At nonzero temperatures, the deconfining phase transition can be analyzed using an effective matrix model to characterize the change in holonomy. The model includes gluons and two-dimensional ghost fields in the adjoint representation, or “teens.” As ghosts, the teen fields are responsible for the decrease of the pressure as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mo stretchy="false">→</mo><msub><mi>T</mi><mi>d</mi></msub></math>, with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mi>d</mi></msub></math> the transition temperature for deconfinement. Using the solution of this matrix model for a large number of colors, the parameters of the teen fields are adjusted so that the expectation value of the Polyakov loop is close to the values from the lattice. The shear, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math>, and bulk, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ζ</mi></math>, viscosities are computed at nonzero holonomy to leading logarithmic order in weak coupling. In the pure glue theory, the value of the Polyakov loop is relatively large in the deconfined phase, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>≈</mo><mn>1</mn><mo>/</mo><mn>2</mn></math> at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mi>d</mi></msub></math>. Consequently, if <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math> is the entropy density, while <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mo>/</mo><mi>s</mi></math> decreases as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mo stretchy="false">→</mo><msub><mi>T</mi><mi>d</mi></msub></math>, it is still well above the conformal bound. In contrast, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ζ</mi><mo>/</mo><mi>s</mi></math> is largest at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mi>d</mi></msub></math>, comparable to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mo>/</mo><mi>s</mi></math>, then falls off rapidly with increasing temperature and is negligible by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><mn>2</mn><msub><mi>T</mi><mi>d</mi></msub></math>.

India

Manas Debnath

United States

Ritesh Ghosh

Najmul Haque

Japan

Yoshimasa Hidaka

Robert D. Pisarski

Shear and bulk viscosity for a pure glue theory using an effective matrix model

We present analytical and numerical calculations for the photon polarization tensor at finite temperature and density in a constant magnetic field. We first discuss the tensor decomposition in the presence of the magnetic field, which breaks rotational symmetry. Then, we analytically perform all the momentum integrations and numerically take the Landau level sum. We confirm that the imaginary part of the photon polarization tensor correctly reproduces the known result from the independent calculation. We utilize the Kramers-Kronig relation to estimate the real part numerically as a function of the momenta, the chemical potential, and the finite temperature. As an application, we consider the real photon limit and estimate the photon decay rate and the Stokes parameter in the hot and dense medium. We specifically quantify the difference between the X-mode and the O-mode with the polarization orthogonal and parallel to the magnetic field. As long as the magnetic field is weak, the decay rate of the X-mode photon is larger than that of the O-mode photon, while the O-mode becomes dominant due to the Landau level suppression of the X-mode at a strong magnetic field. We also find that the eigenmodes of the propagating photon change their polarization state with increasing density.

Kenji Fukushima

Tomoya Uji

Photon polarization tensor at finite temperature and density in a magnetic field

We provide an improved definition of new conserved quantities derived from the energy–momentum tensor in curved spacetime by introducing an additional scalar function. We find that the conserved current and the associated conserved charge become geometric under a certain initial condition of the scalar function, and show that such a conserved geometric current generally exists in curved spacetime. Furthermore, we demonstrate that the geometric conserved current agrees with the entropy current in an effective theory of a perfect fluid, thus the conserved charge is the total entropy of the system. While the geometric charge can be regarded as the entropy for a nondissipative fluid, its physical meaning should be investigated for more general cases.

Sinya Aoki

South Korea

Kiyoharu Kawana

Kengo Shimada

Geometric conservation in curved spacetime and entropy

We propose a novel method to distinguish states of matter by identifying spontaneous symmetry breaking on extended objects, such as vortices, even in the absence of a bulk phase transition. As a specific example, we investigate the phase transition on superfluid vortices in the Higgs-confinement crossover using a U(1) × U(1) model in (3 + 1) dimensions. This model exhibits superfluidity of U(1) symmetry and allows for a crossover between the Higgs and confinement regimes by varying the gauge coupling constant from weak to strong. We demonstrate that, on vortices, spontaneous breaking of the ℤ flavor symmetry occurs in the weak coupling (Higgs) regime, while it does not in the strong coupling (confinement) regime. We also confirm that those regimes are separated by a second-order phase transition through Monte Carlo simulations, whose universality class corresponds to the two-dimensional Ising model.

Tomoya Hayata

Dan Kondo

Phase transition on superfluid vortices in Higgs-Confinement crossover

We simulate Floquet time evolution of a truncated SU(3) lattice Yang-Mills theory on a two-leg ladder geometry under open boundary conditions using IBM’s superconducting 156-qubit device ibm_fez. To this end, we derive the quantum spin representation of the lattice Yang-Mills theory and compose a quantum circuit carefully tailored to hardware, reducing the number of controlled-Z gates. Since it is still challenging to simulate Hamiltonian evolution in present noisy quantum processors, we make the step size in the Suzuki-Trotter decomposition very large and simulate thermalization dynamics in Floquet circuit composed of the Suzuki-Trotter evolution. We demonstrate that IBM’s Heron quantum processor can simulate, by error mitigation, Floquet thermalization dynamics in a large system consisting of 62 qubits. Our work would be a benchmark for further quantum simulations of lattice gauge theories using real devices.

Floquet evolution of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi></math>-deformed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SU</mi><mo stretchy="false">(</mo><mn>3</mn><msub><mo stretchy="false">)</mo><mn>1</mn></msub></mrow></math> Yang-Mills theory on a two-leg ladder

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="double-struck">Z</mi><mn>3</mn></msub></math> lattice gauge theory is the simplest discrete gauge theory with three-quark bound states, i.e., baryons. Since it has a finite-dimensional Hilbert space, it can be used for testing quantum simulation of lattice gauge theory at nonzero baryon density. We discuss global and local gauge symmetries and their importance in quantum simulation. We perform quantum emulator calculation and demonstrate how to study the ground state property of baryonic matter.

Arata Yamamoto

Quantum circuit for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="double-struck">Z</mi><mn>3</mn></msub></math> lattice gauge theory at nonzero baryon density

We study one-flavor SU(2) and SU(3) lattice QCD in (1 + 1) dimensions at zero temperature and finite density using matrix product states and the density matrix renormalization group. We compute physical observables such as the equation of state, chiral condensate, and quark distribution function as functions of the baryon number density. As a physical implication, we discuss the inhomogeneous phase at nonzero baryon density, where the chiral condensate is inhomogeneous, and baryons form a crystal. We also discuss how the dynamical degrees of freedom change from hadrons to quarks through the formation of quark Fermi seas.

Kentaro Nishimura

Dense QCD2 with matrix product states

We propose the (<math><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional <math><msub><mi>Z</mi><mn>3</mn></msub></math> lattice gauge theory coupled with the 2-flavor Wilson-Dirac fermion as a toy model for studying quantum chromodynamics (QCD) at nonzero density. We study its phase diagram in the space of the lattice gauge couplings <math><msup><mi>g</mi><mn>2</mn></msup></math> and the quark chemical potentials <math><mi>μ</mi></math> and discuss the similarity and difference compared with anticipated behaviors of actual QCD. This model also provides a testing ground for various algorithms of the numerical Hamiltonian formalism as its Hilbert space is finite-dimensional in a finite box.

Yuya Tanizaki

<math><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math> lattice gauge theory as a toy model for dense QCD

We study the relaxation dynamics of the spin polarization of baryons (nucleon and <math><mi>Λ</mi></math> baryon), in a thermal pion gas as a simple model of the hadronic phase of the QCD plasma produced in relativistic heavy-ion collisions. For this purpose, we formulate the quantum kinetic theory for the spin density matrix of baryons in the leading order of the gradient expansion. Considering the baryon-pion elastic scattering processes as the dominant interaction between baryons and thermal pions, we compute the spin relaxation rate of nucleons and <math><mi>Λ</mi></math> baryons in a pion gas up to temperature 200 MeV. In the case of nucleons, we evaluate the spin relaxation rate in the <math><mi>s</mi></math>-channel resonance approximation, based on the known experimental data on <math><mi>Δ</mi></math> resonances. We also estimate the spin relaxation rate for <math><mi>Λ</mi></math> baryons, based on experimental inputs and theoretical models for the low-energy <math><mrow><mi>Λ</mi><mi>π</mi></mrow></math> scattering, including the chiral perturbation theory.

Masaru Hongo

Mikhail A. Stephanov

Ho-Ung Yee

Spin relaxation rate for baryons in a thermal pion gas

We propose a novel approach to probe primordial inhomogeneity in hot and dense matter which could be realized in noncentral heavy-ion collisions. Although the Hanbury Brown and Twiss (HBT) interferometry is commonly used to infer the system size, the cluster size should be detected if substructures emerge in space. We demonstrate that a signal peak in the HBT two-particle correlation stands at the relative momentum corresponding to the spatial scale of pseudo one-dimensional modulation. We assess detectability using the data prepared by an event generator (AMPT model) with clustering implemented in the particle distribution.