Itinerant quantum critical point with frustration and non-Fermi-liquid

Employing the self-learning quantum Monte Carlo algorithm, we investigate the frustrated transverse-field triangle-lattice Ising model coupled to a Fermi surface. Without fermions, the spin degrees of freedom undergoes a second-order quantum phase transition between paramagnetic and clock-ordered phases. This quantum critical point (QCP) has an emergent U(1) symmetry and thus belongs to the (2+1)D XY universality class. In the presence of fermions, spin fluctuations introduce effective interactions among fermions and distort the bare Fermi surface towards an interacting one with hot spots and Fermi pockets. Near the QCP, non-Fermi-liquid behavior are observed at the hot spots, and the QCP is rendered into a different universality with Hertz-Millis type exponents. The detailed properties of this QCP and possibly related experimental systems are also discussed.Comment: 9 pages, 8 figure

An Examination of Some Signi cant Approaches to Statistical Deconvolution

We examine statistical approaches to two significant areas of deconvolution - Blind Deconvolution (BD) and Robust Deconvolution (RD) for stochastic stationary signals. For BD, we review some major classical and new methods in a unified framework of nonGaussian signals. The first class of algorithms we look at falls into the class of Minimum Entropy Deconvolution (MED) algorithms. We discuss the similarities between them despite differences in origins and motivations. We give new theoretical results concerning the behaviour and generality of these algorithms and give evidence of scenarios where they may fail. In some cases, we present new modifications to the algorithms to overcome these shortfalls. Following our discussion on the MED algorithms, we next look at a recently proposed BD algorithm based on the correntropy function, a function defined as a combination of the autocorrelation and the entropy functiosn. We examine its BD performance when compared with MED algorithms. We find that the BD carried out via correntropy-matching cannot be straightforwardly interpreted as simultaneous moment-matching due to the breakdown of the correntropy expansion in terms of moments. Other issues such as maximum/minimum phase ambiguity and computational complexity suggest that careful attention is required before establishing the correntropy algorithm as a superior alternative to the existing BD techniques. For the problem of RD, we give a categorisation of different kinds of uncertainties encountered in estimation and discuss techniques required to solve each individual case. Primarily, we tackle the overlooked cases of robustification of deconvolution filters based on estimated blurring response or estimated signal spectrum. We do this by utilising existing methods derived from criteria such as minimax MSE with imposed uncertainty bands and penalised MSE. In particular, we revisit the Modified Wiener Filter (MWF) which offers simplicity and flexibility in giving improved RDs to the standard plug-in Wiener Filter (WF)

Self-Learning Monte Carlo Method

Monte Carlo simulation is an unbiased numerical tool for studying classical and quantum many-body systems. One of its bottlenecks is the lack of general and efficient update algorithm for large size systems close to phase transition or with strong frustrations, for which local updates perform badly. In this work, we propose a new general-purpose Monte Carlo method, dubbed self-learning Monte Carlo (SLMC), in which an efficient update algorithm is first learned from the training data generated in trial simulations and then used to speed up the actual simulation. We demonstrate the efficiency of SLMC in a spin model at the phase transition point, achieving a 10-20 times speedup.Comment: add more refs and correct some typo

Theory of unconventional quantum Hall effect in strained graphene

We show through both theoretical arguments and numerical calculations that graphene discerns an unconventional sequence of quantized Hall conductivity, when subject to both magnetic fields (B) and strain. The latter produces time-reversal symmetric pseudo/axial magnetic fields (b). The single-electron spectrum is composed of two interpenetrating sets of Landau levels (LLs), located at $\pm \sqrt{2 n |b \pm B|}$, $n=0, 1, 2, \cdots$. For $b>B$, these two sets of LLs have opposite \emph{chiralities}, resulting in {\em oscillating} Hall conductivity between 0 and $\mp 2 e^2/h$ in electron and hole doped system, respectively, as the chemical potential is tuned in the vicinity of the neutrality point. The electron-electron interactions stabilize various correlated ground states, e.g., spin-polarized, quantum spin-Hall insulators at and near the neutrality point, and possibly the anomalous Hall insulating phase at incommensurate filling $\sim B$. Such broken-symmetry ground states have similarities as well as significant differences from their counterparts in the absence of strain. For realistic strength of magnetic fields and interactions, we present scaling of the interaction-induced gap for various Hall states within the zeroth Landau level.Comment: 5 pages and 2 figures + supplementary (3.5 pages and 5 figures); Published version, cosmetic changes and updated reference

Mottness induced phase decoherence suggests Bose-Einstein condensation in overdoped cuprate high-temperature superconductors

Recent observations of diminishing superfluid phase stiffness in overdoped cuprate high-temperature superconductors challenges the conventional picture of superconductivity. Here, through analytic estimation and verified via variational Monte Carlo calculation of an emergent Bose liquid, we point out that Mottness of the underlying doped holes dictates a strong phase fluctuation of the superfluid at moderate carrier density. This effect turns the expected doping-increased phase stiffness into a dome shape, in good agreement with the recent observation. Specifically, the effective mass divergence due to "jamming" of the low-energy bosons reproduces the observed nonlinear relation between phase stiffness and transition temperature. Our results suggest a new paradigm, in which the high-temperature superconductivity in the cuprates is dominated by physics of Bose-Einstein condensation, as opposed to pairing-strength limited Cooper pairing.Comment: 6+3 pages, 4+1 figure