arXiv subjects

J. Unmuth-Yockey

Publications and source records attributed to J. Unmuth-Yockey.

7 recordsLinked to original sources

arXiv2018

Quantum simulation of the universal features of the Polyakov loop

Lattice gauge theories are fundamental to our understanding of high-energy physics. Nevertheless, the search for suitable platforms for their quantum simulation has proven difficult. We show that the Abelian Higgs model in 1+1 dimensions is a prime candidate for an experimental quantum simulation of a lattice gauge theory. To this end, we use a discrete tensor reformulation to smoothly connect the space-time isotropic version used in most numerical lattice simulations to the continuous-time limit corresponding to the Hamiltonian formulation. The eigenstates of the Hamiltonian are neutral for periodic boundary conditions, but we probe the nonzero charge sectors by either introducing a Polyakov loop or an external electric field. In both cases we obtain universal functions relating the mass gap, the gauge coupling, and the spatial size which are invariant under the deformation of the temporal lattice spacing. We propose to use a physical multi-leg ladder of atoms trapped in optical lattices and interacting with Rydberg-dressed interactions to quantum simulate the model and check the universal features. Our results provide a path to the analog quantum simulation of lattice gauge theories with atoms in optical lattices.

hep-lat↗

arXiv2017

RG inspired Machine Learning for lattice field theory

Machine learning has been a fast growing field of research in several areas dealing with large datasets. We report recent attempts to use Renormalization Group (RG) ideas in the context of machine learning. We examine coarse graining procedures for perceptron models designed to identify the digits of the MNIST data. We discuss the correspondence between principal components analysis (PCA) and RG flows across the transition for worm configurations of the 2D Ising model. Preliminary results regarding the logarithmic divergence of the leading PCA eigenvalue were presented at the conference and have been improved after. More generally, we discuss the relationship between PCA and observables in Monte Carlo simulations and the possibility of reduction of the number of learning parameters in supervised learning based on RG inspired hierarchical ansatzes.

hep-lat↗

arXiv2017

Estimating the central charge from the Rényi entanglement entropy

We calculate the von Neumann and Rényi bipartite entanglement entropy of the $O(2)$ model with a chemical potential on a 1+1 dimensional Euclidean lattice with open and periodic boundary conditions. We show that the Calabrese-Cardy conformal field theory predictions for the leading logarithmic scaling with the spatial size of these entropies are consistent with a central charge $c=1$. This scaling survives the time continuum limit and truncations of the microscopic degrees of freedom, modifications which allow us to connect the Lagrangian formulation to quantum Hamiltonians. At half-filling, the forms of the subleading corrections imposed by conformal field theory allow the determination of the central charge with an accuracy better than two percent for moderately sized lattices. We briefly discuss the possibility of estimating the central charge using quantum simulators.

hep-lat↗

arXiv2017

Probing the conformal Calabrese-Cardy scaling with cold atoms

We demonstrate that current experiments using cold bosonic atoms trapped in one-dimensional optical lattices and designed to measure the second-order Renyi entanglement entropy S_2, can be used to verify detailed predictions of conformal field theory (CFT) and estimate the central charge c. We discuss the adiabatic preparation of the ground state at half-filling where we expect a CFT with c=1. This can be accomplished with a very small hoping parameter J, in contrast to existing studies with density one where a much larger J is needed. We provide two complementary methods to estimate and subtract the classical entropy generated by the experimental preparation and imaging processes. We compare numerical calculations for the classical O(2) model with a chemical potential on a 1+1 dimensional lattice, and the quantum Bose-Hubbard Hamiltonian implemented in the experiments. S_2 is very similar for the two models and follows closely the Calabrese-Cardy scaling, (c/8)\ln(N_s), for N_s sites with open boundary conditions, provided that the large subleading corrections are taken into account.

cond-mat.quant-gas↗

arXiv2016

Tensor RG calculations and quantum simulations near criticality

We discuss the reformulation of the O(2) model with a chemical potential and the Abelian Higgs model on a 1+1 dimensional space-time lattice using the Tensor Renormalization Group (TRG) method. The TRG allows exact blocking and connects smoothly the classical Lagrangian approach to the quantum Hamiltonian approach. We calculate the entanglement entropy in the superfluid phase of the O(2) model and show that it approximately obeys the logarithmic Calabrese-Cardy scaling obtained from Conformal Field Theory (CFT). We calculate the Polyakov loop in the Abelian Higgs model and discuss the possibility of a deconfinement transition at finite volume. We propose Bose-Hubbard Hamiltonians implementable on optical lattices as quantum simulators for CFT models.

hep-lat↗

arXiv2014

Progress towards quantum simulating the classical O(2) model

We connect explicitly the classical $O(2)$ model in 1+1 dimensions, a model sharing important features with $U(1)$ lattice gauge theory, to physical models potentially implementable on optical lattices and evolving at physical time. Using the tensor renormalization group formulation, we take the time continuum limit and check that finite dimensional projections used in recent proposals for quantum simulators provide controllable approximations of the original model. We propose two-species Bose-Hubbard models corresponding to these finite dimensional projections at strong coupling and discuss their possible implementations on optical lattices using a $^{87}$Rb and $^{41}$K Bose-Bose mixture.

hep-lat↗

arXiv2013

Exact blocking formulas for spin and gauge models

Using the example of the two-dimensional (2D) Ising model, we show that in contrast to what can be done in configuration space, the tensor renormalization group (TRG) formulation allows one to write exact, compact, and manifestly local blocking formulas and exact coarse grained expressions for the partition function. We argue that similar results should hold for most models studied by lattice gauge theorists. We provide exact blocking formulas for several 2D spin models (the O(2) and O(3) sigma models and the SU(2) principal chiral model) and for the 3D gauge theories with groups Z_2, U(1) and SU(2). We briefly discuss generalizations to other groups, higher dimensions and practical implementations.

hep-lat↗