Session Y25: Focus Session: Novel Theories and Methods in Computational Physics

Beyond standard model physics using lattice techniques

I will review the recent results of beyond standard model lattice calculations. The focus is on the models of dynamical electroweak symmetry breaking, Technicolor, and dark matter. A lot of effort has been devoted to finding out which models are conformal and which exhibit a chiral symmetry breaking. Lately also phenomenologically interesting observables, like mass anomalous dimension, glueball spectrum, and a contribution to scalar meson mass, have been calculated. I will briefly comment about the implications of these calculations to the phenomenology.   

Conformal and near-conformal field theories

Non-Abelian gauge fermion systems could be chirally broken and confining or conformal, depending on the number of fermions and their representation. Models near the conformal boundary are important as they could be relevant in describing physics beyond the Standard Model. These models are strongly coupled and require non-perturbative investigations. Lattice techniques that were developed for QCD studies can be used to simulate these systems but there is growing evidence that new observables, new approaches are needed to study the properties of conformal or near conformal models. In this talk I will briefly summarize the most promising models and describe some standard and some promising new methods to study their properties.   

Gradient corrections to finite-temperature exchange-correlation functionals

In principle, the only approximation in Kohn-Sham DFT is for the exchange-correlation (XC) energy. As such, about 40 years of development for the zero-temperature XC density functional has resulted in a ladder of functionals from simple LDA (based on essentially exact QMC results) to orbital-dependent functionals including virtuals. The non-zero temperature situation is different. To date, a handful of $T \ne 0$ K XC functionals have been introduced based on approximate electron gas calculations or interpolations. Except for a finite-T gradient expansion of X, all are local density approximations. Here we present calculations for the XC energy of the electron gas in the dielectric formalism, specifically with approximate local field corrections (LFC). Analysis of the LCF is used to evaluate the first term of the gradient expansion of the XC energy in the slowly varying limit. The resulting gradient expansion finite temperature XC functional will be presented and possible generalized gradient approximations will be considered.   

High-Throughput Investigation of Delafossite materials

We present the application of high-throughput calculations to the intriguing problem of the forbidden optical transition in the CuGa$_{1-x}$Fe$_x$O$_2$ delafossites, which is prototypical of many delafossite systems. When 5\% or more of the Ga sites are replaced with Fe, there is a sudden shift to an optical band gap of 1.5eV from 2.5eV. Using high-throughput calculations and data mining techniques, we show the most likely positional configurations for x = 0.00 through x = 0.10 of the Fe atoms relative to one another. Implications of this result and applications of the techniques used are discussed, including the development of candidate materials via high-throughput analysis of constituent search-space.   

Classical representation of quantum systems at equilibrium

A classical system has been constructed that reproduces the thermodynamics of a quantum system at equilibrium.The classical system has an effective temperature, local chemical potential, and pair interaction that are defined by requiring equivalence of the pressure, density and pair correlation functions for the classical and quantum systems. The thermodynamic parameters of the classical system are determined such that the ideal gas and weak coupling RPA limits are preserved. The pair correlations predicted from this model are in excellent agreement with Diffusion Monte Carlo results at $T=0$ and with the finite-temperature results from the Perrot-Dharmawardana model [1]. Systems in harmonic confinement have also been studied to look into the quantum effects on shell formation. [1] M. W. C. Dharma-wardana and F. Perrot, Phys. Rev. Lett. 84, 959 (2000).   

Phase Diagram and Isentropic Curves for Ferromagnetic and Antiferromagnetic Transverse Ising Model on a Triangular Lattice

We study both the ferromagnetic and anti-ferromagnetic Ising model on a triangular lattice with a transverse magnetic field. Quantum Monte Carlo simulations and series expansions techniques are employed to determine the isentropes and phase diagrams for the system. Quantum Phase Transitions in the transverse field Ising model have recently been observed experimentally for linear chains and for small clusters with long range interactions. They are currently under investigation for triangular lattices.   

Critical behavior of the XY model on fractal lattices

There has been considerable interest in determining whether the universality hypothesis extends to systems which are of non-integer dimension or to systems which are scale invariant (fractals). Specifically, research into these types of systems is concerned with determining the relevance of topological properties to their critical phenomena. We have performed Monte Carlo simulations for the XY model on three fractal lattices with different topological properties: the Sierpinski pyramid, Menger sponge, and Sierpinski carpet (which underwent unusual Berezinskii-Kosterlitz-Thouless transition). We will discuss the details of our results and show that while some properties, such as the order of ramification, are important in determining the critical behavior of these structures, the fractal dimension is not.   

Strong curvature effects in wave problems

Linear-in-curvature contributions to wave-problem eigenvalues in quantum mechanics and acoustics are evaluated analytically using differential geometry methods and perturbation theory. It is demonstrated that in the case of Neumann boundary conditions, relevant for electromagnetic and acoustic problems, linear-in-curvature contributions are nonvanishing if the geometry supports eigenstates that do not satisfy parity. If Dirichlet boundary conditions apply, however, linear-in-curvature vanish identically. We continue to compute analytically eigenvalue changes for a toroidal angular-sector geometry in the case of both Dirichlet and Neumann boundary conditions. Eigenstate and eigenvalue results are finally verified qualitatively and quantitatively against Comsol finite element model results.   

Computing the response functions of topological insulators with non-commutative geometry

For periodic systems, the correlation functions take closed-form expression involving integrations and derivations of ordinary functions defined over the Brillouin torus (Bloch-Floquet calculus). The non-commutative geometry provides an analog of the Bloch-Floquet calculus for aperiodic systems under magnetic fields, and this formalism was used in the past to derive closed-form expressions for Kubo-formula, orbital electric and magnetic polarization and much more, for strongly disordered systems under magnetic fields. In this talk I will describe how these non-commutative formulas can be evaluated on a computer, enabling us to investigate the response coefficients of strongly disordered topological with unprecedented precision and efficiency.   

Disordered Floquet Topological Insulators

We study the problem of localization in the recently proposed two-dimensional Floquet topological insulators in semiconductor quantum wells. We compute the single particle Green's function for the system using a real-time simulation. The phase diagram obtained indicates that at weak disorder the system remains delocalized. The edge-states are protected and only destroyed when the disorder closes the gap in the Floquet spectrum. The system localizes only at disorder strength which is much larger than the gap in the Floquet spectrum, long after this gap has been closed due to disorder. Analytically we compare these results with the results obtained using disorder averaged Floquet Green's functions in the Born approximation.