From relativistic quantum fields to condensed matter and back again: updating the Gross–Neveu phase diagram

Thies, Michael

doi:10.1088/0305-4470/39/41/s04

Cited by 159 publications

(250 citation statements)

References 55 publications

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“…(41) is limited to lower-dimensional modulations, the problem can be mapped onto a lower-dimensional one. In particular, the analytically known solutions of the 1 + 1 dimensional GN and NJL 2 models [51,52,53] can be utilized to construct solutions with one-dimensional modulations in 3 + 1 dimensions. The details of this very powerful method are discussed in the following.…”

Section: One-dimensional Modulationsmentioning

confidence: 99%

“…The lower part of Fig. 10 shows the quark number density for the solitonic solutions, which is proportional to [82,107,52,53] …”

Section: Solitonic Solutionsmentioning

confidence: 99%

“…[51,52,53]. In 1 + 1 dimensions, the mechanism described above is very effective and basically corresponds to the Peierls instability in one-dimensional electron chains [54].…”

Section: Introductionmentioning

confidence: 99%

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Inhomogeneous chiral condensates

Buballa

Carignano

2015

Progress in Particle and Nuclear Physics

247

258

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The chiral condensate, which is constant in vacuum, may become spatially modulated at moderately high densities where in the traditional picture of the QCD phase diagram a first-order chiral phase transition occurs. We review the current status of this idea, which originally dates back to Migdal's pion condensation, but recently received new momentum through studies on the nature of the chiral critical point and by the conjecture of a quarkyonic-matter phase. We discuss how these nonuniform phases emerge in generalized Ginzburg-Landau analyses as well as in specific calculations, both within effective models and in Dyson-Schwinger or large-N c approaches to QCD. Questions about the most favored shape of the modulations and its dimension, and about the effects of nonzero isospin chemical potential, strange quarks, color superconductivity, and external magnetic fields on these inhomogeneous phases will be addressed as well.

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Section: One-dimensional Modulationsmentioning

confidence: 99%

“…The lower part of Fig. 10 shows the quark number density for the solitonic solutions, which is proportional to [82,107,52,53] …”

Section: Solitonic Solutionsmentioning

confidence: 99%

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Inhomogeneous chiral condensates

Buballa

Carignano

2015

Progress in Particle and Nuclear Physics

247

258

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“…We choose the Gross-Neveu (GN) model in 1+1 dimensions [17] where in the large N limit all thermodynamic observables can easily be computed at both real and imaginary chemical potential, to any desired accuracy. Nevertheless the phase diagram at real µ is non-trivial, sharing qualitative properties with QCD (see [18] for a recent review). We then pretend that we are only able to compute all quantities at imaginary µ and try to extrapolate them to real µ, controlling our procedure against the exact results at each step.…”

Section: Introductionmentioning

confidence: 99%

How to get from imaginary to real chemical potential

Karbstein

Thies

2007

Phys. Rev. D

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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.

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“…More generally, the interaction of fermions with solitonic backgrounds could produce or affect a variety of interesting physical phenomena such as charge and fermion number fractionalization [79][80][81][82][83], hadron physics [68,69,[84][85][86], superfluidity [87,88], superconductivity [89], BoseEinstein condensation [90,91], conducting polymers [83,[92][93][94] and localization of fermions [95][96][97][98]. The spectrum of the fermion can in general be distorted due to the presence of such a background; bound states can appear and continuum states can change as compared with the free fermion.…”

Section: Introductionmentioning

confidence: 99%

An investigation of the Casimir energy for a fermion coupled to the sine-Gordon soliton with parity decomposition

2014

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We consider a fermion chirally coupled to a prescribed pseudoscalar field in the form of the soliton of the sine-Gordon model and calculate and investigate the Casimir energy and all of the relevant quantities, i.e. the spectrum of the states and the phase shifts, for each parity channel, separately. We present and use a simple prescription to construct the simultaneous eigenstates of the Hamiltonian and parity in the continua from the scattering states. We also use a prescription we had introduced earlier to calculate unique expressions for the phase shifts and check their consistency with both the weak and the strong forms of the Levinson theorem. In the graphs of the total and parity decomposed Casimir energies as a function of the parameters of the pseudoscalar field distinctive deformations appear whenever a fermionic bound state energy level with definite parity crosses the line of zero energy. However, the latter graphs show considerable sensitivity to the fine details of the shape of the background field which cannot be seen from the graph of the total Casimir energy. Finally, we consider a system consisting of a valence fermion in the ground state and find that the most energetically favorable configuration is the one with a soliton of winding number one, and this conclusion does not hold for each parity, separately.

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From relativistic quantum fields to condensed matter and back again: updating the Gross–Neveu phase diagram

Cited by 159 publications

References 55 publications

Inhomogeneous chiral condensates

Inhomogeneous chiral condensates

How to get from imaginary to real chemical potential

An investigation of the Casimir energy for a fermion coupled to the sine-Gordon soliton with parity decomposition

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