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.

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)