmark | Wiese Uwe-Jens; |

XXIV Quark Matter | Talk given at a conference | New theoretical developments for the physics of strongly coupled systems | 19.05.2014 | Darmstadt, Germany | Wiese Uwe-Jens; |

PPCM Workshop | Talk given at a conference | Classical and Quantum Simulation of Gauge Theories in Particle and Condensed Matter Physics | 08.05.2014 | Boston, United States of America | Wiese Uwe-Jens; |

Number | Title | Start | Funding scheme |
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140424 | Lattice Field Theory: from Classical to Quantum Simulation | 01.04.2012 | Project funding |

172616 | Nonperturbative Problems in Particle, Condensed Matter, and Quantum Information Physics | 01.04.2017 | Project funding |

140424 | Lattice Field Theory: from Classical to Quantum Simulation | 01.04.2012 | Project funding |

Lattice gauge theories play an important role in several areas of physics. In particle physics, Wilson's lattice Quantum Chromodynamics (QCD) describes the strong interactions between quarks and gluons beyond perturbation theory. In condensed matter physics, quantum dimer models are lattice gauge theories that can describe spin liquid phases of strongly correlated electron systems, and Kitaev's toric code is a lattice gauge theory with applications to quantum information theory.Quantum link models provide an alternative non-perturbative formulation of gauge field theories including QCD, which I developed a long time ago in collaboration with Shailesh Chandrasekharan. In fact, quantum dimer models as well as the toric code represent specific U(1) or Z(2) quantum link models. Quantum links thus provide a unified description of gauge theories with applications in particle and condensed matter physics, as well as in quantum information theory. In the unconventional quantum link model regularization, classical gluon fields emerge dynamically via the dimensional reduction of fundamental discrete quantum degrees of freedom. Just as Wilson's group-valued SU(N) parallel transporters, quantum links are NxN matrices. However, their matrix elements are not just complex numbers, but non-commuting operators. In this sense, quantum links are gauge covariant generalizations of quantum spins. Their low-energy collective dynamics in a (4+1)-d non-Abelian Coulomb phase give rise to the 4-d gluon field as an emergent concept. Using quantum variables rather than classical fields can have both conceptual and algorithmic advantages beyond perturbation theory. For example, using an unconventional regularization based on SU(N) quantum spin ladders, we have been able to simulate CP(N-1) models at both non-zero chemical potential and at non-zero vacuum angle theta, which is impossible with standard lattice field theory techniques due to very severe sign and complex action problems. While continuous progress is being made in applications of Wilson's lattice QCD, the sign and complex action problems arising at non-zero quark chemical potential and in real-time evolution remain far beyond reach of classical computational methods.A major new idea underlying my previous SNF funded project "Lattice Field Theory: from Classical to Quantum Simulation'' was to use quantum link models to construct quantum simulators for dynamical Abelian and non-Abelian gauge fields with applications in both particle and condensed matter physics. In contrast to classical computers, quantum simulators do not suffer from sign problems, because the quantum dynamics is directly implemented in their hardware. A single plaquette of toric code, the simplest Z(2) quantum link model, has already been realized experimentally with trapped ultra-cold Rydberg ions. In close collaboration with Peter Zoller and his group at IQOQI in Innsbruck, we have recently proposed constructions of quantum simulators for Abelian and non-Abelian gauge theories, where ultra-cold atoms in an optical lattice embody quantum links. In contrast to Wilson's continuous classical link variables, the discrete states of quantum links can be naturally represented by quantum matter. The research groups of Ignacio Cirac (MPI Garching) and Maciej Lewenstein (ICFO, Barcelona) pursue similar goals in this new emerging interdisciplinary field of research connecting particle, condensed matter, and atomic physics, which I have recently summarized in a first review article. In the future, the quantum simulator research that was initiated in my previous SNF funded project will be continued in the framework of an ERC Advanced Grant that was approved to start in February 2014. The projects proposed here continue and significantly extend those parts of the previous SNF project, that are not covered by the ERC Advanced Grant.One goal of the proposed research is to gain further insight into the structure of non-Abelian quantum link models, by dualization of their underlying discrete variables. Abelian quantum link models are intimately related to quantum dimer models in condensed matter physics and their potential spin liquid phases, whose dual representation is given in terms of quantum height models. These models have intriguing confining dynamics with possible relations to unconventional deconfined quantum critical points, which are a controversially discussed topic in condensed matter physics. These studies shall be extended to the dualization of non-Abelian quantum link models, which is expected to reveal qualitatively new confining and deconfining dynamics also in non-Abelian gauge theories.A further extension of the gauge theory concept shall be explored within Wilson's framework, by the technique of self-adjoint extensions of Hermitean quantum mechanical Hamiltonians. In this way a connection shall be established between specific quantum link models and self-adjointly extended Wilsonian lattice gauge theories. In the Abelian case, the resulting gauge theory suffers from a sign problem which can, however, be eliminated by dualization. This shall enable us to search for unconventional deconfined quantum critical points also within this extended framework of Wilson's lattice field theory.Another goal of the proposed work is to improve the standard Wilson formulation of lattice gauge theory by the application of drastically improved lattice actions. Such actions have recently been discovered in our studies of "topological'' lattice actions, which are invariant against small deformations of the lattice fields. Despite the fact that they do not have a meaningful classical limit and are not accessible in perturbation theory, they do have the correct quantum continuum limit, which is often approached from another direction than with the standard action. In the context of asymptotically free 2-d O(N) models, by combining features of standard and topological lattice actions, drastically improved lattice actions have been constructed. These actions have extremely small cut-off effects, and yet are very simple and ultra-local. Some analytic insight why they work in this way has been gained in the large N limit. In the proposed research, similar improved actions shall be applied to SU(3) Yang-Mills theory, both at zero and non-zero temperature. We shall generalize a method for statistical error reduction --- first proposed by Hasenbusch, and recently used by us to calculate theta-vacuum effects in the 2-d O(3) model --- to gauge theories and shall apply it to precise calculations of glueball masses and of the confined-deconfined interface tension. It is conceivable that the continuum limit can be reached on rather coarse lattices, which would be most interesting also in the context of full lattice QCD.

Swiss National Science Foundation (SNSF)

Wildhainweg 3P.O. Box

CH-3001 Bern

Phone +41 31 308 22 22

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