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Nonperturbative Problems in Particle, Condensed Matter, and Quantum Information Physics

English title Nonperturbative Problems in Particle, Condensed Matter, and Quantum Information Physics
Applicant Wiese Uwe-Jens
Number 172616
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 01.04.2017 - 31.03.2021
Approved amount 721'753.00
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Keywords (3)

quantum link models; quantum spin systems; Chern Simons theory

Lay Summary (German)

Lead
Im Rahmen des Projekts ''Nonperturbative Problems in Particle, Condensed Matter, and Quantum Information Physics'' werden physikalische Systeme mit vielen stark gekoppelten Freiheitsgraden untersucht. Solche Systeme spielen sowohl in der Teilchenphysik als auch in der Physik der kondensierten Materie eine zentrale Rolle. Dabei gibt es interessante Bezüge zur Quanten Informationstheorie. Im Rahmen dieses Projekts soll den interdisziplinären Aspekten dieser Thematik ein besonderes Gewicht gegeben werden.
Lay summary

Das Projekt gliedert sich in fünf Teilprojekte, die im Folgenden kurz beschrieben werden.

Quantenspinsysteme sind einerseits stark korrelierte Systeme der Physik der kondensierten Materie. Andererseits führt ihr Verhalten bei niedrigen Energien auf effektive Quantenfeldtheorien, die in der Teilchenphysik eine zentrale Rolle spielen. Solche Systeme haben den grossen Vorteil, dass sie auch in sogenannten Quantensimulatoren mit ultrakalten Atomen realisiert werden können.

Eichfeldtheorien spielen eine zentrale Rolle im Standardmodell der Teilchenphysik, werden aber auch in Quantendimer Modellen der kondensierten Materie verwendet. Im Rahmen sogenannter Quantenlinkmodelle sollen neue Bezüge zwischen diesen Teilgebieten der Physik hergestellt werden.

Eichfeldtheorien auf einem Gitter spielen auch eine zentrale Rolle in der Quanten Informationstheorie, insbesondere beim Versuch, Quanteninformation vor den störenden Einflüssen der Umgebung zu schützen. Diesem Thema widmet sich ein weiteres Teilprojekt.

Antiferromagnetische Quantenspinsysteme mit Kristallgittern, die Dreiecke enthalten, sind geometrisch frustriert. Die numerische Berechnung solcher Systeme wird durch das sogenannte Vorzeichenproblem erheblich erschwert. Cluster Algorithmen bieten einen vielversprechenden numerischen Zugang zu diesen Systemen, der im Rahmen dieses Projekts weiterentwickelt werden soll.

In der Teilchenphysik stellt die starke Wechselwirkung zwischen Quarks und Gluonen eine grosse Herausforderung dar, da sie in der Regel nur mit grossem numerischem Aufwand zu berechnen ist. Dazu werden wiederum Eichfeldtheorien auf einem Gitter verwendet. Im Rahmen eines weiteren Teilprojekts sollen solche Rechnungen durch analytische Rechnungen in einer sogenannten effektiven Feldtheorie ergänzt werden, die in diesem Fall das Energiesprektrum stark wechselwirkender Teilchen wie Pionen oder Baryonen mit sogenannter Strangeness in einem endlichen Volumen behandelt.

Direct link to Lay Summary Last update: 04.04.2017

Responsible applicant and co-applicants

Employees

Publications

Publication
Meron- and Semi-Vortex-Clusters as Physical Carriers of Topological Charge and Vorticity
Bietenholz Wolfgang, Pinto Barros João C., Caspar Stephan, Hornung Manes, Wiese Uwe-Jens (2020), Meron- and Semi-Vortex-Clusters as Physical Carriers of Topological Charge and Vorticity, SISSA, Trieste.
Simulating Lattice Gauge Theories within Quantum Technologies
Bañuls M. C., others (2020), Simulating Lattice Gauge Theories within Quantum Technologies, in Eur. Phys. J. D, 74(8), 165-165.
String tension and robustness of confinement properties in the Schwinger-Thirring model
Barros Joao C. Pinto, Dalmonte Marcello, Trombettoni Andrea (2019), String tension and robustness of confinement properties in the Schwinger-Thirring model, in Physical Review D, 100(3), 036009-036009.
SU(3) quantum spin ladders as a regularization of the CP(2) model at non-zero density: From classical to quantum simulation
Evans W., Gerber U., Hornung M., Wiese U.-J. (2018), SU(3) quantum spin ladders as a regularization of the CP(2) model at non-zero density: From classical to quantum simulation, in Annals of Physics, 398, 94-122.
Rotor spectra and Berry phases in the chiral limit of QCD on a torus
Vlasii N. D., Wiese U.-J. (2018), Rotor spectra and Berry phases in the chiral limit of QCD on a torus, in Physical Review D, 97(11), 114029-114029.
SO(3) “Nuclear Physics” with ultracold Gases
Rico E., Dalmonte M., Zoller P., Banerjee D., Bögli M., Stebler P., Wiese U.-J. (2018), SO(3) “Nuclear Physics” with ultracold Gases, in Annals of Physics, 393, 466-483.
From the SU(2) quantum link model on the honeycomb lattice to the quantum dimer model on the kagome lattice: Phase transition and fractionalized flux strings
Banerjee D., Jiang F.-J., Olesen T. Z., Orland P., Wiese U.-J. (2018), From the SU(2) quantum link model on the honeycomb lattice to the quantum dimer model on the kagome lattice: Phase transition and fractionalized flux strings, in Physical Review B, 97(20), 205108-205108.
On spinodal points and Lee-Yang edge singularities
An X, Mesterházy D, Stephanov M A (2018), On spinodal points and Lee-Yang edge singularities, in Journal of Statistical Mechanics: Theory and Experiment, 2018(3), 033207-033207.
Solvable Markovian dynamics of lattice quantum spin models
Mesterházy D., Hebenstreit F. (2017), Solvable Markovian dynamics of lattice quantum spin models, in Physical Review A, 96(1), 010104-010104.

Collaboration

Group / person Country
Types of collaboration
Christoph Hofmann, Colima University Mexico (North America)
- in-depth/constructive exchanges on approaches, methods or results
Wolfgang Bietenholz, Universidad Autonoma de Mexico (UNAM Mexico (North America)
- Publication
Debasish Banerjee, Saha Institute, Kolkata India (Asia)
- in-depth/constructive exchanges on approaches, methods or results

Scientific events

Active participation

Title Type of contribution Title of article or contribution Date Place Persons involved
Workshop Quantum Simulation: Gauge Fields, Holography, and Topology Poster Merons as the Relevant Topological Charge Carriers in the 2d-O(3) Model 10.07.2019 Bilbao, Spain Pinto Barros Joao Carlos;
37th Annual International Symposium on Lattice Field Theory (Lattice 2019) Talk given at a conference Merons as the Relevant Topological Charge Carriers in the 2-d O(3) Model 16.06.2019 Wuhan, China Pinto Barros Joao Carlos;
Effective Theories of Quantum Phases of Matter Talk given at a conference Merons and theta-vacuum effects in the 2-d O(3) model 06.05.2019 Stockholm, Sweden Wiese Uwe-Jens;
High-energy physics at ultra-cold temperatures Talk given at a conference 2-d CP(N-1) models and merons as the relevant topological charge carriers in CP(1) 10.04.2019 Trento, Italy Pinto Barros Joao Carlos;
Universität Innsbruck, IQOQI Individual talk Exactly solvable Markovian dynamics of lattice quantum spin models 03.05.2017 Innsbruck, Austria Mesterhazy David;
4th Nottingham Workshop on Quantum Non-Equilibrium Dynamics Talk given at a conference Exactly solvable Markovian dynamics of quantum spin lattice models 24.04.2017 Nottingham, Great Britain and Northern Ireland Mesterhazy David;
Universidad Autonoma de Madrid Individual talk Quantum Simulation of Abelian and non-Abelian Gauge Theories 18.04.2017 Madrid, Spain Wiese Uwe-Jens;
Lattice QCD at the physical pion mass: results, challenges and modern techniques Talk given at a conference Functional Integrals for SPDEs: The what, why, and how 10.04.2017 DESY, Zeuthen, Germany Mesterhazy David;


Associated projects

Number Title Start Funding scheme
153245 Lattice Gauge Theory: Improvement, Extension, and Dualization 01.04.2014 Project funding
200424 Non-Perturbative Quantization of Topological Excitations in Quantum Field Theory and Quantum Spin Systems 01.04.2021 Project funding

Abstract

Nonperturbative problems arise in many areas of physics, ranging from particle and condensed matter physics to quantum information theory. In many cases, these problems are associated with the dynamics of gauge fields. Quantum Chromodynamics (QCD) is the non-Abelian SU(3) gauge theory that describes the strong interaction between quarks and gluons. Beyond perturbation theory QCD is studied in the framework of Wilson's lattice gauge theory. In condensed matter physics gauge theories may arise as effective descriptions of low-energy dynamics. For example, quantum dimer models are Abelian U(1) gauge theories realizing Anderson's resonating valence bond picture for strongly correlated electron systems. Finally, Kitaev's toric code is an Abelian Z(2) gauge theory that may serve as a topologically protected storage device for quantum information.Quantum link models, which I developed in collaboration with Shailesh Chandrasekharan in 1996, provide a unified framework for lattice gauge theory, encompassing the different cases mentioned before, and thus providing a bridge connecting particle physics, condensed matter, and quantum information applications of gauge theories. In lattice gauge theory, the fundamental gauge degrees of freedom are associated with the links connecting neighboring lattice sites. In Wilson's lattice gauge theory the gauge field is described by classical parallel transporter matrices that take values in the gauge group. This gives rise to an infinite-dimensional Hilbert space per link. In quantum link models the fundamental gauge degrees of freedom are intrinsically quantum mechanical objects - so-called quantum links - which are gauge covariant generalizations of quantum spins associated with a finite-dimensional link Hilbert space. Quantum link models are formulated in terms of discrete quantum degrees of freedom and yet have an exact continuous gauge symmetry. Wilson's lattice gauge theory can be recovered from a quantum link model in the "classical'' limit of a large representation of the link Hilbert space. It turns out that quantum dimer models and the toric code are also special cases of quantum link models with a U(1) or Z(2) gauge symmetry, respectively.While lattice QCD continues to make tremendous progress towards providing precise experimentally relevant results for the static properties of hadrons as well as for strongly interacting matter in thermal equilibrium at small baryon density, its applications to real-time dynamics or high-density environments are prevented by very severe sign and complex action problems. In a former SNF funded project "Lattice Field Theory: from Classical to Quantum Simulation'' my collaborators and I have used quantum link models for the construction of quantum simulators for dynamical Abelian and non-Abelian gauge fields with applications to both particle and condensed matter physics. Quantum simulators are special purpose digital or analog quantum computers. Unlike classical computers, quantum simulators do not suffer from the sign problem because they operate with quantum hardware, for example, with ultracold atoms in an optical lattice. Due to the quantum nature of their fundamental degrees of freedom, which reside in a finite-dimensional Hilbert space, quantum link models are ideally suited for implementations in ultracold matter. In collaboration with Peter Zoller and his atomic physics and quantum optics group at IQOQI in Innsbruck, we have proposed quantum simulators for Abelian and non-Abelian gauge theories, aiming at the quantum simulation of QCD as the ultimate long-term goal. The development of quantum simulators for gauge theories in particle and condensed matter physics is currently pursued in the framework of an ERC Advanced Grant that started in February 2014. The projects proposed here are partly based on my previous SNF grant "Lattice Gauge Theory: Improvement, Extension, and Dualization''. They add numerous new directions of research, which are not covered by the ERC Advanced Grant.Directly quantum simulating QCD itself will not yet be practical in the foreseeable future. Right now, we are thus concentrating on simpler models that share important features with QCD. In collaboration with Peter Zoller and his group, we have recently proposed a quantum simulator for CP(N-1) models using ultracold alkaline-earth atoms in an optical lattice, which can address the real-time and finite-density dynamics of these systems, approaching the continuum limit by dimensional reduction of an SU(N) quantum spin ladder. Already today experimentalists are able to build such systems in the laboratory. We have recently investigated (2+1)-d square lattice U(1) quantum link and quantum dimer models, in particular, for the first time correctly identifying their phase structure. These models are characterized by "crystalline" confinement, i.e. by qualitatively new confined phases with spontaneously broken translation symmetries, and by the presence of Rokhsar-Kivelson (RK) points which display deconfinement already at zero temperature. In the framework of the previous SNF grant, we have constructed self-adjoint extensions of Wilson's lattice gauge theory that share similar features. In order to reach a deeper understanding of the possible phases of gauge theories on the lattice, in the proposed research these studies shall be extended to non-Abelian gauge theories, with potential condensed matter applications to quantum spin liquids and deconfined quantum critical points. In particular, we anticipate to find qualitatively new confined phases with fractionalized or delocalized non-Abelian center-electric flux.In the framework of the previous SNF grant, we have studied Abelian (2+1)-d Chern-Simons gauge theories on the lattice. In contrast to the standard approach using a link-based gauge algebra, we have investigated a doubled theory with a local Hilbert space associated with a link and its corresponding dual link. Motivated by the idea of topological quantum computation, we have recently extended our investigations to doubled Chern-Simons lattice theories with discrete gauge group. Here I propose to investigate the anyonic character of the corresponding charged excitations, in particular, whether they obey non-Abelian braid statistics and facilitate universal quantum computation.Geometrically frustrated quantum antiferromagnets form a fascinating class of strongly correlated condensed matter systems, including Herbertsmithites on a Kagome lattice, which are promising candidates for highly entangled spin liquid states. Here I propose to characterize the nature of the sign problem of geometrically frustrated quantum magnets in a systematic manner, which will shed light on their entanglement structure and may lead to new solutions of the sign problem, at least in some regions of parameter space.Systems with spontaneously broken continuous symmetries show characteristic finite-size effects when placed in a finite periodic volume. In particular, the order parameter precesses through the manifold of degenerate vacuum states, which gives rise to a quantum mechanical rotor spectrum. Here I propose to extend these calculations to the one-pion sector and to the one-baryon sector with non-zero strangeness. Since many years, my research is characterized by an interdisciplinary approach that aims at connecting apparently disconnected areas of theoretical physics. In this way, we have gained some new insights that would otherwise seem difficult to obtain. Again, this is the key to the research proposed here. In particular, quantum link models provide a unified framework for a wide variety of gauge theories, low-energy effective field theories provide universally applicable analytic tools for strongly correlated systems, and cluster algorithms provide efficient numerical methods that are even capable of solving some severe sign problems.
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