Judah Unmuth-Yockey

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 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 three-dimensional gauge theories with groups Z(2), U(1) and SU(2). We briefly discuss generalizations to other groups, higher dimensions and practical implementations.

Tensor renormalization group study of the 2d O(3) model

We present our progress on a study of the

Gauge-invariant implementation of the Abelian-Higgs model on optical lattices

O(3)

Progress towards quantum simulating the classical O(2) model

model in two-dimensions using the Tensor Renormalization Group method. We first construct the theory in terms of tensors, and show how to construct

Fisher zeros and conformality in lattice models

n

Estimating the central charge from the Rényi entanglement entropy

-point correlation functions. We then give results for thermodynamic quantities at finite and infinite volume, as well as 2-point correlation function data. We discuss some of the advantages and challenges of tensor renormalization and future directions in which to work.

Probing the conformal Calabrese-Cardy scaling with cold atoms

© 2015 American Physical Society. We present a gauge-invariant effective action for the Abelian-Higgs model (scalar electrodynamics) with a chemical potential μ on a (1+1)-dimensional lattice. This formulation provides an expansion in the hopping parameter κ which we test with Monte Carlo simulations for a broad range of the inverse gauge coupling bpl=1/g2 and small values of the scalar self-coupling λ. In the opposite limit of infinitely large λ, the partition function can be written as a traced product of local tensors which allows us to write exact blocking formulas. Gausss law is automatically satisfied and the introduction of μ has consequences only if we have an external electric field, g2=0 or an explicit gauge symmetry breaking. The time-continuum limit of the blocked transfer matrix can be obtained numerically and, for g2=0 and a spin-1 truncation, the small volume energy spectrum is identical to the low energy spectrum of a two-species Bose-Hubbard model in the limit of large on-site repulsion. We extend this procedure for finite bpl and derive a spin-1 approximation of the Hamiltonian. It involves new terms corresponding to transitions among the two species in the Bose-Hubbard model. We propose an optical lattice implementation involving a ladder structure.

Comparing Tensor Renormalization Group and Monte Carlo calculations for spin and gauge models

Department of Energy under DOE [DE-FG02-05ER41368, DE-SC0010114, DE-FG02-91ER40664]; Army Research Office of the Department of Defense [W911NF-13-1-0119]; NSF [DMR-1411345]

RG-inspired machine learning for lattice field theory

Fisher zeros are the zeros of the partition function in the co mplex β = 2Nc/g 2 plane. When they pinch the real axis, finite size scaling allows one to disting uish between first and second order transition and to estimate exponents. On the other hand, a gap signals confinement and the method can be used to explore the boundary of the conformal window. We present recent numerical results for 2D O(N) sigma models, 4D U(1) and SU(2) pure gauge and SU(3) gauge theory with Nf = 4 and 12 flavors. We discuss attempts to understand some of the se results using analytical methods. We discuss the 2-lattice matching and qualitative aspects of the renormalization group (RG) flows in the Migdal-Kadanoff approximation, in particu lar how RG flows starting at large β seem to move around regions where bulk transitions occur. We consider the effects of the boundary conditions on the nonperturbative part of the average energy and on the Fisher zeros for the 1D O(2) model.

Tensor RG calculations and quantum simulations near criticality

Author(s): Bazavov, A; Meurice, Y; Tsai, SW; Unmuth-Yockey, J; Yang, LP; Zhang, J | Abstract: