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

A first-order splitting method for solving a large-scale composite convex optimization problem

The forward-backward operator splitting algorithm is one of the most important methods for solving the optimization problem of the sum of two convex functions, where one is differentiable with a Lipschitz continuous gradient and the other is possibly nonsmooth but proximable. It is convenient to solve some optimization problems in the form of dual or primal-dual problems. Both methods are mature in theory. In this paper, we construct several efficient first-order splitting algorithms for solving a multi-block composite convex optimization problem. The objective function includes a smooth function with a Lipschitz continuous gradient, a proximable convex function that may be nonsmooth, and a finite sum of a composition of a proximable function and a bounded linear operator. To solve such an optimization problem, we transform it into the sum of three convex functions by defining an appropriate inner product space. On the basis of the dual forward-backward splitting algorithm and the primal-dual forward-backward splitting algorithm, we develop several iterative algorithms that involve only computing the gradient of the differentiable function and proximity operators of related convex functions. These iterative algorithms are matrix-inversion-free and completely splitting algorithms. Finally, we employ the proposed iterative algorithms to solve a regularized general prior image constrained compressed sensing (PICCS) model that is derived from computed tomography (CT) image reconstruction under sparse sampling of projection measurements. Numerical results show that the proposed iterative algorithms outperform other algorithms.Comment: 27 pages, 4 figures, J. Comp. Math. 201

A general framework for solving convex optimization problems involving the sum of three convex functions

In this paper, we consider solving a class of convex optimization problem which minimizes the sum of three convex functions $f(x)+g(x)+h(Bx)$, where $f(x)$ is differentiable with a Lipschitz continuous gradient, $g(x)$ and $h(x)$ have a closed-form expression of their proximity operators and $B$ is a bounded linear operator. This type of optimization problem has wide application in signal recovery and image processing. To make full use of the differentiability function in the optimization problem, we take advantage of two operator splitting methods: the forward-backward splitting method and the three operator splitting method. In the iteration scheme derived from the two operator splitting methods, we need to compute the proximity operator of $g+h \circ B$ and $h \circ B$, respectively. Although these proximity operators do not have a closed-form solution in general, they can be solved very efficiently. We mainly employ two different approaches to solve these proximity operators: one is dual and the other is primal-dual. Following this way, we fortunately find that three existing iterative algorithms including Condat and Vu algorithm, primal-dual fixed point (PDFP) algorithm and primal-dual three operator (PD3O) algorithm are a special case of our proposed iterative algorithms. Moreover, we discover a new kind of iterative algorithm to solve the considered optimization problem, which is not covered by the existing ones. Under mild conditions, we prove the convergence of the proposed iterative algorithms. Numerical experiments applied on fused Lasso problem, constrained total variation regularization in computed tomography (CT) image reconstruction and low-rank total variation image super-resolution problem demonstrate the effectiveness and efficiency of the proposed iterative algorithms.Comment: 37 pages, 10 figure

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

Distinguishing the right-handed up/charm quarks from top quark via discrete symmetries in the standard model extensions

We propose a class of the two Higgs doublet Standard models (SMs) with a SM singlet and a class of supersymmetric SMs with two pairs of Higgs doublets, where the right-handed up/charm quarks and the right-handed top quark have different quantum numbers under extra discrete symmetries. Thus, the right-handed up and charm quarks couple to one Higgs doublet field, while the right-handed top quark couples to another Higgs doublet. The quark CKM mixings can be generated from the down-type quark sector. As one of phenomenological consequences in our models, we explore whether one can accommodate the observed direct CP asymmetry difference in singly Cabibbo-suppressed D decays. We show that it is possible to explain the measured values of CP violation under relevant experimental constraints.Comment: 20 pages; matches published versio

Crystallized and amorphous vortices in rotating atomic-molecular Bose-Einstein condensates

Vortex is a topological defect with a quantized winding number of the phase in superfluids and superconductors. Here, we investigate the crystallized (triangular, square, honeycomb) and amorphous vortices in rotating atomic-molecular Bose-Einstein condensates (BECs) by using the damped projected Gross-Pitaevskii equation. The amorphous vortices are the result of the considerable deviation induced by the interaction of atomic-molecular vortices. By changing the atom-molecule interaction from attractive to repulsive, the configuration of vortices can change from an overlapped atomic-molecular vortices to carbon-dioxide-type ones, then to atomic vortices with interstitial molecular vortices, and finally into independent separated ones. The Raman detuning can tune the ratio of the atomic vortex to the molecular vortex. We provide a phase diagram of vortices in rotating atomic-molecular BECs as a function of Raman detuning and the strength of atom-molecule interaction.Comment: 32 pages, 6 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

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

Coupled Wire description of the Correlated Physics in Twisted Bilayer Graphene

Since the discovery of superconductivity and correlated insulator at fractional electron fillings in the twisted bilayer graphene, most theoretical efforts have been focused on describing this system in terms of an effective extended Hubbard model. However, it was recognized that an exact tight binding model on the Moir\'{e} superlattice which captures all the subtleties of the bands can be exceedingly complicated. Here we pursue an alternative coupled wire description of the system based on the observation that the lattice relaxation effect is strong at small twist angle, which substantially enlarges the AB and BA stacking domains. Under an out-of-plane electric field which can have multiple origins, the low energy physics of the system is dominated by interconnected wires with (approximately) gapless $1d$ conducting quantum valley hall domain wall states. We demonstrate that the Coulomb interaction likely renders the wires a $U(2)_2$ $(1+1)d$ conformal field theory with a tunable Luttinger parameter for the charge $U(1)$ sector. Spin triplet and singlet Cooper pair operator both have quasi-long range order in this CFT. The junction between the wires at the AA stacking islands can lead to either a two dimensional superconductor, or an insulator.Comment: 8 pages, 2 figure

Anisotropic Spin Relaxation Induced by Surface Spin-Orbit Effects

It is a common perception that the transport of a spin current in polycrystalline metal is isotropic and independent of the polarization direction, even though spin current is a tensorlike quantity and its polarization direction is a key variable. We demonstrate surprising anisotropic spin relaxation in mesoscopic polycrystalline Cu channels in nonlocal spin valves. For directions in the substrate plane, the spin-relaxation length is longer for spins parallel to the Cu channel than for spins perpendicular to it, by as much as 9% at 10 K. Spin-orbit effects on the surfaces of Cu channels can account for this anisotropic spin relaxation. The finding suggests novel tunability of spin current, not only by its polarization direction but also by electrostatic gating.Comment: (#) C. Zhou and F. Kandaz contributed equally to this work. Main text (22 pages, 4 figures) + Supplementary material (9 pages, 3 figures