We derive the general continuum model for a bilayer system of staggered-flux square lattices, with arbitrary elastic deformation in each layer. Applying this general continuum model to the case where the two layers are rigidly rotated relative to each other by a small angle, we obtain the band structure of the twisted bilayer staggered-flux square lattice. We show that this band structure exhibits a magic continuum in the sense that an exponential reduction of the Dirac velocity and bandwidths occurs in a large parameter regime.

We consider quantum many body systems with generalized symmetries, such as the higher form symmetries introduced recently, and the 'tensor symmetry'. We consider a general form of lattice Hamiltonians which allow a certain level of nonlocality. Based on the assumption of dual generalized symmetries, we explicitly construct low energy excited states. We also derive the 't Hooft anomaly for the general Hamiltonians after 'gauging' the dual generalized symmetries.

We discuss physical constructions and the boundary properties of various symmetry-protected topological phases that involve 1-form symmetries from one spatial dimension to four spatial dimensions (4d). For example, the prototype three-dimensional (3d) boundary state of 4d SPT states involving 1-form symmetries can be either a gapless photon phase (quantum electrodynamics) or gapped topological order enriched by 1-form symmetries; that is, the loop excitations of these topological orders carry nontrivial 1-form symmetry charges.

One dimensional (1d) interacting systems with local Hamiltonians can be studied with various well-developed analytical methods. Recently novel 1d physics was found numerically in systems with either spatially nonlocal interactions, or at the 1d boundary of 2d quantum critical points, and the critical fluctuation in the bulk also yields effective nonlocal interactions at the boundary. This work studies the edge states at the 1d boundary of 2d strongly interacting symmetry protected topological (SPT) states, when the bulk is driven to a disorder-order phase transition.

Abstract We study 3D pure Einstein quantum gravity with negative cosmological constant, in the regime where the AdS radius l is of the order of the Planck scale. Specifically, when the Brown-Henneaux central charge c = 3l/2GN (GN is the 3D Newton constant) equals c = 1/2, we establish duality between 3D gravity and 2D Ising conformal field theory by matching gravity and conformal field theory partition functions for AdS spacetimes with general asymptotic boundaries. This duality was suggested by a genus-one calculation of Castro et al. [Phys. Rev. D85 (2012) 024032].

Motivated by multiple possible physical realizations, we study the SU(4) quantum antiferromagnet with a fundamental representation on each site of the triangular lattice. We provide evidence for a gapless liquid ground state of this system with an emergent Fermi surface of fractionalized fermionic partons coupled with a U(1) gauge field. Our conclusions are based on numerical simulations using the density matrix renormalization group method, which we support with a field theory analysis. © 2020 American Physical Society.

The unified mathematical theory of gapped and gapless edges of two-dimensional (2d) topological orders was developed by two of the authors. According to this theory, the critical point of a purely edge topological phase transition of a 2d topological order can be mathematically characterized by an enriched fusion category. In this work, we provide a physical proof of this fact in a concrete example: the 2d Z2 topological order. In particular, we construct an enriched fusion category, which describes a gappable nonchiral gapless edge of the 2d Z2 topological order.

Non-Fermi liquid and unconventional quantum critical points (QCP) with strong fractionalization are two exceptional phenomena beyond the classic condensed matter doctrines, both of which could occur in strongly interacting quantum many-body systems. This work demonstrates that using a controlled method one can construct a non-Fermi liquid within a considerable energy window based on the unique physics of unconventional QCPs.

We study the interplay between two nontrivial boundary effects: (1) the two-dimensional (2d) edge states of three-dimensional (3d) strongly interacting bosonic symmetry-protected topological states, and (2) the boundary fluctuations of 3d bulk disorder-to-order phase transitions. We then generalize our study to 2d gapless states localized at an interface embedded in a 3d bulk, when the bulk undergoes a quantum phase transition. Our study is based on generic long-wavelength descriptions of these systems and controlled analytic calculations.

Motivated by recent observation of nematicity in moiré systems, we study three different orbital orders that potentially can happen in moiré systems: (1) the nematic order, (2) the valley polarization, and (3) the "compass order." Each order parameter spontaneously breaks part of the spatial symmetries of the system. We explore physics caused by the quantum fluctuations close to the order-disorder transition of these order parameters.