# Chiral soliton lattice in QCD-like theories

## TL;DR

This paper demonstrates the emergence of a chiral soliton lattice phase in certain QCD-like theories without a sign problem, revealing inhomogeneous phases and challenging previous conjectures about their absence.

## Contribution

It shows that inhomogeneous phases like the CSL can exist in vector-like gauge theories free of the sign problem, providing explicit counterexamples to longstanding conjectures.

## Key findings

- CSL phase appears in sign-problem-free theories under magnetic fields and chemical potential.
- Inhomogeneous order manifests via a roton-like minimum in quasiparticle dispersion.
- Counterexamples to the conjecture linking positivity of the Dirac determinant to absence of inhomogeneous phases.

## Abstract

Recently, it has been shown that the ground state of quantum chromodynamics (QCD) in sufficiently strong magnetic fields and at moderate baryon number chemical potential carries a crystalline condensate of neutral pions: the chiral soliton lattice (CSL). While the result was obtained in a model-independent manner using effective field theory techniques, its realization from first principles using lattice Monte Carlo simulation is hampered by the infamous sign problem. Here we show that CSL, or a similar inhomogeneous phase, also appears in the phase diagram of a class of vector-like gauge theories that do not suffer from the sign problem even in the presence of a baryon chemical potential and external magnetic field. We also show that the onset of nonuniform order manifests itself already in the adjacent homogeneous Bose-Einstein-condensation phase through a characteristic roton-like minimum in the dispersion relation of the lowest-lying quasiparticle mode. Last but not least, our work gives a class of explicit counterexamples to the long-standing conjecture that positivity of the determinant of the Dirac operator (that is, absence of the sign problem) in a vector-like gauge theory precludes spontaneous breaking of translational invariance, and thus implies the absence of inhomogeneous phases in the phase diagram of the theory.