arXiv subjects

Lauren E. Hayward

Publications and source records attributed to Lauren E. Hayward.

5 recordsLinked to original sources

arXiv2021

Generative models for sampling of lattice field theories

We explore a self-learning Markov chain Monte Carlo method based on the Adversarial Non-linear Independent Components Estimation Monte Carlo, which utilizes generative models and artificial neural networks. We apply this method to the scalar $φ^4$ lattice field theory in the weak-coupling regime and, in doing so, greatly increase the system sizes explored to date with this self-learning technique. Our approach does not rely on a pre-existing training set of samples, as the agent systematically improves its performance by bootstrapping samples collected by the model itself. We evaluate the performance of the trained model by examining its mixing time and study the ergodicity of generated samples. When compared to methods such as Hamiltonian Monte Carlo, this approach provides unique advantages such as the speed of inference and a compressed representation of Monte Carlo proposals for potential use in downstream tasks.

cond-mat.dis-nn↗

arXiv2020

Multidimensional super- and subradiance in waveguide quantum electrodynamics

We study the collective decay rates of multi-dimensional quantum networks in which one-dimensional waveguides form an intersecting hyper-rectangular lattice, with qubits located at the lattice points. We introduce and motivate the \emph{dimensional reduction of poles} (DRoP) conjecture, which identifies all collective decay rates of such networks via a connection to waveguides with a one-dimensional topology (e.g. a linear chain of qubits). Using DRoP, we consider many-body effects such as superradiance, subradiance, and bound-states in continuum in multi-dimensional quantum networks. We find that, unlike one-dimensional linear chains, multi-dimensional quantum networks have superradiance in distinct levels, which we call multi-dimensional superradiance. Furthermore, we generalize the $N^{-3}$ scaling of subradiance in a linear chain to $d$-dimensional networks.

quant-ph↗

arXiv2020

Recurrent Neural Network Wave Functions

A core technology that has emerged from the artificial intelligence revolution is the recurrent neural network (RNN). Its unique sequence-based architecture provides a tractable likelihood estimate with stable training paradigms, a combination that has precipitated many spectacular advances in natural language processing and neural machine translation. This architecture also makes a good candidate for a variational wave function, where the RNN parameters are tuned to learn the approximate ground state of a quantum Hamiltonian. In this paper, we demonstrate the ability of RNNs to represent several many-body wave functions, optimizing the variational parameters using a stochastic approach. Among other attractive features of these variational wave functions, their autoregressive nature allows for the efficient calculation of physical estimators by providing independent samples. We demonstrate the effectiveness of RNN wave functions by calculating ground state energies, correlation functions, and entanglement entropies for several quantum spin models of interest to condensed matter physicists in one and two spatial dimensions.

cond-mat.dis-nn↗

arXiv2014

Diamagnetism and density wave order in the pseudogap regime of YBa$_2$Cu$_3$O$_{6+x}$

Clear experimental evidence of charge density wave correlations competing with superconducting order in YBCO have thrust their relationship with the pseudogap regime into the spotlight. To aid in characterizing the pseudogap regime, we propose a dimensionless ratio of the diamagnetic susceptibility to the correlation length of the charge density wave correlations. Using Monte Carlo simulations, we compute this ratio on the classical model of Hayward et. al. (Science 343, 1336 (2014)), which describes angular fluctuations of a multicomponent order, capturing both superconducting and density wave correlations. We compare our results with available data on YBa$_2$Cu$_3$O$_{6+x}$, and propose experiments to clarify the value of this dimensionless ratio using existing samples and techniques.

cond-mat.supr-con↗

arXiv2013

Angular fluctuations of a multi-component order describe the pseudogap regime of the cuprate superconductors

The hole-doped cuprate high temperature superconductors enter the pseudogap regime as their superconducting critical temperature, $T_c$, falls with decreasing hole density. Experiments have probed this regime for over two decades, but we argue that decisive new information has emerged from recent X-ray scattering experiments (arXiv:1207.0915, arXiv:1206.4333, arXiv:1207.3667). The experiments observe incommensurate charge density wave fluctuations whose strength rises gradually over a wide temperature range above $T_c$, but then decreases as the temperature is lowered below $T_c$. We propose a theory in which the superconducting and charge-density wave orders exhibit angular fluctuations in a 6-dimensional space. The theory provides a natural quantitative fit to the X-ray data, and can be a basis for understanding other characteristics of the pseudogap.

cond-mat.supr-con↗