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 po- tential carries a crystalline condensate of neutral pions: the chiral soliton lattice (CSL) [1]. While the result was obtained in a model-independent manner using effective field the- ory 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 inhomoge- neous 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 quasipar- ticle 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.
Highlights
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) [1]
We show that CSL, or a similar inhomogeneous phase, 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
The goal of this paper is to show that the CSL phase, or a similar inhomogeneous phase, appears in the phase diagram of an infinite class of QCD-like theories free of the sign problem
Summary
We consider a class of QCD-like theories where quarks transform in a real or pseudoreal representation of the gauge group. It is well-known that for N flavors of massless quarks, (pseudo)real QCD-like theories possess an enlarged global symmetry, G = SU(2N ) This includes the usual chiral symmetry of QCD, SU(N )L × SU(N )R × U(1)B, as a subgroup. The low-energy EFT for the NG degrees of freedom is constructed as a nonlinear sigma model on the coset space G/H It would appear from our above discussion that we need two different EFTs, one for real and one for pseudoreal theories. The low-energy physics will be dominated by the electrically neutral NG modes To construct their EFT description, it is sufficient to consider the subgroups of G and H, left intact by the magnetic field. This has to be specified concretely before we can proceed with the analysis of the EFT
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