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.

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We demonstrate the following conclusion: If |Ψ is a 1d or 2d nontrivial short range entangled state, and |Ω is a trivial disordered state defined on the same Hilbert space, then the following quantity (so called strange correlator) C(r, r ) = Ω|φ(r)φ(r )|Ψ Ω|Ψ either saturates to a constant or decays as a power-law in the limit |r − r | → +∞, even though both |Ω and |Ψ are quantum disordered states with short-range correlation. φ(r) is some local operator in the Hilbert space. This result is obtained based on both field theory analysis, and also an explicit computation of C(r, r ) for four different examples: 1d Haldane phase of spin-1 chain, 2d quantum spin Hall insulator with a strong Rashba spin-orbit coupling, 2d spin-2 AKLT state on the square lattice, and the 2d bosonic symmetry protected topological phase with Z2 symmetry. This result can be used as a diagnosis for short range entangled states in 1d and 2d. PACS numbers:A short range entangled (SRE) state is a ground state of a quantum many-body system that does not have ground state degeneracy or bulk topological entanglement entropy. But a SRE state (for example the integer quantum Hall state) can still have protected stable gapless edge states. Thus it appears that the bulk of all the SRE states are identically trivial, and a nontrivial SRE state is usually characterized by its edge states. In this paper we propose a diagnosis to determine whether a given many-body wave function defined on a lattice without boundary is a nontrivial SRE state or a trivial one. This diagnosis is based on the following quantity called "strange correlator" [36]:Here |Ψ is the wave function that needs diagnosis, |Ω is a direct product trivial disordered state defined on the same Hilbert space. Our conclusion is that if |Ψ is a nontrivial SRE state in one or two spatial dimensions, then for some local operator φ(r), C(r, r ) will either saturate to a constant or decay as a power-law in the limit |r − r | → +∞, even though both |Ω and |Ψ are disordered states with short-range correlation. Another possible way of diagnosing a SRE wave function is through its entanglement spectrum [1]. If a SRE state has nontrivial edge states, an analogue of its edge states should also exist in its entanglement spectrum [2]. However, many SRE states are protected by certain symmetry, some SRE states are protected by lattice symmetries (for example the spin-2 AKLT state on the square lattice requires translation symmetry). If the cut we make to compute the entanglement spectrum breaks such lattice symmetry, then the entanglement spectrum would be trivial, even if the original state is a nontrivial SRE state. By contrast, the strange correlator in Eq. (1) is defined on a lattice without edge, thus it already preserves all the symmetries of the system, including all the lattice symmetries. Thus the strange correlator can reliably diagnose SRE states protected by lattice symmetries as well.The strange correlator can be roughly understood as follows: |Ψ can be viewed as a generic initial state evol...

Recently it has been established that two-dimensional bosonic symmetry-protected topological(SPT) phases with on-site unitary symmetry G can be completely classified by the group cohomology H 3 (G, U(1)). Later, group super-cohomology was proposed as a partial classification for SPT phases of interacting fermions. In this work, we revisit this problem based on the algebraic theory of symmetry and defects in two-dimensional topological phases. We reproduce the partial classifications given by group super-cohomology, and we also show that with an additional H 1 (G, Z2) structure, a complete classification of SPT phases for two-dimensional interacting fermion systems with a total symmetry group G × Z f 2 is obtained. We also discuss the classification of interacting fermionic SPT phases protected by time reversal symmetry.