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Symmetry
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New Applications of Symmetry in Lattice Field Theory
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New Applications of Symmetry in Lattice Field Theory

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: closed (28 February 2023) | Viewed by 15448

Special Issue Editors

Prof. Simon Hands

E-Mail Website
Guest Editor
Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, UK
Interests: lattice field theory; high performance computing; quantum field theory
Prof. Simon Catterall

E-Mail Website
Co-Guest Editor
Department of Physics, Syracuse University, Syracuse, NY 13244, USA
Interests: theoretical and computational studies of quantum field theory; quantum gravity and string theory; lattice gauge theory for physics beyond the standard model; lattice supersymmetry and applications to gauge-gravity duality; lattice studies of dynamical electroweak symmetry breaking; application of supercomputer simulation to particle physics

Special Issue Information

Dear Colleagues,

Symmetry has been at the heart of lattice field theory since its inception. The method furnishes a robust and rigorous means of formulating the gauge symmetries lying at the heart of particle physics, at the cost of breaking another cherished symmetry, Poincaré invariance. One of the greatest challenges in lattice field theory has been to identify faithful implementations of the chiral symmetry protecting fermions from acquiring mass. Symmetry considerations, sometimes in idealised limits, also determine phenomenologically important strong-interaction issues such as confinement of quarks.

This special issue highlights symmetry applications and consequences in several fast-developing directions in both gauge and non-gauge theories: long-standing issues of the nature of color confinement and the role of topological excitations; new quantum critical points in lower-dimensional fermionic theories with relevance to layered condensed-matter systems; symmetry-protected topological phases yielding edge states; robust quantum computation; dynamical mass generation without symmetry breaking; exact lattice implementations of supersymmetry and applications to gravitationally bound systems such as black holes; formulation of chiral gauge theories needed for the Standard Model and Extended Technicolor; tensor networks as a powerful new means to explore interacting quantum systems; and formulations of quantum gravity using dynamical triangulation of spacetime.

Prof. Simon Hands
Prof. Simon Catterall
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • lattice
  • confinement
  • supersymmetry
  • topological phases
  • quantum criticality
  • symmetric mass generation
  • chiral gauge theories
  • quantum computation/simulation
  • dynamical triangulation
  • tensor networks

Published Papers (7 papers)

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Editorial

Jump to: Research, Review

4 pages, 211 KiB  
Editorial
Review of Contributions to the Special Edition: New Applications of Symmetry in Lattice Field Theory
by Simon Catterall and Simon Hands
Symmetry 2023, 15(3), 606; https://doi.org/10.3390/sym15030606 - 27 Feb 2023
Viewed by 766
Abstract
Symmetry has been at the heart of lattice field theory since its inception [...] Full article
(This article belongs to the Special Issue New Applications of Symmetry in Lattice Field Theory)

Research

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31 pages, 2472 KiB  
Article
Large-S and Tensor-Network Methods for Strongly-Interacting Topological Insulators
by Emanuele Tirrito, Simon Hands and Alejandro Bermudez
Symmetry 2022, 14(4), 799; https://doi.org/10.3390/sym14040799 - 12 Apr 2022
Cited by 4 | Viewed by 1746
Abstract
The study of correlation effects in topological phases of matter can benefit from a multidisciplinary approach that combines techniques drawn from condensed matter, high-energy physics and quantum information science. In this work, we exploit these connections to study the strongly-interacting limit of certain [...] Read more.
The study of correlation effects in topological phases of matter can benefit from a multidisciplinary approach that combines techniques drawn from condensed matter, high-energy physics and quantum information science. In this work, we exploit these connections to study the strongly-interacting limit of certain lattice Hubbard models of topological insulators, which map onto four-Fermi quantum field theories with a Wilson-type discretisation and have been recently shown to be at reach of cold-atom quantum simulators based on synthetic spin-orbit coupling. We combine large-S and tensor-network techniques to explore the possible spontaneous symmetry-breaking phases that appear when the interactions of the topological insulators are sufficiently large. In particular, we show that varying the Wilson parameter r of the lattice discretisations leads to a novel Heisenberg–Ising compass model with critical lines that flow with the value of r. Full article
(This article belongs to the Special Issue New Applications of Symmetry in Lattice Field Theory)
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20 pages, 1558 KiB  
Article
Symmetries of Thirring Models on 3D Lattices
by Andreas W. Wipf and Julian J. Lenz
Symmetry 2022, 14(2), 333; https://doi.org/10.3390/sym14020333 - 06 Feb 2022
Cited by 6 | Viewed by 1684
Abstract
We review some recent developments about strongly interacting relativistic Fermi theories in three spacetime dimensions. These models realize the asymptotic safety scenario and are used to describe the low-energy properties of Dirac materials in condensed matter physics. We begin with a general discussion [...] Read more.
We review some recent developments about strongly interacting relativistic Fermi theories in three spacetime dimensions. These models realize the asymptotic safety scenario and are used to describe the low-energy properties of Dirac materials in condensed matter physics. We begin with a general discussion of the symmetries of multi-flavor Fermi systems in arbitrary dimensions. Then we review known results about the critical flavor number Ncrit of Thirring models in three dimensions. Only models with a flavor number below Ncrit show a phase transition from a symmetry-broken strong-coupling phase to a symmetric weak-coupling phase. Recent simulations with chiral fermions show that Ncrit is smaller than previously extracted with various non-perturbative methods. Our simulations with chiral SLAC fermions reveal that for four-component flavors Ncrit=0.80(4). This means that all reducible Thirring models with Nr=1,2,3,… show no phase transition with order parameter. Instead, we discover footprints of phase transitions without order parameter. These new transitions are probably smooth and could be used to relate the lattice Thirring models to Thirring models in the continuum. For a single irreducible flavor, we provide previously unpublished values for the critical couplings and critical exponents. Full article
(This article belongs to the Special Issue New Applications of Symmetry in Lattice Field Theory)
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22 pages, 392 KiB  
Article
Qubit Regularization and Qubit Embedding Algebras
by Hanqing Liu and Shailesh Chandrasekharan
Symmetry 2022, 14(2), 305; https://doi.org/10.3390/sym14020305 - 02 Feb 2022
Cited by 15 | Viewed by 1332
Abstract
Qubit regularization is a procedure to regularize the infinite dimensional local Hilbert space of bosonic fields to a finite dimensional one, which is a crucial step when trying to simulate lattice quantum field theories on a quantum computer. When the qubit-regularized lattice quantum [...] Read more.
Qubit regularization is a procedure to regularize the infinite dimensional local Hilbert space of bosonic fields to a finite dimensional one, which is a crucial step when trying to simulate lattice quantum field theories on a quantum computer. When the qubit-regularized lattice quantum fields preserve important symmetries of the original theory, qubit regularization naturally enforces certain algebraic structures on these quantum fields. We introduce the concept of qubit embedding algebras (QEAs) to characterize this algebraic structure associated with a qubit regularization scheme. We show a systematic procedure to derive QEAs for the O(N) lattice spin models and the SU(N) lattice gauge theories. While some of the QEAs we find were discovered earlier in the context of the D-theory approach, our method shows that QEAs are far richer. A more complete understanding of the QEAs could be helpful in recovering the fixed points of the desired quantum field theories. Full article
(This article belongs to the Special Issue New Applications of Symmetry in Lattice Field Theory)
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109 pages, 4632 KiB  
Article
Notes on Confinement on R3 × S1: From Yang–Mills, Super-Yang–Mills, and QCD (adj) to QCD(F)
by Erich Poppitz
Symmetry 2022, 14(1), 180; https://doi.org/10.3390/sym14010180 - 17 Jan 2022
Cited by 12 | Viewed by 3386
Abstract
This is a pedagogical introduction to the physics of confinement on R3×S1, using SU(2) Yang–Mills with massive or massless adjoint fermions as the prime example; we also add fundamental flavours to conclude. The small- [...] Read more.
This is a pedagogical introduction to the physics of confinement on R3×S1, using SU(2) Yang–Mills with massive or massless adjoint fermions as the prime example; we also add fundamental flavours to conclude. The small-S1 limit is remarkable, allowing for controlled semiclassical determination of the nonperturbative physics in these, mostly non-supersymmetric, theories. We begin by reviewing the Polyakov confinement mechanism on R3. Moving on to R3×S1, we show how introducing adjoint fermions stabilizes center symmetry, leading to abelianization and semiclassical calculability. We explain how monopole–instantons and twisted monopole–instantons arise. We describe the role of various novel topological excitations in extending Polyakov’s confinement to the locally four-dimensional case, discuss the nature of the confining string, and the θ-angle dependence. We study the global symmetry realization and, when available, present evidence for the absence of phase transitions as a function of the S1 size. As our aim is not to cover all work on the subject, but to prepare the interested reader for its study, we also include brief descriptions of topics not covered in detail: the necessity for analytic continuation of path integrals, the study of more general theories, and the ’t Hooft anomalies involving higher-form symmetries. Full article
(This article belongs to the Special Issue New Applications of Symmetry in Lattice Field Theory)
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17 pages, 375 KiB  
Article
Symmetry, Confinement, and the Higgs Phase
by Jeff Greensite and Kazue Matsuyama
Symmetry 2022, 14(1), 177; https://doi.org/10.3390/sym14010177 - 17 Jan 2022
Cited by 10 | Viewed by 1510
Abstract
We show that the Higgs and confinement phases of a gauge Higgs theory, with the Higgs field in the fundamental representation of the gauge group, are distinguished both by a broken or unbroken realization of the global center subgroup of the gauge group, [...] Read more.
We show that the Higgs and confinement phases of a gauge Higgs theory, with the Higgs field in the fundamental representation of the gauge group, are distinguished both by a broken or unbroken realization of the global center subgroup of the gauge group, and by the type of confinement in each phase. This is color confinement in the Higgs phase, and a stronger property, which we call “separation-of-charge” confinement, in the confining phase. Full article
(This article belongs to the Special Issue New Applications of Symmetry in Lattice Field Theory)
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Review

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51 pages, 1322 KiB  
Review
Symmetric Mass Generation
by Juven Wang and Yi-Zhuang You
Symmetry 2022, 14(7), 1475; https://doi.org/10.3390/sym14071475 - 19 Jul 2022
Cited by 46 | Viewed by 3777
Abstract
The most well-known mechanism for fermions to acquire a mass is the Nambu–Goldstone–Anderson–Higgs mechanism, i.e., after a spontaneous symmetry breaking, a bosonic field that couples to the fermion mass term condenses, which grants a mass gap for the fermionic excitation. In the last [...] Read more.
The most well-known mechanism for fermions to acquire a mass is the Nambu–Goldstone–Anderson–Higgs mechanism, i.e., after a spontaneous symmetry breaking, a bosonic field that couples to the fermion mass term condenses, which grants a mass gap for the fermionic excitation. In the last few years, it was gradually understood that there is a new mechanism of mass generation for fermions without involving any symmetry breaking within an anomaly-free symmetry group, also applicable to chiral fermions with anomaly-free chiral symmetries. This new mechanism is generally referred to as the symmetric mass generation (SMG). It is realized that the SMG has deep connections with interacting topological insulator/superconductors, symmetry-protected topological states, perturbative local and non-perturbative global anomaly cancellations, and deconfined quantum criticality. It has strong implications for the lattice regularization of chiral gauge theories. This article defines the SMG, summarizes the current numerical results, introduces an unifying theoretical framework (including the parton-Higgs and the s-confinement mechanisms, as well as the symmetry-extension construction), and presents an overview of various features and applications of SMG. Full article
(This article belongs to the Special Issue New Applications of Symmetry in Lattice Field Theory)
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