Adventure in Topological Phase Transitions in 3+1 -D: Non-Abelian Deconfined Quantum Criticalities and a Possible Duality

Abstract

Continuous quantum phase transitions that are beyond the conventional paradigm of fluctuations of a symmetry breaking order parameter are challenging for theory. These phase transitions often involve emergent deconfined gauge fields at the critical points[1-4] as demonstrated in 2 + 1-dimensions. Examples include phase transitions in quantum magnetism as well as those between Symmetry Protected Topological phases. In this paper, we present several examples of Deconfined Quantum Critical Points (DQCP) between Symmetry Protected Topological phases in 3 + 1-D for both bosonic and fermionic systems. Some of the critical theories can be formulated as non-abelian gauge theories either in their Infra-Red free regime, or in the conformal window when they flow to the Banks-Zaks[5, 6] fixed points.We explicitly demonstrate several interesting quantum critical phenomena. We describe situations in which the same phase transition allows for multiple universality classes controlled by distinct fixed points. We exhibit the possibility -which we dub "unnecessary quantum critical points" -of stable generic continuous phase transitions within the same phase. We present examples of interaction driven band-theoryforbidden continuous phase transitions between two distinct band insulators. The understanding we develop leads us to suggest an interesting possible 3 + 1-D field theory duality between SU (2) gauge theory coupled to one massless adjoint Dirac fermion and the theory of a single massless Dirac fermion augmented by a decoupled topological field theory. arXiv:1808.07465v1 [cond-mat.str-el]

Generalized ’t Hooft anomalies on non-spin manifolds

“…further restrictions on various scenarios for their IR dynamics. Many aspects of what we find have been previously recognized in [16,19,23,28,31], especially in the framework of QCD(adj), our first example below. Nonetheless, we include it in order to show how it fits in the present more general and explicit framework.…”

“…Examples of using only gauge backgrounds (i.e. modifying only the gauge bundles being summed over in the path integral) are known in the literature [27][28][29] and we give a few more at the end of Appendix B; a common feature of gauge theories where this can be done is their possible interpretation as emergent descriptions near quantum critical points in theories of only bosons [28].…”

“…by only modifying the gauge bundles summed over. These gauge theories share a feature common with examples discussed in [27,28]: they have only bosonic gauge invariant operators and can be taught as emergent descriptions near quantum critical points of purely bosonic systems.…”

“…It is known that manifolds that do not permit a spin structure [24,25] can accommodate theories with fermions, but only if appropriate gauge fluxes are turned on [26]. These fluxes can correspond to dynamical or background fields, as in the recent studies [23,[27][28][29]. We focus on the canonical example of non-spin manifold, CP 2 .…”

“…In Section 3.1.1 we discuss QCD(adj). Our intention is to use the present study to investigate the various scenarios for IR behavior, whose consistency has been recently elaborated upon in [16,19,23,28,[30][31][32]. In Section 3.1.2, we study an SU (6) gauge theory with a single Dirac flavor in the two-index antisymmetric representation and, in Section 3.1.3, its generalization to SU (4k+2) with a single flavor of twoindex symmetric or antisymmetric representations.…”