There is substantial evidence that the ground state of the 2D chiral Gross-Neveu model, in the presence of a U(1) fermion number chemical potential μ and in the large N limit, is given by a "chiral spiral" phase, namely an inhomogeneous phase with a chiral condensate having a spatially periodic phase. We show that the chiral spiral configuration persists at finite N and T=0 for any μ>0. Our analysis is based on nonabelian bosonization, that relates the model to a U(N)_{1} Wess-Zumino-Witten model deformed by current-current interactions. In this description, the appearance of the inhomogeneous phase is surprisingly simple. We also rederive the phase diagram of the large N chiral Gross-Neveu model via a direct diagrammatic computation, finding agreement with previous results in the literature.
In the limit of a large number of flavors, the ground state of the chiral Gross-Neveu model at finite fermion density exhibits a spatially periodic mean field in the form of the chiral spiral, thereby breaking translational invariance. Here we show that the ground state of the same model at finite fermion current density gives rise to a mean field which is periodic in time, a temporal chiral spiral. Since the current density is the same as axial charge density in two dimensions and axial charge is conserved, this may serve as an example of a time crystal. More specifically, as mean field theory is invoked in the large N limit, we are dealing with a semiclassical time crystal.
We explore the finite-density phase diagram of the single-flavour Gross-Neveu-Wilson (GNW) model in (1+1) dimensions using matrix product state (MPS) simulations. At zero temperature and along the symmetry line of the phase diagram, we find a sequence of inhomogeneous ground states that arise through a real-space version of the mechanism of Hilbert-space fragmentation. For weak interactions, doping the symmetry-protected topological (SPT) phase of the GNW model leads to localised charges or holes at periodic arrangements of immobile topological defects separating the fragmented subchains: a topological crystal. Increasing the interactions, we observe a transition into a parity-broken phase with a pseudoscalar condensate displaying a modulated periodic pattern. This soliton lattice is a sequence of topological charges corresponding to anti-kinks, which also bind the doped fermions at their respective centres. Out of this symmetry line, we show that quasi-spiral profiles appear with a characteristic wavevector set by the density k = 2\pi\rho k = 2 π ρ , providing non-perturbative evidence for chiral spirals beyond the large- N N limit. These results demonstrate that various exotic inhomogeneous phases can arise in lattice field theories, and motivate the use of quantum simulators to confirm such QCD-inspired phenomena in future experiments.
During the last few years, the phase diagram of the large N Gross-Neveu model in 1+1 dimensions at finite temperature and chemical potential has undergone a major revision. Here we present a streamlined account of this development, collecting the most important results. Quasi-one-dimensional condensed matter systems like conducting polymers provide real physical systems which can be approximately described by the Gross-Neveu model and have played some role in establishing its phase structure. The kink-antikink phase found at low temperatures is closely related to inhomogeneous superconductors in the Larkin-Ovchinnikov-Fulde-Ferrell phase. With the complete phase diagram at hand, the Gross-Neveu model can now serve as a firm testing ground for new algorithms and theoretical ideas.
During the last few years, the phase diagram of the large N Gross–Neveu model in 1 + 1 dimensions at finite temperature and chemical potential has undergone a major revision. Here, we present a streamlined account of this development, collecting the most important results. Quasi-one-dimensional condensed matter systems like conducting polymers provide real physical systems which can be approximately described by the Gross–Neveu model and have played some role in establishing its phase structure. The kink–antikink phase found at low temperatures is closely related to inhomogeneous superconductors in the Larkin–Ovchinnikov–Fulde–Ferrell phase. With the complete phase diagram at hand, the Gross–Neveu model can now serve as a firm testing ground for new algorithms and theoretical ideas.
The
N-flavor interacting Su-Schrieffer-Heeger (i-SSH) model realizable in cold atoms in an optical lattice is studied. We clarify the relationship between the i-SSH model and the Chiral-Gross-Neveu-Wilson (CGNW) model. Following the previous study of the CGNW model in the high-energy physics community, the ground-state phases of the i-SSH model are investigated and interpreted from the viewpoint of the phases of the CGNW model. The interaction effect on the i-SSH model, belonging to the topological BDI class, is grasped by following the view of the dynamical breakdown of chiral symmetry in the CGNW model. Furthermore, we compare the large-
N ground-state phase diagram with that of the
N=1 case obtained by exact diagonalization, and then we propose a tabletop cold-atom quantum simulator to test the model.
We reinterpret the chiral
U(N) Wess-Zumino-Witten (WZW) model at level
k>1 in
(1+1) dimensions as an interacting chiral metal in two space dimensions. In this reinterpretation, spatial translations along one of the spatial dimensions in the two-dimensional chiral metal arise from a generator of the
U(N) symmetry of the WZW model. The WZW model at
k=1 is equivalent to Balents and Fisher's free chiral metal [L. Balents and M. P. A. Fisher, Phys. Rev. Lett. 76, 2782 (1996)]. Here, the
U(N) symmetry corresponds to the IR symmetry of a chiral Fermi gas with (half of a) Fermi surface, with
N equal to the number of points on the Fermi surface. We argue that exactly solvable interacting generalizations occur for levels
k>1. Importantly, these interacting chiral metals maintain the
U(N) symmetry of the free system. We calculate two-point correlation functions of the single-particle fermion operator, the
U(1) number density, and current operators in these theories for general
k. We find that interactions (
k>1) produce
1/N corrections to scaling of the single-particle fermion operator as $N\ensuremath{\rightarrow}\ensuremath{\infty}$ and renormalize the amplitudes of the density and current two-point functions. This construction illustrates the ersatz Fermi liquid proposal of Else et al. [Phys. Rev. X 11, 021005 (2021)].