How to get from imaginary to real chemical potential

Abstract

Using the exactly solvable Gross-Neveu model as theoretical laboratory, we analyse in detail the relationship between a relativistic quantum field theory at real and imaginary chemical potential. We find that one can retrieve the full information about the phase diagram of the theory from an imaginary chemical potential calculation. The prerequisite is to evaluate and analytically continue the effective potential for the chiral order parameter, rather than thermodynamic observables or phase boundaries. In the case of an inhomogeneous phase, one needs to compute the full effective action, a functional of the space-dependent order parameter, at imaginary chemical potential.

revtex, 9 pages, 10 figures; v2: add more references, modify concluding section

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Cited by in corpus (37)

• Inhomogeneous Condensates in the Thermodynamics of the Chiral NJL_2 model
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• The critical line of two-flavor QCD at finite isospin or baryon densities from imaginary chemical potentials
• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Analytic continuation of the critical line: suggestions for QCD
• Adjoint QCD on ${\mathbb{R}}^3\times S^1$ with twisted fermionic boundary conditions
• On the critical line of 2+1 flavor QCD
• Analytic continuation from imaginary to real chemical potential in two-color QCD
• The critical line from imaginary to real baryonic chemical potentials in two-color QCD
• The phase diagram of QCD with four degenerate quarks
• Anomaly matching in QCD thermal phase transition
• Crystals of superconducting Baryonic tubes in the low energy limit of QCD at finite density
• Roberge-Weiss endpoint and chiral symmetry restoration in $N_f=2+1$ QCD
• Pion crystals hosting topologically stable baryons
• Probing QCD Phase Structure by Baryon Multiplicity Distribution
• Imaginary polarization as a way to surmount the sign problem in ab initio calculations of spin-imbalanced Fermi gases
• Mapping the phase diagram of strongly interacting matter
• $3d$ fermion-boson map with imaginary chemical potential
• Strong-interaction matter under extreme conditions from chiral quark models with nonlocal separable interactions
• Thermal equation of state of polarized fermions in one dimension via complex chemical potentials
• The fermion-boson map for large d
• Gauge-invariant screening masses and static quark free energies in $N_f=2+1$ QCD at non-zero baryon density
• Fermi gases with imaginary mass imbalance and the sign problem in Monte Carlo calculations
• Dependence of the static quark free energy on ${\mu }_B$ and the crossover temperature of $N_f=2+1$ QCD
• Notes on massless scalar field partition functions, modular invariance and Eisenstein series
• Critical point signatures in the cluster expansion in fugacities
• Analytic non-homogeneous condensates in the $(2+1)$-dimensional Yang-Mills-Higgs-Chern-Simons theory at finite density
• Complex singularities around the QCD critical point at finite densities
• Analytic Baby Skyrmions at Finite Density
• Stable Yang-Lee zeros in truncated fugacity series from net-baryon number multiplicity distribution
• Modular invariance in finite temperature Casimir effect
• Sharp disentanglement in holographic charged local quench
• Analytic continuation in two-color QCD: new results on the critical line
• Lattice QCD at finite density: imaginary chemical potential
• Detecting inhomogeneous chiral condensation from the bosonic two-point function in the $(1+1)$-dimensional Gross-Neveu model in the mean-field approximation
• Exploring new states of matter with a photonic emulator
• Analytic continuation in QCD-like theories at finite density and finite isospin