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We investigate in detail the phase diagram of the Abelian-Higgs model in one spatial dimension and time (1+1D) on a lattice. We identify a line of first order phase transitions separating the Higgs region from the confined one. This line terminates in a quantum critical point above which the two regions are connected by a smooth crossover. We analyze the critical point and find compelling evidences for its description as the product of two non-interacting systems, a massless free fermion and a massless free boson. However, we find also some surprizing results that cannot be explained by our simple picture, suggesting this newly discovered critical point to be an unusual one.
We study 2d U(1) gauge Higgs systems with a $theta$-term. For properly discretizing the topological charge as an integer we introduce a mixed group- and algebra-valued discretization (MGA scheme) for the gauge fields, such that the charge conjugation
We simulate the 2d U(1) gauge Higgs model on the lattice with a topological angle $theta$. The corresponding complex action problem is overcome by using a dual representation based on the Villain action appropriately endowed with a $theta$-term. The
The magnetic fluctuations associated with a quantum critical point (QCP) are widely believed to cause the non-Fermi liquid behaviors and unconventional superconductivities, for example, in heavy fermion systems and high temperature cuprate supercondu
We develop new tools for isolating CFTs using the numerical bootstrap. A cutting surface algorithm for scanning OPE coefficients makes it possible to find islands in high-dimensional spaces. Together with recent progress in large-scale semidefinite p
We study the Ising model in $d=2+epsilon$ dimensions using the conformal bootstrap. As a minimal-model Conformal Field Theory (CFT), the critical Ising model is exactly solvable at $d=2$. The deformation to $d=2+epsilon$ with $epsilonll 1$ furnishes