We study the effects of heterostrain on moiré bands in twisted bilayer graphene and bilayer transition metal dichalcogenide (TMD) systems. For bilayer graphene with twist angle near 1 • , we show that heterostrain significantly increases the energy separation between conduction and valence bands as well as the Dirac velocity at charge neutrality, which resolves several puzzles in scanning tunneling spectroscopy and quantum oscillation experiments at once. For bilayer TMD, we show that applying small heterostrain generally leads to flat moiré bands that are highly tunable.

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In this paper we systematically classify and describe bosonic symmetry protected topological (SPT) phases in all physical spatial dimensions using semiclassical nonlinear Sigma model (NLSM) field theories. All the SPT phases on a d−dimensional lattice discussed in this paper can be described by the same NLSM, which is an O(d+2) NLSM in (d+1)−dimensional space-time, with a topological Θ−term. The field in the NLSM is a semiclassical Landau order parameter with a unit length constraint. The classification of SPT phases discussed in this paper based on their NLSMs is Completely Identical to the more mathematical classification based on group cohomology given in Ref. 1,2. Besides the classification, the formalism used in this paper also allows us to explicitly discuss the physics at the boundary of the SPT phases, and it reveals the relation between SPT phases with different symmetries. For example, it gives many of these SPT states a natural "decorated defect" construction.

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]

We study a series of perturbations on the Sachdev-Ye-Kitaev (SYK) model. We show that the maximal chaotic non-Fermi liquid phase described by the ordinary q = 4 SYK model has marginally relevant/irrelevant (depending on the sign of the coupling constants) four-fermion perturbations allowed by symmetry. Changing the sign of one of these four-fermion perturbations leads to a continuous chaotic-nonchaotic quantum phase transition of the system accompanied by a spontaneous time-reversal symmetry breaking. Starting with the SYKq model with a q−fermion interaction, similar perturbations can lead to a series of new fixed points with continuously varying exponents.