Topological Edge and Interface states at Bulk disorder-to-order Quantum Critical Points

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. Our results are summarized as follows: ($i.$) The edge state of a prototype bosonic symmetry protected states can be driven to a new fixed point by coupling to the boundary fluctuations of a bulk quantum phase transition; ($ii.$) the states localized at a $2d$ interface of a $3d$ SU(N) quantum antiferromagnet may be driven to a new fixed point by coupling to the bulk quantum critical modes. Properties of the new fixed points identified are also studied.Comment: 8 pages, 7 figure

Lattice models for Non-Fermi Liquids with Tunable Transport Scalings

A variety of exotic non-fermi liquid (NFL) states have been observed in many condensed matter systems, with different scaling relations between transport coefficients and temperature. The "standard" approach to studying these NFLs is by coupling a Fermi liquid to quantum critical fluctuations, which potentially can drive the system into a NFL. In this work we seek for an alternative understanding of these various NFLs in a unified framework. We first construct two "elementary" randomness-free models with four-fermion interactions only, whose many properties can be analyzed exactly in certain limit just like the Sachdev-Ye-Kitaev (SYK) model. The most important new feature of our models is that, the fermion scaling dimension in the conformal invariant solution in the infrared limit is tunable by charge density. Then based on these elementary models, we propose two versions of lattice models with four fermion interactions which give us non-fermi liquid behaviors with DC resistivity scaling $\varrho \sim T^\alpha$ in a finite temperature window, and $\alpha \in [1, 2)$ depends on the fermion density in the model, which is a rather universal feature observed in many experimental systems.Comment: 13 pages, 2 figure

Boundary Criticality of Topological Quantum Phase Transitions in 2d2d systems

We discuss the boundary critical behaviors of two dimensional quantum phase transitions with fractionalized degrees of freedom in the bulk, motivated by the fact that usually it is the $1d$ boundary that is exposed and can be conveniently probed in many experimental platforms. In particular, we mainly discuss boundary criticality of two examples: i. the quantum phase transition between a $2d$ $Z_2$ topological order and an ordered phase with spontaneous symmetry breaking; ii. the continuous quantum phase transition between metal and a particular type of Mott insulator (U(1) spin liquid). This theoretical study could be relevant to many purely $2d$ systems, where recent experiments have found correlated insulator, superconductor, and metal in the same phase diagram.Comment: 6 pages, 2 figure

Image Ordinal Classification and Understanding: Grid Dropout with Masking Label

Image ordinal classification refers to predicting a discrete target value which carries ordering correlation among image categories. The limited size of labeled ordinal data renders modern deep learning approaches easy to overfit. To tackle this issue, neuron dropout and data augmentation were proposed which, however, still suffer from over-parameterization and breaking spatial structure, respectively. To address the issues, we first propose a grid dropout method that randomly dropout/blackout some areas of the raining image. Then we combine the objective of predicting the blackout patches with classification to take advantage of the spatial information. Finally we demonstrate the effectiveness of both approaches by visualizing the Class Activation Map (CAM) and discover that grid dropout is more aware of the whole facial areas and more robust than neuron dropout for small training dataset. Experiments are conducted on a challenging age estimation dataset - Adience dataset with very competitive results compared with state-of-the-art methods.Comment: IEEE International Conference on Multimedia Expo (ICME Oral Presentation

Ferromagnetism and Spin-Valley liquid states in Moir\'{e} Correlated Insulators

Motivated by the recent observation of evidences of ferromagnetism in correlated insulating states in systems with Moir\'{e} superlattices, we study a two-orbital quantum antiferromagnetic model on the triangular lattice, where the two orbitals physically correspond to the two valleys of the original graphene sheet. For simplicity this model has a SU(2)$^s$$\otimes$SU(2)$^v$ symmetry, where the two SU(2) symmetries correspond to the rotation within the spin and valley space respectively. Through analytical argument, Schwinger boson analysis and also DMRG simulation, we find that even though all the couplings in the Hamiltonian are antiferromagnetic, there is still a region in the phase diagram with fully polarized ferromagnetic order. We argue that a Zeeman field can drive a metal-insulator transition in our picture, as was observed experimentally. We also construct spin liquids and topological ordered phases at various limits of this model. Then after doping this model with extra charge carriers, the system most likely becomes spin-triplet/valley-singlet $d+id$ topological superconductor as was predicted previously.Comment: 6 pages, 1 figur

Continuum study on QCD phase diagram through an OPE-modified gluon propagator

Within the Dyson-Schwinger equations (DSEs) framework, a gluon propagator model incorporating quark's feedback through operator product expansion (OPE) is introduced to investigate the QCD phase diagram in the temperature--chemical-potential ($T-\mu$) plane. Partial restoration of chiral symmetry at zero temperature and finite temperature are both studied, suggesting a first order phase transition point on the $\mu$ axis and a critical end point at $(T_E,\mu_E)/T_c = (0.85,1.11)$, where $T_c$ is the pseudo-critical temperature. In addition, we find the pseudo-critical line can be well parameterized with the curvature parameter $\kappa$ and a consistent decrease in $\kappa$ with more of gluon propagator distributed to quark's feedback.Comment: 9 pages, 8 figure

Physics of Symmetry Protected Topological phases involving Higher Symmetries and their Applications

We discuss physical constructions, and the boundary properties of various symmetry protected topological phases that involve 1-form symmetries, from one spatial dimension (1d) to four spatial dimensions (4d). For example, the prototype 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, namely the loop excitations of these topological orders carry nontrivial 1-form symmetry charges. This study also serves the purpose of diagnosing anomaly of 3d states of matter. Connection between SPT states with 1-form symmetries and condensed matter systems such as quantum dimer models at one lower dimension will also be discussed. Whether a quantum dimer model can have a trivial gapped phase or not depends on the nature of its corresponding bulk state in one higher dimension.Comment: 10 pages, 1 figur

Interacting Valley Chern Insulator and its Topological Imprint on Moir\'{e} Superconductors

One salient feature of systems with Moir\'{e} superlattice is that, Chern number of "minibands" originating from each valley of the original graphene Brillouin zone becomes a well-defined quantized number because the miniband from each valley can be isolated from the rest of the spectrum due to the Moir\'{e} potential. Then a Moir\'{e} system with a well-defined valley Chern number can become a nonchiral topological insulator with $U(1) \times Z_3$ symmetry and a $\mathbb{Z}$ classification at the free fermion level. Here we demonstrate that the strongly interacting nature of the Moir\'{e} system reduces the classification of the valley Chern insulator from $\mathbb{Z}$ to $\mathbb{Z}_3$, and it is topologically equivalent to a bosonic symmetry protected topological state made of local boson operators. We also demonstrate that, even if the system becomes a superconductor when doped away from the valley Chern insulator, the valley Chern insulator still leaves a topological imprint as the localized Majorana fermion zero mode in certain geometric configuration.Comment: 6 pages, 4 figure

Continuous N\'{e}el-VBS Quantum Phase Transition in Non-Local one-dimensional systems with SO(3) Symmetry

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. We will take the $2d$ Affleck-Kennedy-Lieb-Tasaki (AKLT) state as an example, which is a SPT state protected by the SO(3) spin symmetry and spatial translation. We found that the original $(1+1)d$ boundary conformal field theory of the AKLT state is unstable due to coupling to the boundary avatar of the bulk quantum critical fluctuations. When the bulk is fixed at the quantum critical point, within the accuracy of our expansion method, we find that by tuning one parameter at the boundary, there is a generic direct transition between the long range antiferromagnetic N\'{e}el order and the valence bond solid (VBS) order. This transition is very similar to the N\'{e}el-VBS transition recently found in numerical simulation of a spin-1/2 chain with nonlocal spatial interactions. Connections between our analytical studies and recent numerical results concerning the edge states of the $2d$ AKLT-like state at a bulk quantum phase transition will also be discussed.Comment: 7 pages, 3 figure

Orbital Orders and non-Fermi Liquid in Moir\'{e} systems

Motivated by recent observation of nematicity in Moir\'{e} systems, we study three different orbital orders that potentially can happen in Moir\'{e} 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. Especially, we recognize that the symmetry of the Moir\'{e} systems leads to a crucial difference of the effective theory describing the nematic order from the standard Hertz-Millis formalism. We demonstrate that this key difference may lead to a special non-Fermi liquid behavior near the order-disorder nematic transition, different from the standard non-Fermi liquid behavior usually expected when a Fermi surface is coupled to the critical fluctuations of orbital orders. We also discuss the interplay of the three order parameters and the possible rich phase diagram at finite temperature. Within the three orbital orders, the valley polarization and the "compass order" likely strongly compete with the superconductor.Comment: 7 pages, 3 figure