Investigations in1+1dimensional latticeϕ4theory

Abstract

In this work we perform a detailed numerical analysis of (1+1) dimensional lattice φ 4 theory. We explore the phase diagram of the theory with two different parameterizations. We find that symmetry breaking occurs only with a negative mass-squared term in the Hamiltonian. The renormalized mass m R and the field renormalization constant Z are calculated from both coordinate space and momentum space propagators in the broken symmetry phase. The critical coupling for the phase transition and the critical exponents associated with m R , Z and the order parameter are extracted using a finite size scaling analysis of the data for several volumes. The scaling behavior of Z has the interesting consequence that φ R does not scale in 1 + 1 dimensions. We also calculate the renormalized coupling constant λ R in the broken symmetry phase.The ratio λ R /m 2 R does not scale and appears to reach a value independent of the bare parameters in the critical region in the infinite volume limit.

Cooling stochastic quantization with colored noise

“…IV. Our simulation with maximal s Λ (white noise) reproduces the results in [34]. In the second part we focus on the relation between colored noise and the real space renormalization group.…”

Matrix product states and variational methods applied to critical quantum field theory

“…We can thus obtain an estimate for c from values of S taken from a number of ground state approximations with varying D. For this to work, we must be close enough to the critical point so that (22) is valid and use small enough D so that S is limited by finiteentanglement effects. We can then use linear regression to fit (23) and obtain c.…”

Complex Langevin simulations for $PT$-symmetric models

“…If 𝜙 = 0 the theory is in a symmetric phase, otherwise it is in a symmetry broken phase. There exist comprehensive studies of the 𝜙 4 theory on the lattice [7][8][9][10]. We will utilize this model as a testbed for our Langevin analysis.…”