Emergent macroscopic descriptions of matter, such as hydrodynamics, are central to our description of complex physical systems across a wide spectrum of energy scales. The conventional understanding of these many-body phenomena has recently been shaken by a number of experimental findings. Collective behavior of matter has been observed in mesoscopic systems, such as high-energy hadron–hadron collisions, or ultracold gases with only a few strongly interacting fermions. In such systems, the separation of scales between macroscopic and microscopic dynamics (at the heart of any effective theory) is inapplicable. To address the conceptual challenges that arise from these observations and explore the universality of emergent descriptions of matter, the EMMI Rapid Reaction Task Force was assembled. This document summarizes the RRTF discussions on recent theoretical and experimental advances in this rapidly developing field. Leveraging technological breakthroughs in the control of quantum systems, we can now quantitatively explore what it means for a system to exhibit behavior beyond the sum of its individual parts. In particular, the report highlights how the (in)applicability of hydrodynamics and other effective theories can be probed across three principal frontiers: the size frontier, the equilibrium frontier, and the interaction frontier.

We describe numerical simulations of the critical dynamics near the superfluid phase transition. The calculations are based on an implementation of a stochastic hydrodynamic theory known as model F in the classification of Hohenberg and Halperin. This theory is expected to describe dynamic scaling near the lambda transition in liquid ^4He, Bose-Einstein condensation in ultracold atomic gases, and the superfluid transition in the unitary Fermi gas. Our simulation is based on a Metropolis algorithm previously applied to the critical endpoint of the liquid-gas phase transition in ordinary fluids. In the model E truncation of model F we obtain the expected dynamical exponent z≃ 3/2. We observe the emergence of a propagating second sound mode at the phase transition. The second sound diffusivity D_s is consistent with the scaling relation D_s∼ ξ^x_κ, where ξ is the correlation length and x_κ=1/2.

We present simulations of the real time dynamics of a fluid in the vicinity of a critical endpoint in the phase diagram. The relevant hydrodynamic theory is known as model H, and it is expected to describe the long-distance dynamics of QCD matter in the vicinity of a possible critical endpoint in the QCD phase diagram.

We investigate dynamical mean-field calculations of the three-band Emery model at the one- and two-particle level for material-realistic parameters of high-T_c superconductors. Our study shows that even within dynamical mean-field theory, which accounts solely for temporal fluctuations, the intrinsic multi-orbital nature of the Emery model introduces effective non-local correlations. These correlations lead to a non-Curie-like temperature dependence of the magnetic susceptibility, consistent with nuclear magnetic resonance experiments in the pseudogap regime. By analyzing the temperature dependence of the uniform static spin susceptibility obtained by single-site and cluster dynamical mean-field theory, we find indications of emerging oxygen-copper singlet fluctuations, explicitly captured by the model. Despite correctly describing the hallmark of the pseudogap at the two-particle level, such as the drop in the Knight shift of nuclear magnetic resonance, dynamical mean-field theory fails to capture the spectral properties of the pseudogap.

The destruction of metallicity due to the mutual Coulomb interaction of quasiparticles gives rise to fascinating phenomena of solid state physics such as the Mott metal-insulator transition and pseudogap. A key observable characterizing their occurrences is the single-particle spectral function, determined by the fermionic self-energy. In this paper, we investigate in detail how real space fluctuations are responsible for a self-energy that drives the Mott-Hubbard metal-insulator transition. To this aim, we first introduce a real space fluctuation diagnostics approach to the Hedin equation, which connects the fermion-boson coupling vertex λ to the self-energy Σ. Second, by using cellular dynamical mean-field theory calculations, we unambiguously identify nearest-neighbor antiferromagnetic excitations as the leading physical processes responsible for the destruction of metallicity across the transition.

We compute the complete set of second-order transport coefficients of the unitary Fermi gas, a dilute gas of spin-1/2 particles interacting via an s-wave interaction tuned to infinite scattering length. The calculation is based on kinetic theory and the Chapman-Enskog method at second order in the Knudsen expansion. We take into account the exact two-body collision integral. We extend previous results on second-order coefficients related to shear stress by including terms related to heat flow and gradients of the fugacity. We confirm that the thermal relaxation time is given by the simple estimate tau kappa = kappa m/(cPT ) even if the full collision kernel is taken into account. Here, kappa is the thermal conductivity, m is the mass of the particles, cP is the specific heat at constant pressure, and T is the temperature.

We study heat conduction and momentum transport in the context of stochastic fluid dynamics. We consider a fluid described by model H in the classification of Hohenberg and Halperin. We study both noncritical and critical fluids, and we investigate transport properties in two as well as three dimensions. Our results are based on numerical simulations of model H using a Metropolis algorithm, and we employ Kubo relations to extract transport coefficients. We observe the expected logarithmic divergence of the shear viscosity in a two-dimensional noncritical fluid. At a critical point, we find that the transport coefficients exhibit power-law scaling with the system size L. The strongest divergence is seen for the thermal conductivity kappa in two dimensions. We find kappa similar to Lx kappa with x kappa = 1.6 + 0.1. The divergence is weaker in three dimensions, x kappa = 1.25 + 0.3, and the scaling exponent for the shear viscosity, x eta, is significantly smaller than x kappa in both two and three dimensions.

This White Paper presents an overview of the current status and future perspective of QCD research, based on the community inputs and scientific conclusions from the 2022 Hot and Cold QCD Town Meeting. We present the progress made in the last decade toward a deep understanding of both the fundamental structure of the sub-atomic matter of nucleon and nucleus in cold QCD, and the hot QCD matter in heavy ion collisions. We identify key questions of QCD research and plausible paths to obtaining answers to those questions in the near future, hence defining priorities of our research over the coming decades.

There are two distinct regimes of Yang-Mills theory where we can demonstrate confinement, the existence of a mass gap, and fractional theta angle dependence using a reliable semi-classical calculation. The two regimes are Yang-Mills theory on S^1 ×ℝ^3 with a small circle and a double-trace deformation, and Yang-Mills theory on T^2 ×ℝ^2 where the torus T^2 is small and threaded by a 't Hooft flux. In the first case the confinement mechanism is related to self-dual monopoles, whereas in the second case self-dual center-vortices play a crucial role. These two topological objects are distinct. In particular, they have different mutual statistics with Wilson loops. On the other hand, they carry the same topological charge and action. On ℝ× T^2 × S^1, we are able to extrapolate both monopole regime and vortex regime to a quantum mechanical domain, where a cross-over takes place. Both sides of the cross-over are described by a deformed ℤ_N TQFT. On ℝ^2 × S^1 × S^1, we derive the effective field theory of vortices from the effective theory of monopoles in the presence of a 't Hooft flux. This results from a two-stage adjoint Higgs mechanism, to U(1)^N-1 in 3d first and a ℤ_N EFT in 2d second. This proves adiabatic continuity of the two confinement mechanisms across dimensions and shows how monopoles and their magnetic flux transmute into center-vortices. This basic mechanism is flux fractionalization: The magnetic flux of the monopoles fractionalizes and collimates in such a way that 2d Wilson loops detect it as a center vortex.

There are two distinct regimes of Yang-Mills theory where we can demonstrate confinement, the existence of a mass gap, and the multi-branch structure of the effective potential as a function of the theta angle using a reliable semi-classical calculation. The two regimes are deformed Yang-Mills theory on ℝ3 × S1, and Yang-Mills theory on ℝ2 × T2 where the torus is threaded by a ’t Hooft flux. The weak coupling regime is ensured by the small size of the circle or torus. In the first case the confinement mechanism is related to self-dual monopoles, whereas in the second case self-dual center-vortices play a crucial role. These two topological objects are distinct. In particular, they have different mutual statistics with Wilson loops. On the other hand, they carry the same topological charge and action. We consider the theory on ℝ × T2 × S1 and extrapolate both the monopole and vortex regimes to a quantum mechanical domain, where a cross-over takes place. Both sides of the cross-over are described by a deformed ℤN TQFT. On ℝ2 × S1 × S1, we derive an effective field theory (EFT) of vortices from the EFT of monopoles in the presence of a ’t Hooft flux. This construction is based on a two-stage Higgs mechanism, reducing SU(N) to U(1)N−1 in 3d first, followed by reduction to a ℤN EFT in 2d in the second step. This result shows how monopoles transmute into center-vortices, and suggests adiabatic continuity between the two confinement mechanisms. The basic mechanism is flux fractionalization: the magnetic flux of the monopoles splits up and is collimated in such a way that 2d Wilson loops detect it as a center vortex.

Abstract There are two distinct regimes of Yang-Mills theory where we can demonstrate confinement, the existence of a mass gap, and the multi-branch structure of the effective potential as a function of the theta angle using a reliable semi-classical calculation. The two regimes are deformed Yang-Mills theory on ℝ 3 × S 1, and Yang-Mills theory on ℝ 2 × T 2 where the torus is threaded by a ’t Hooft flux. The weak coupling regime is ensured by the small size of the circle or torus. In the first case the confinement mechanism is related to self-dual monopoles, whereas in the second case self-dual center-vortices play a crucial role. These two topological objects are distinct. In particular, they have different mutual statistics with Wilson loops. On the other hand, they carry the same topological charge and action. We consider the theory on ℝ × T 2 × S 1 and extrapolate both the monopole and vortex regimes to a quantum mechanical domain, where a cross-over takes place. Both sides of the cross-over are described by a deformed ℤ N TQFT. On ℝ 2 × S 1 × S 1, we derive an effective field theory (EFT) of vortices from the EFT of monopoles in the presence of a ’t Hooft flux. This construction is based on a two-stage Higgs mechanism, reducing SU(N) to U(1) N−1 in 3d first, followed by reduction to a ℤ N EFT in 2d in the second step. This result shows how monopoles transmute into center-vortices, and suggests adiabatic continuity between the two confinement mechanisms. The basic mechanism is flux fractionalization: the magnetic flux of the monopoles splits up and is collimated in such a way that 2d Wilson loops detect it as a center vortex.

There are two distinct regimes of Yang-Mills theory where we can demonstrate confinement, the existence of a mass gap, and the multi-branch structure of the effective potential as a function of the theta angle using a reliable semi-classical calculation. The two regimes are deformed Yang-Mills theory on R-3 x S-1, and Yang-Mills theory on R-2 x T-2 where the torus is threaded by a 't Hooft flux. The weak coupling regime is ensured by the small size of the circle or torus. In the first case the confinement mechanism is related to self-dual monopoles, whereas in the second case self-dual center-vortices play a crucial role. These two topological objects are distinct. In particular, they have different mutual statistics with Wilson loops. On the other hand, they carry the same topological charge and action. We consider the theory on R x T-2 x S-1 and extrapolate both the monopole and vortex regimes to a quantum mechanical domain, where a cross-over takes place. Both sides of the cross-over are described by a deformed Z(N) TQFT. On R-2 x S-1 x S-1, we derive an effective field theory (EFT) of vortices from the EFT of monopoles in the presence of a 't Hooft flux. This construction is based on a two-stage Higgs mechanism, reducing SU(N) to U(1) N-1 in 3d first, followed by reduction to a Z(N) EFT in 2d in the second step. This result shows how monopoles transmute into center-vortices, and suggests adiabatic continuity between the two confinement mechanisms. The basic mechanism is flux fractionalization: the magnetic flux of the monopoles splits up and is collimated in such a way that 2d Wilson loops detect it as a center vortex.

We introduce a spin-symmetry-broken extension of the connected determinant algorithm [Riccardo Rossi, Determinant diagrammatic Monte Carlo algorithm in the thermodynamic limit, Phys. Rev. Lett. 119, 045701 (2017).PRLTAO0031-900710.1103/PhysRevLett.119.045701]. The resulting systematic perturbative expansions around an antiferromagnetic state allow for numerically exact calculations directly inside a magnetically ordered phase. We show new precise results for the magnetic phase diagram and thermodynamics of the three-dimensional cubic Hubbard model at half-filling. With detailed computations of the order parameter in the low to intermediate-coupling regime, we establish the Néel phase boundary. The critical behavior in its vicinity is shown to be compatible with the O(3) Heisenberg universality class. By determining the evolution of the entropy with decreasing temperature through the phase transition we identify the different physical regimes at U/t=4. We provide quantitative results for several thermodynamic quantities deep inside the antiferromagnetic dome up to large interaction strengths and investigate the crossover between the Slater and Heisenberg regimes.

We explore the far-off-equilibrium aspects of the (1+1)-dimensional early-stage evolution of a weakly-coupled quark-gluon plasma using kinetic theory and hydrodynamics. For a large set of far-off-equilibrium initial conditions the system exhibits a peculiar phenomenon where its total equilibrium entropy decreases with time. Using a non-equilibrium definition of entropy based on Boltzmann's H-function, we demonstrate how this apparently anomalous behavior is consistent with the second law of thermodynamics. We also use the H-function to formulate `maximum-entropy' hydrodynamics, a far-off-equilibrium macroscopic theory that can describe both free-streaming and near-equilibrium regimes of quark-gluon plasma in a single framework.

The ability to control the properties of twisted bilayer transition metal dichalcogenides in situ makes them an ideal platform for investigating the interplay of strong correlations and geometric frustration. Of particular interest are the low energy scales, which make it possible to experimentally access both temperature and magnetic fields that are of the order of the bandwidth or the correlation scale. In this manuscript we analyze the moiré Hubbard model, believed to describe the low energy physics of an important subclass of the twisted bilayer compounds. We establish its magnetic and the metal-insulator phase diagram for the full range of magnetic fields up to the fully spin polarized state. We find a rich phase diagram including fully and partially polarized insulating and metallic phases of which we determine the interplay of magnetic order, Zeeman-field, and metallicity, and make connection to recent experiments.

We present simulations of stochastic fluid dynamics in the vicinity of a critical endpoint belonging to the universality class of the Ising model.This study is motivated by the challenge of modeling the dynamics of critical fluctuations near a conjectured critical endpoint in the phase diagram of Quantum Chromodynamics (QCD).We focus on the interaction of shear modes with a conserved scalar density, which is known as model H.We show that the observed dynamical scaling behavior depends on the correlation length and the shear viscosity of the fluid.As the correlation length is increased or the viscosity is decreased we observe a cross-over from the dynamical exponent of critical diffusion, z ≃ 4, to the expected scaling exponent of model H, z ≃ 3. We use our method to investigate time-dependent correlation function of non-Gaussian moments M n (t) of the order parameter.We find that the relaxation time depends in non-trivial manner on the power n.

We describe numerical simulations of the stochastic diffusion equation with a conserved charge. We focus on the dynamics in the vicinity of a critical point in the Ising universality class. The model we consider is expected to describe the critical dynamics near a possible QCD critical point if the coupling of the order parameter to the momentum density of the fluid can be neglected. The simulations are performed on a spatial lattice, and the time evolution is performed using a Metropolis algorithm. We determine the dynamical critical exponent $z\simeq 3.972(2)$, which agrees with predictions of the epsilon expansion. We also study non-equilibrium sweeps of the reduced temperature and observe approximate Kibble-Zurek scaling.

We consider the hydrodynamic evolution of a quark-gluon gas with non-zero quark masses and net baryon number in its phase diagram. For far-off-equilibrium initial conditions the expansion trajectories appear to violate simple rules based on the second law of thermodynamics that were previously established for ideal or weakly dissipative fluids. For Bjorken flow we present a detailed analysis within kinetic theory that provides a full microscopic understanding of these macroscopic phenomena and establishes their thermodynamic consistency. We point out that, for certain far-off-equilibrium initial conditions, the well-known phenomenon of "viscous heating" turns into "viscous cooling" where, driven by dissipative effects, the temperature decreases faster than in adiabatic expansion.

Abstract We construct one- and two-particle irreducible (1PI and 2PI) effective actions for the stochastic fluid dynamics of a conserved density undergoing diffusive motion. We compute the 1PI action in one-loop order and the 2PI action in two-loop approximation. We derive a set of Schwinger-Dyson equations and regularize the resulting equations using Pauli-Villars fields. We numerically solve the Schwinger-Dyson equations for a non-critical fluid. We find that higher-loop effects summed by the Schwinger-Dyson renormalize the non-linear coupling. We also find indications of a diffuson-cascade, the appearance of n-loop correction with smaller and smaller exponential suppression.

Hot QCD physics studies the nuclear strong force under extreme temperature and densities. Experimentally these conditions are achieved via high-energy collisions of heavy ions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). In the past decade, a unique and substantial suite of data was collected at RHIC and the LHC, probing hydrodynamics at the nucleon scale, the temperature dependence of the transport properties of quark-gluon plasma, the phase diagram of nuclear matter, the interaction of quarks and gluons at different scales and much more. This document, as part of the 2023 nuclear science long range planning process, was written to review the progress in hot QCD since the 2015 Long Range Plan for Nuclear Science, as well as highlight the realization of previous recommendations, and present opportunities for the next decade, building on the accomplishments and investments made in theoretical developments and the construction of new detectors. Furthermore, this document provides additional context to support the recommendations voted on at the Joint Hot and Cold QCD Town Hall Meeting, which are reported in a separate document.