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Register a new userTopological superfluids on a lattice with non-Abelian gauge fields
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Two-component fermionic superfluids on a lattice with an external non-Abelian gauge field give access to a variety of topological phases in presence of a sufficiently large spin imbalance. We address here the important issue of superfluidity breakdown induced by spin imbalance by a self-consistent calculation of the pairing gap, showing which of the predicted phases will be experimentally accessible. We present the full topological phase diagram, and we analyze the connection between Chern numbers and the existence of topologically protected and non-protected edge modes. The Chern numbers are calculated via a very efficient and simple method.
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We construct the local Hamiltonian description of the Chern-Simons theory with discrete non-Abelian gauge group on a lattice. We show that the theory is fully determined by the phase factors associated with gauge transformations and classify all possible non-equivalent phase factors. We also construct the gauge invariant electric field operators that move fluxons around and create/anihilate them. We compute the resulting braiding properties of the fluxons. We apply our general results to the simplest class of non-Abelian groups, dihedral groups D_n.
The existence and stability of non-Abelian half-quantum vortices (HQVs) are established in ${}^{3}P_{2}$ superfluids in neutron stars with strong magnetic fields, the largest topological quantum matter in our Universe. Using a self-consistent microscopic framework, we find that one integer vortex is energetically destabilized into a pair of two non-Abelian HQVs due to the strong spin-orbit coupled gap functions. We find a topologically protected Majorana fermion on each HQV, thereby providing two-fold non-Abelian anyons characterized by both Majorana fermions and a non-Abelian first homotopy group.
We consider a noncompact lattice formulation of the three-dimensional electrodynamics with $N$-component complex scalar fields, i.e., the lattice Abelian-Higgs model with noncompact gauge fields. For any $Nge 2$, the phase diagram shows three phases differing for the behavior of the scalar-field and gauge-field correlations: the Coulomb phase (short-ranged scalar and long-ranged gauge correlations), the Higgs phase (condensed scalar-field and gapped gauge correlations), and the molecular phase (condensed scalar-field and long-ranged gauge correlations). They are separated by three transition lines meeting at a multicritical point. Their nature depends on the coexisting phases and on the number $N$ of components of the scalar field. In particular, the Coulomb-to-molecular transition line (where gauge correlations are irrelevant) is associated with the Landau-Ginzburg-Wilson $Phi^4$ theory sharing the same SU($N$) global symmetry but without explicit gauge fields. On the other hand, the Coulomb-to-Higgs transition line (where gauge correlations are relevant) turns out to be described by the continuum Abelian-Higgs field theory with explicit gauge fields. Our numerical study is based on finite-size scaling analyses of Monte Carlo simulations with $C^*$ boundary conditions (appropriate for lattice systems with noncompact gauge variables, unlike periodic boundary conditions), for several values of $N$, i.e., $N=2, 4, 10, 15$, and $25$. The numerical results agree with the renormalization-group predictions of the continuum field theories. In particular, the Coulomb-to-Higgs transitions are continuous for $Ngtrsim 10$, in agreement with the predictions of the Abelian-Higgs field theory.
Topology ultimately unveils the roots of the perfect quantization observed in complex systems. The 2D quantum Hall effect is the celebrated archetype. Remarkably, topology can manifest itself even in higher-dimensional spaces in which control parameters play the role of extra, synthetic dimensions. However, so far, a very limited number of implementations of higher-dimensional topological systems have been proposed, a notable example being the so-called 4D quantum Hall effect. Here we show that mesoscopic superconducting systems can implement higher-dimensional topology and represent a formidable platform to study a quantum system with a purely nontrivial second Chern number. We demonstrate that the integrated absorption intensity in designed microwave spectroscopy is quantized and the integer is directly related to the second Chern number. Finally, we show that these systems also admit a non-Abelian Berry phase. Hence, they also realize an enlightening paradigm of topological non-Abelian systems in higher dimensions.
We introduce a non-Abelian kagome lattice model that has both time-reversal and inversion symmetries and study the flat band physics and topological phases of this model. Due to the coexistence of both time-reversal and inversion symmetries, the energy bands consist of three doubly degenerate bands whose energy and conditions for the presence of flat bands could be obtained analytically, allowing us to tune the flat band with respect to the other two dispersive bands from the top to the middle and then to the bottom of the three bands. We further study the gapped phases of the model and show that they belong to the same phase as the band gaps only close at discrete points of the parameter space, making any two gapped phases adiabatically connected to each other without closing the band gap. Using the Pfaffian approach based on the time-reversal symmetry and parity characterization from the inversion symmetry, we calculate the bulk topological invariants and demonstrate that the unique gapped phases belong to the $Z_2$ quantum spin Hall phase, which is further confirmed by the edge state calculations.
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