Browsing by Author "Liao, Yunxiang"
Now showing 1 - 6 of 6
Results Per Page
Sort Options
Item Critical Percolation without Fine-Tuning on the Surface of a Topological Superconductor(American Physical Society, 2018) Ghorashi, Sayed Ali Akbar; Liao, Yunxiang; Foster, Matthew S.We present numerical evidence that most two-dimensional surface states of a bulk topological superconductor (TSC) sit at an integer quantum Hall plateau transition. We study TSC surface states in class CI with quenched disorder. Low-energy (finite-energy) surface states were expected to be critically delocalized (Anderson localized). We confirm the low-energy picture, but find instead that finite-energy states are also delocalized, with universal statistics that are independent of the TSC winding number, and consistent with the spin quantum Hall plateau transition (percolation).Item Dephasing Catastrophe in 4−ε Dimensions: A Possible Instability of the Ergodic (Many-Body-Delocalized) Phase(American Physical Society, 2018) Liao, Yunxiang; Foster, Matthew S.; Rice Center for Quantum MaterialsIn two dimensions, dephasing by a bath cuts off Anderson localization that would otherwise occur at any energy density for fermions with disorder. For an isolated system with short-range interactions, the system can be its own bath, exhibiting diffusive (non-Markovian) thermal density fluctuations. We recast the dephasing of weak localization due to a diffusive bath as a self-interacting polymer loop. We investigate the critical behavior of the loop in d=4−ε dimensions, and find a nontrivial fixed point corresponding to a temperature T∗∼ε>0 where the dephasing time diverges. Assuming that this fixed point survives to ε=2, we associate it with a possible instability of the ergodic phase. Our approach may open a new line of attack against the problem of the ergodic to many-body-localized phase transition in d>1 spatial dimensions.Item Low Resolution ab initio Phasing Method by Modification of Density and Phase in Real and Reciprocal Space(2013-09-30) Liao, Yunxiang; Ma, Jianpeng; Raphael, Robert M.; Kiang, Ching-HwaPhasing problem in X-ray structure determination can be challenging. Several methods, such as Isomorphous Replacement and Molecule Replacement, are frequently used. But their success relies on the availability of either an isomorphous heavy-atom derivative or a high identity homologous model. In this thesis, a low resolution ab initio phasing method is proposed. A large number of trial phases value and their corresponding high density masks are generated and modified alternately in reciprocal and real space. Then, the output phase sets are averaged to give the estimated phases and figure of merit which are capable of capturing key feature of the molecules’ low resolution envelope by Fourier synthesis. Smoothed particle hydrodynamics is employed to animate the high density masks’ modification process. The method is tested and compared with Lunin’s connectivity-based phasing method which also takes advantage of geometric properties of high density masks.Item Probes of nonequilibrium quantum matter and many-body delocalization(2018-03-09) Liao, Yunxiang; Foster, Matthew SIn this thesis, we consider two different topics: the probes of out-of-equilibrium topological matter and many-body-localization (MBL) in higher dimensions. The first part focuses on the two-dimensional (2D) topological Floquet p+ip superfluid induced by an instantaneous quench of the interaction strength. We investigate radio-frequency (rf) spectroscopy, metal-to-superconductor tunneling, and angle-resolved photoemission spectroscopy (ARPES) as probes of this out-of-equilibrium quantum system in both the cold-atomic and solid-state realizations. We notice a single avoided crossing in the Floquet band structure and a population inversion in the occupation of these bands. In addition, the rf spectrum is well captured by a quasiequilibrium approximation and shows a robust gap. We also compute the rf signal when only the lower Floquet band is occupied as well as the tunneling signal. In both cases, the spectra show wildly different behaviors compared with the rf signal from the post-quench state, and the gap disappears for strong quenches. We attribute this to the fact that the distribution function influences the rf but not the tunneling signal. Finally, we look into the ARPES spectrum which exhibits a clear series of Floquet copies. The second part is devoted to interacting fermions in the presence of quenched disorder. We derive a finite-temperature Keldysh response theory for such a system in the delocalized phase, in the form of the Finkel'stein nonlinear sigma model (FNLσM). Applicable to any symmetry class with at least a U(1) symmetry, our formulation automatically incorporates the correct infrared cutoffs for quantum corrections to transport, and provides a framework to study the real and virtual scattering processes. In particular, we are able to rederive from the FNLσM the Altshuler-Aronov-Khmelnitsky equations for dephasing. We then propose a strategy to approach the 2D ergodic-to-MBL transition from the ergodic side. Such a transition is explored as a dephasing catastrophe in an isolated system with short-range interactions. In this case, the self-generated heat bath responsible for dephasing exhibits diffusive (non-Markovian) density fluctuations. We recast the dephasing of quantum interference corrections as a self-interacting polymer loop, and study its critical behavior using renormalization group approach. In dimensions d=4-ε, we identify a nontrivial fixed point corresponding to a finite temperature where the dephasing time diverges. This fixed point can be associated with a toy version of 2D ergodic-to-MBL transition, provided that it survives to ε=2.Item Response theory of the ergodic many-body delocalized phase: Keldysh Finkel'stein sigma models and the 10-fold way(Elsevier, 2017) Liao, Yunxiang; Levchenko, Alex; Foster, Matthew S.; Rice Center for Quantum MaterialsWe derive the finite temperature Keldysh response theory for interacting fermions in the presence of quenched short-ranged disorder, as applicable to any of the 10 Altland–Zirnbauer classes in an Anderson delocalized phase with at least a U(1) continuous symmetry. In this formulation of the interacting Finkel’stein nonlinear sigma model, the statistics of one-body wave functions are encoded by the constrained matrix field, while physical correlations follow from the hydrodynamic density or spin response field, which decouples the interactions. Integrating out the matrix field first, we obtain weak (anti) localization and Altshuler–Aronov quantum conductance corrections from the hydrodynamic response function. This procedure automatically incorporates the correct infrared cutoff physics, and in particular gives the Altshuler–Aronov–Khmelnitsky (AAK) equations for dephasing of weak (anti)localization due to electron–electron collisions. We explicate the method by deriving known quantumcorrections in two dimensions for the symplectic metal class AII, as well as the spin-SU(2) invariant superconductor classes C and CI. We show that quantum conductance corrections due to the special modes at zero energy in nonstandard classes are automatically cut off by temperature, as previously expected, while the Wigner–Dyson class Cooperon modes that persist to all energies are cut by dephasing. We also show that for short-ranged interactions, the standard self-consistent solution for the dephasing rate is equivalent to a particular summation of diagrams via the self-consistent Born approximation. This should be compared to the corresponding AAK solution for long-ranged Coulomb interactions, which exploits the Markovian noise correlations induced by thermal fluctuations of the electromagnetic field. We discuss prospects for exploring the many-body localization transition as a dephasing catastrophe in short-range interacting models, as encountered by approaching from the ergodic side.Item Spectroscopic probes of isolated nonequilibrium quantum matter: Quantum quenches, Floquet states, and distribution functions(American Physical Society, 2015) Liao, Yunxiang; Foster, Matthew S.We investigate radio-frequency (rf) spectroscopy, metal-to-superconductor tunneling, and angle-resolved photoemission spectroscopy (ARPES) as probes of isolated out-of-equilibrium quantum systems, and examine the crucial role played by the nonequilibrium distribution function. As an example, we focus on the induced topological time-periodic (Floquet) phase in a two-dimensional p+ip superfluid, following an instantaneous quench of the coupling strength. The post-quench Cooper pairs occupy a linear combination of “ground” and “excited” Floquet states, with coefficients determined by the distribution function. While the Floquet band structure exhibits a single avoided crossing relative to the equilibrium case, the distribution function shows a population inversion of the Floquet bands at low energies. For a realization in ultracold atoms, these two features compensate, producing a bulk average rf signal that is well captured by a quasiequilibrium approximation. In particular, the rf spectrum shows a robust gap. The single crossing occurs because the quench-induced Floquet phase belongs to a particular class of soliton dynamics for the BCS equation. The population inversion is a consequence of this, and ensures the conservation of the pseudospin winding number. As a comparison, we compute the rf signal when only the lower Floquet band is occupied; in this case, the gap disappears for strong quenches. The tunneling signal in a solid-state realization is ignorant of the distribution function, and can show wildly different behaviors. We also examine rf, tunneling, and ARPES for weak quenches, such that the resulting topological steady state is characterized by a constant nonequilibrium order parameter. In a system with a boundary, tunneling reveals the Majorana edge states. However, the local rf signal due to the edge states is suppressed by a factor of the inverse system size, and is spatially deconfined throughout the bulk of the sample.