Imaginary Isospin Research Articles

Light Roberge-Weiss tricritical endpoint at imaginary isospin and baryon chemical potential

Imaginary chemical potentials serve as a useful tool to constrain the QCD phase diagram and to gain insight into the thermodynamics of strongly interacting matter. In this study, we report on the first determination of the phase diagram for arbitrary imaginary baryon and isospin chemical potentials at high temperature using one-loop perturbation theory, revealing a nontrivial structure of Roberge-Weiss (RW) phase transitions in this plane. Subsequently, this system is simulated numerically with Nf=2 unimproved staggered quarks on Nτ=4 lattices at a range of temperatures at one of the RW phase transitions. We establish a lower bound for the light quark mass, where the first-order transition line terminates in a tricritical point. It is found that this tricritical mass is increased as compared to the case of purely baryonic imaginary chemical potentials, indicating that our setup is more advantageous for identifying critical behavior toward the chiral limit. Finally, the dynamics of local Polyakov loop clusters is also studied in conjunction with the RW phase transition. Published by the American Physical Society 2024

Finite-density massless two-color QCD at the isospin Roberge-Weiss point and the 't Hooft anomaly

We study the phase diagram of two-flavor massless two-color QCD (QC$_2$D) under the presence of quark chemical potentials and imaginary isospin chemical potentials. At the special point of the imaginary isospin chemical potential, called the isospin Roberge--Weiss (RW) point, two-flavor QC$_2$D enjoys the $\mathbb{Z}_2$ center symmetry that acts on both quark flavors and the Polyakov loop. We find a $\mathbb{Z}_2$ 't Hooft anomaly of this system, which involves the $\mathbb{Z}_2$ center symmetry, the baryon-number symmetry, and the isospin chiral symmetry. Anomaly matching, therefore, constrains the possible phase diagram at any temperatures and quark chemical potentials at the isospin RW point, and we compare it with previous results obtained by chiral effective field theory and lattice simulations. We also point out an interesting similarity of two-flavor massless QC$_2$D with $(2+1)$d quantum anti-ferromagnetic systems.

Confinement and symmetry in three-flavor QCD

We investigate the relation between theconfinement and the symmetry in three-flavor QCD with imaginary isospin chemical potentials (μu, μd, μs) = (iθT, −iθT, 0), using the Polyakov-loop extended Nambu–Jona–Lasinio (PNJL) model, where T is temperature. As for three-degenerate flavors, the system has symmetry at θ = 2π/3 and hence the Polyakov loop Φ vanishes there for small T. As for 2+1 flavors, the symmetry is not preserved for any θ, but Φ becomes zero at θ = θconf < 2π/3 for small T. The confinement phase defined by Φ = 0 is realized, even if the system does not have symmetry exactly. In the θ–T plane, there is a critical endpoint of deconfinement transition. The deconfinement crossover at zero chemical potential is a remnant of the first-order deconfinement transition at θ = θconf. The relation between the non-diagonal element χus of quark-number susceptibilities and the deconfinement transition is studied. The present results can be checked by lattice QCD simulations directly, since the simulations are free from the sign problem for any θ.

Critical line of two-flavor QCD at finite isospin or baryon densities from imaginary chemical potentials

We determine the (pseudo)critical lines of QCD with two degenerate staggered fermions at nonzero temperature and quark or isospin density, in the region of imaginary chemical potentials; analytic continuation is then used to prolongate to the region of real chemical potentials. We obtain an accurate determination of the curvatures at zero chemical potential, quantifying the deviation between the case of finite quark and of finite isospin chemical potential. Deviations from a quadratic dependence of the pseudocritical lines on the chemical potential are clearly seen in both cases: we try different extrapolations and, for the case of nonzero isospin chemical potential, confront them with the results of direct Monte Carlo simulations. Finally we find that, as for the finite quark density case, an imaginary isospin chemical potential can strengthen the transition till turning it into strong first order.

The kth smallest Dirac operator eigenvalue and the pion decay constant

We derive an analytical expression for the distribution of the kth smallest Dirac eigenvalue in QCD with an imaginary isospin chemical potential in the Dirac operator for arbitrary gauge field topology ν. Because of its dependence on the pion decay constant Fπ through the chemical potential in the epsilon regime of chiral perturbation theory, this can be used for lattice determinations of that low-energy constant. On the technical side, we use a chiral random-two matrix theory, where we express the kth eigenvalue distribution through the joint probability of the ordered k smallest eigenvalues. The latter can be computed exactly for finite and infinite N, for which we derive generalizations of Dyson’s integration theorem and Sonine’s identity.

Entanglement between deconfinement transition and chiral symmetry restoration

We extend the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model by introducing an effective four-quark vertex depending on Polyakov loop. The effective vertex generates entanglement interactions between Polyakov loop and chiral condensate. The new model is consistent with lattice QCD data at imaginary quark-number chemical potential and real and imaginary isospin chemical potentials, particularly on strong correlation between the chiral and deconfinement transitions and also on the quark-mass dependence of the order of the Roberge-Weiss endpoint predicted by lattice QCD very lately. We investigate an influence of the entanglement interactions on a location of the tricritical point at real isospin chemical potential and a location of the critical endpoint at real quark-number chemical potential.

Parameters of the lowest order chiral Lagrangian from fermion eigenvalues

Recent advances in random matrix theory enable one to determine the pseudoscalar decay constant from the dependence of the eigenvalues of the valence Dirac operator on an imaginary isospin chemical potential. We perform a pilot test of this idea, from simulations with two flavors of dynamical overlap fermions.

MATRIX MODELS AND QCD WITH CHEMICAL POTENTIAL

The random matrix model approach to quantum chromodynamics (QCD) with nonvanishing chemical potential is reviewed. The general concept using global symmetries is introduced, as well as its relation to field theory, the so-called epsilon regime of chiral perturbation theory (∊χPT). Two types of matrix model results are distinguished: phenomenological applications leading to phase diagrams, and an exact limit of the QCD Dirac operator spectrum matching with ∊χPT. All known analytic results for the spectrum of complex and symplectic matrix models with chemical potential are summarised for the symmetry classes of ordinary and adjoint QCD, respectively. These include correlation functions of Dirac operator eigenvalues in the complex plane for real chemical potential, and in the real plane for imaginary isospin chemical potential. Comparisons of these predictions to recent lattice simulations are also discussed.

Determining Fπ from spectral sum rules

We derive spectral sum rules for a system with two quarks coupled to an imaginary isospin chemical potential in the \epsilon regime. The sum rules show an explicit dependence on the pion decay constant which should make it possible to measure F_pi from the eigenvalue spectrum of this particular Dirac operator.

Microscopic eigenvalue correlations in QCD with imaginary isospin chemical potential

We consider the chiral limit of QCD subjected to an imaginary isospin chemical potential. In the epsilon-regime of the theory we can perform precise analytical calculations based on the zero-momentum Goldstone modes in the low-energy effective theory. We present results for the spectral correlation functions of the associated Dirac operators.

ExtractingFπfrom small lattices: Unquenched results

We calculate the response of the microscopic Dirac spectrum to an imaginary isospin chemical potential for QCD with two dynamical flavors in the chiral limit. This extends our previous calculation from the quenched to the unquenched theory. The resulting spectral correlation function in the $\epsilon$-regime provides here, too, a new and efficient way to measure $F_\pi$ on the lattice. We test the method in a hybrid Monte Carlo simulation of the theory with two staggered quarks.

The Lattice NJL Model at Non-zero Baryon and Isospin Densities

We present initial results of a numerical investigation of the chiral symmetry restoring transition in the (3+1)-dimensional Nambu – Jona-Lasinio model with both non-zero baryon chemical potential ( μ B ≠ 0 ) and isospin chemical potential ( μ I ≠ 0 ). With non-zero isospin chemical potential, the model suffers from a sign problem. We proceed in two ways: ( i ) We perform “partially quenched” simulations in which μ I is made non-zero only during the measurement of chiral observables; ( ii ) We perform full simulations with imaginary isospin chemical potential with the aim to analytically continue results to real μ I .