<p>We investigate the properties of charmonium systems in strong external magnetic fields using a relativistic light-front Hamiltonian approach within the basis light-front quantization framework. By solving the eigenvalue problem for the invariant mass squared operator with confinement potentials and one-gluon-exchange interactions, we obtain the mass spectrum and wave functions under varying magnetic fields. Our results reveal significant spectral modifications through the Zeeman effect, including <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>η</mi></mrow><mrow><mi>c</mi></mrow></msub><mtext>−</mtext><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> mixing and magnetic sublevel splitting. Momentum density analysis demonstrates wave function deformation, with transverse momentum broadening and longitudinal narrowing under strong fields, alongside structural shifts in parton distributions such as double-hump profiles in excited states. Relativistic corrections and center-of-mass coupling critically drive these dynamics, highlighting the necessity of a relativistic framework for QCD bound states in extreme magnetic environments.</p>

China

Liuyuan Wen

Spain

Meijian Li

Italy

Yiyu Zhou

Yang Li

United States

James P. Vary

Relativistic dynamics of charmonia in strong magnetic fields

This paper introduces a novel systematic construction of gapped domain walls (GDWs) within the Levin-Wen (LW) model. By gluing two LW models along their open sides in a compatible way, we achieve a complete GDW classification by subsets of bulk input data, which encompass the classifications in terms of bimodule categories. A generalized bimodule structure is introduced to capture domain-wall excitations. Furthermore, we demonstrate that folding along any GDW yields a gapped boundary (GB) described by a Frobenius algebra of the input UFC for the folded model, thus bridging our GDW classification and the GB classification in [1].

Yanyan Chen

Siyuan Wang

Yu Zhao

Yuting Hu

Yidun Wan

Classification of gapped domain walls of topological orders in 2+1 dimensions: a Levin-Wen model realization

We study the <math altimg='si1.svg'><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msubsup></math> production in Pb-Pb collisions at <math altimg='si2.svg'><msqrt><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi>N</mi><mi>N</mi></mrow></msub></mrow></msqrt><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>5.02</mn></math> TeV. In the quark-gluon plasma (QGP) produced in heavy-ion collisions, heavy quarks make random motions with the energy loss. We employ the Langevin equations to study the non-equilibrium distributions of heavy quarks and the Instantaneous Coalescence Model (ICM) to study the hadronization process. Due to abundant charm and bottom quarks in the QGP, their coalescence probability is significantly enhanced compared with the situations in proton-proton collisions. We find that the final production of <math altimg='si1.svg'><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msubsup></math> is increased by the coalescence process, which makes the nuclear modification factor ( <math altimg='si3.svg'><msub><mrow><mi>R</mi></mrow><mrow><mi>A</mi><mi>A</mi></mrow></msub></math>) of <math altimg='si1.svg'><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msubsup></math> larger than unit. Our model explains the experimental data well at semi-central and central collisions. The observation of <math altimg='si4.svg'><msub><mrow><mi>R</mi></mrow><mrow><mi>A</mi><mi>A</mi></mrow></msub><mo stretchy='false'>(</mo><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msubsup><mo stretchy='false'>)</mo><mo linebreak='goodbreak' linebreakstyle='after'>&gt;</mo><mn>1</mn></math> is regarded as an evident and strong signal of the existence of the deconfined medium generated in heavy-ion collisions.

Baoyi Chen

Yunpeng Liu

<math altimg='si1.svg'><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msubsup></math> formation from random charm and anti-bottom quarks in the quark-gluon plasma

Levin-Wen string-net models provide a construction of (2+1)D topologically ordered phases of matter with anyonic localized excitations described by the Drinfeld center of a unitary fusion category. Anyon condensation is a mechanism for phase transitions between (2+1)D topologically ordered phases. We construct an extension of Levin-Wen models in which tuning a parameter implements anyon condensation. We also describe the classification of anyons in Levin-Wen models via representation theory of the tube algebra, and use a variant of the tube algebra to classify low-energy localized excitations in the condensed phase.

Jessica Christian

David Green

Peter Huston

David Penneys

A lattice model for condensation in Levin-Wen systems

We employ the time-dependent Schrödinger equation with different complex potentials to study the bottomonium sequential suppression in Pb-Pb collisions at <math><msqrt><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi>N</mi><mi>N</mi></mrow></msub></mrow></msqrt><mo>=</mo><mn>2.76</mn></math> TeV and 5.02 TeV and Au-Au collisions at <math><msqrt><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi>N</mi><mi>N</mi></mrow></msub></mrow></msqrt><mo>=</mo><mn>200</mn></math> GeV. Both color screening effect and the random scatterings with thermal partons are considered in the real and imaginary parts of the heavy-quark potentials. As the real part of the heavy-quark potential is between the free energy <math><mi>F</mi><mo>(</mo><mi>T</mi><mo>,</mo><mi>r</mi><mo>)</mo></math> and the internal energy <math><mi>U</mi><mo>(</mo><mi>T</mi><mo>,</mo><mi>r</mi><mo>)</mo></math> of heavy quarkonium, we parametrize different potentials with a function of F and U to evolve the bottomonium wave packages in the medium. We find that when the real part of the potential is close to <math><mi>U</mi><mo>(</mo><mi>T</mi><mo>,</mo><mi>r</mi><mo>)</mo></math>, it can explain well the pattern of bottomonium sequential suppression where their nuclear modification factors satisfy the relation <math><msub><mrow><mi>R</mi></mrow><mrow><mi>A</mi><mi>A</mi></mrow></msub><mo>(</mo><mn>1</mn><mi>s</mi><mo>)</mo><mo>&gt;</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>A</mi><mi>A</mi></mrow></msub><mo>(</mo><mn>2</mn><mi>s</mi><mo>)</mo><mo>&gt;</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>A</mi><mi>A</mi></mrow></msub><mo>(</mo><mn>3</mn><mi>s</mi><mo>)</mo></math> observed in experiments. In the other limit of <math><mi>F</mi><mo>(</mo><mi>T</mi><mo>,</mo><mi>r</mi><mo>)</mo></math>, bottomonium wave packages tend to expand due to weak attracted force, which results in evident transitions from <math><mi>ϒ</mi><mo>(</mo><mn>2</mn><mi>s</mi><mo>)</mo></math> to <math><mi>ϒ</mi><mo>(</mo><mn>3</mn><mi>s</mi><mo>)</mo></math> components and does not satisfy the sequential suppression pattern. We suggest that the bottomonium sequential suppression can be a probe of strong heavy-quark potential in the medium.

Bottomonium sequential suppression and strong heavy-quark potential in heavy-ion collisions

A realistic material may possess defects, which often bring the material new properties that have practical applications. The boundary defects of a two-dimensional topologically ordered system are thought of as an alternative way of realizing topological quantum computation. To facilitate the study of such boundary defects, in this paper, we construct an exactly solvable Hamiltonian model of topological orders with gapped boundary junctions, where the boundary defects reside, by placing the Levin-Wen model on a disk, whose gapped boundary is separated into multiple segments by junctions. We derive a formula of the ground state degeneracy and an explicit ground-state basis of our model. We propose the notion of mobile and immobile charges on the boundary and find that they are quantum observables and label the ground-state basis. Our model is computation friendly.

Hongyu Wang

Extend the Levin-Wen model to two-dimensional topological orders with gapped boundary junctions

The honeycomb lattice Kitaev model <math><msub><mrow><mi>H</mi></mrow><mrow><mi>K</mi></mrow></msub></math> with two kinds of Wen–Toric-code four-body interactions <math><msub><mrow><mi>H</mi></mrow><mrow><mi>W</mi><mi>T</mi></mrow></msub></math> is investigated exactly using a new fermionization method, and the ground state phase diagram is obtained. Six kinds of three-body interactions are also considered. A Hamiltonian equivalent to the honeycomb lattice Kitaev model is also introduced. The fermionization method is generalized to two-dimensional systems, and the two-dimensional Jordan–Wigner transformation is obtained as a special case of this formula. The model <math><msub><mrow><mi>H</mi></mrow><mrow><mi>K</mi></mrow></msub><mo>+</mo><msub><mrow><mi>H</mi></mrow><mrow><mi>W</mi><mi>T</mi></mrow></msub></math> is symmetric in four-dimensional space of coupling constants, and the anyon type excitations appear in each phase.

Japan

Kazuhiko Minami

Honeycomb lattice Kitaev model with Wen–Toric-code interactions, and anyon excitations