Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn the phase diagram of 1+1D Abelian-Higgs model and its critical point
100
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
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 symmetry at $theta = pi$ is implemented exactly. The complex action problem from the $theta$-term is overcome by exactly mapping the partition sum to a worldline/worldsheet representation. Using Monte Carlo simulation of the worldline/worldsheet representation we study the system at $theta = pi$ and show that as a function of the mass parameter the system undergoes a phase transition. Determining the critical exponents from a finite size scaling analysis we show that the transition is in the 2d Ising universality class. We furthermore study the U(1) gauge Higgs systems at $theta = pi$ also with charge 2 matter fields, where an additional $Z_2$ symmetry is expected to alter the phase structure. Our results indicate that for charge 2 a true phase transition is absent and only a rapid crossover separates the large and small mass regions.
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 Villain action is interpreted as a non-compact gauge theory whose center symmetry is gauged and has the advantage that the topological term is correctly quantized so that $2pi$ periodicity in $theta$ is intact. Because of this the $theta = pi$ theory has an exact $Z_2$ charge-conjugation symmetry $C$, which is spontaneously broken when the mass-squared of the scalars is large and positive. Lowering the mass squared the symmetry becomes restored in a second order phase transition. Simulating the system at $theta = pi$ in its dual form we determine the corresponding critical endpoint as a function of the mass parameter. Using a finite size scaling analysis we determine the critical exponents and show that the transition is in the 2d Ising universality class, as expected.
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 superconductors. Recently, superconductivity has been discovered in iron-based layered compound $LaO_{1-x}F_xFeAs$ with $T_c$=26 Kcite{yoichi}, and it competes with spin-density-wave (SDW) ordercite{dong}. Neutron diffraction shows a long-rang SDW-type antiferromagnetic (AF) order at $sim 134$ K in LaOFeAscite{cruz,mcguire}. Therefore, a possible QCP and its role in this system are of great interests. Here we report the detailed phase diagram and anomalous transport properties of the new high-Tc superconductors $SmO_{1-x}F_xFeAs$ discovered by uscite{chenxh}. It is found that superconductivity emerges at $xsim$0.07, and optimal doping takes place in the $xsim$0.20 sample with highest $T_c sim $54 K. While $T_c$ increases monotonically with doping, the SDW order is rapidly suppressed, suggesting a QCP around $x sim$0.14. As manifestations, a linear temperature dependence of the resistivity shows up at high temperatures in the $x<0.14$ regime, but at low temperatures just above $T_c$ in the $x>0.14$ regime; a drop in carrier density evidenced by a pronounced rise in Hall coefficient are observed, which mimic the high-$T_c$ cuprates. The simultaneous occurrence of order, carrier density change and criticality makes a compelling case for a quantum critical point in this system.
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 programming, this enables bootstrap studies of much larger systems of correlation functions than was previously practical. We apply these methods to correlation functions of charge-0, 1, and 2 scalars in the 3d $O(2)$ model, computing new precise values for scaling dimensions and OPE coefficients in this theory. Our new determinations of scaling dimensions are consistent with and improve upon existing Monte Carlo simulations, sharpening the existing decades-old $8sigma$ discrepancy between theory and experiment.
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 a relatively simple system at strong coupling outside of even dimensions. At $d=2+epsilon$, the scaling dimensions and correlation function coefficients receive $epsilon$-dependent corrections. Using numerical and analytical conformal bootstrap methods in Lorentzian signature, we rule out the possibility that the leading corrections are of order $epsilon^{1}$. The essential conflict comes from the $d$-dependence of conformal symmetry, which implies the presence of new states. A resolution is that there exist corrections of order $epsilon^{1/k}$ where $k>1$ is an integer. The linear independence of conformal blocks plays a central role in our analyses. Since our results are not derived from positivity constraints, this bootstrap approach can be extended to the rigorous studies of non-positive systems, such as non-unitary, defect/boundary and thermal CFTs.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
