Simple Z2 lattice gauge theories at finite fermion density

Abstract

Lattice gauge theories are a powerful language to theoretically describe a variety of strongly correlated systems, including frustrated magnets, high-Tc superconductors, and topological phases. However, in many cases gauge fields couple to gapless matter degrees of freedom and such theories become notoriously difficult to analyze quantitatively. In this paper we study several examples of Z2 lattice gauge theories with gapless fermions at finite density, in one and two spatial dimensions, that are either exactly soluble or whose solution reduces to that of a known problem. We consider complex fermions (spinless and spinful) as well as Majorana fermions, and study both theories where Gauss' law is strictly imposed and those where all background charge sectors are kept in the physical Hilbert space. We use a combination of duality mappings and the Z2 slave-spin representation to map our gauge theories to models of gauge-invariant fermions that are either free, or with on-site interactions of the Hubbard or Falicov-Kimball type that are amenable to further analysis. In 1D, the phase diagrams of these theories include free-fermion metals, insulators, and superconductors; Luttinger liquids; and correlated insulators. In 2D, we find a variety of gapped and gapless phases, the latter including uniform and spatially modulated flux phases featuring emergent Dirac fermions, some violating Luttinger's theorem. arXiv:1708.08507v2 [cond-mat.str-el]

Orthogonal metal in the Hubbard model with liberated slave spins

“…taking U > 0,Ĥ c + (Ĥ c − ) corresponds to repulsive (attractive) interactions. This identification relies on the highly symmetric form of interactions in the FKM (1) with only a single interaction parameter U , in contrast to more general multi-component FKMs with independent interaction matrix elements and onsite energies [36,37].…”

“…Regarding the first possibility, we show in Fig. 8 the momentum distribution function (36) and the local Green function defined in Eq. (31), which depend only on |U |.…”

“…In fact, the duality reveals that the Ising variables of the FKM are exactly the constraints of the slave-spin representation. Considerations regarding the relevance of the latter lead to the generalized phase diagram of the unconstrained [36] slave-spin Hubbard model shown in Fig. 2 and discussed in Sec.…”

Dynamics of compact quantum electrodynamics at large fermion flavor

“…For several decades, the topic of dynamical coupling between lattice gauge fields and fermionic matter fields have attracted considerable attention among physicists from highenergy [2][3][4][5][6][7][8] and condensed matter [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] communities. Previous works have quickly established the understanding at the large fermion flavor (N f ) limit [9][10][11][12][13][14][15][16][17], as 1/N f expansion is controlled thence, but left the physically most interesting cases of small N f -for example N f = 2 corresponds to the spin-1/2 case of electrons -unsolved.…”

Native three-body interaction in superconducting circuits

“…Alternatively to a three-qubit gate, direct threebody interactions are useful for quantum simulation of lattice gauge theories. For example an XXX-coupling is needed for the hopping of particles between lattice sites mediated by a U(1) gauge field living on the link between sites [7], and the matter-gauge interaction in Z 2 gauge theories is an XXZ-coupling [46]. Our approach could be used to derive circuits which implements such interactions directly.…”