#### 2024-04-26 16:00 Virtual

# Quantum pion liquid in finite-density QCD? A tale in two acts

#### Marc Winstel

In the intermediate density region of the QCD phase diagram, there have

been conjectures about different phenomena involving spatial modulations

of the chiral order parameter. The most prominent one in the discussion

is the so-called inhomogeneous chiral phase, where the chiral condensate

spontaneously breaks translational invariance in addition to chiral

symmetry. A recent Functional Renormalization group study finds a

so-called Moat regime in the vicinity of the critical point, where

mesonic dispersion relations favor non-vanishing momenta. This regime is

understood as a precursor for an inhomogeneous phase, but, in general,

favors all phenomena related to spatial inhomogeneities in mesonic

correlation functions.

In this talk, I am going to discuss a scenario recently termed ‘‘quantum

pion liquid’’, which is a regime with oscillating, exponentially

suppressed spatial correlation functions of mesonic fields. I present

results, where this regime is observed in two-different low-energy

effective models with different field content and different

methodologies. In the first part of the talk a scalar O(N) model, which

is tuned to classically feature an inhomogeneous phase, is studied using

lattice field theory in order to investigate the effect of bosonic

quantum fluctuations on the inhomogeneous condensate. First results

indicate that the inhomogeneous condensate is indeed disordered through

bosonic quantum fluctuations. Instead, a quantum pion liquid behavior is

obtained in the two-point correlation functions. A mechanism for the

disordering as well as possible alternative regimes are discussed.

In the second part of the talk, I am going to study 2+1-dimensional

four-fermion and Yukawa models in the mean-field approximation. Using a

stability analysis based on homogeneous ground states, strong evidence

for the absence of inhomogeneous chiral condensates in this model is

presented. By accessing the inverse of the mesonic two-point correlation

functions in the mean-field approach, a quantum pion liquid with

oscillating, but exponentially suppressed two-point correlation

functions is observed at non-vanishing chemical potential. The existence

of this regime aligns with expectations based on symmetry arguments,

that are also applicable to QCD at non-vanishing baryon density. The

phase diagram of the model at non-vanishing temperature and chemical

potential is presented.

References:

1. Pannullo, Winstel, Physical Review D 108, 036011

2. Winstel, arXiv: 2403.07430 (under consideration at Physical Review D)

3. Winstel, Valgushev, arXiv: 2403.18606 (conference talk at Excited QCD 2024)