Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userRSOS Quantum Chains Associated with Off-Critical Minimal Models and $mathbb{Z}_n$ Parafermions
110
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We consider the $varphi_{1,3}$ off-critical perturbation ${cal M}(m,m;t)$ of the general non-unitary minimal models where $2le mle m$ and $m, m$ are coprime and $t$ measures the departure from criticality corresponding to the $varphi_{1,3}$ integrable perturbation. We view these models as the continuum scaling limit in the ferromagnetic Regime III of the Forrester-Baxter Restricted Solid-On-Solid (RSOS) models on the square lattice. We also consider the RSOS models in the antiferromagnetic Regime II related in the continuum scaling limit to $mathbb{Z}_n$ parfermions with $n=m-2$. Using an elliptic Yang-Baxter algebra of planar tiles encoding the allowed face configurations, we obtain the Hamiltonians of the associated quantum chains defined as the logarithmic derivative of the transfer matrices with periodic boundary conditions. The transfer matrices and Hamiltonians act on a vector space of paths on the $A_{m-1}$ Dynkin diagram whose dimension is counted by generalized Fibonacci numbers.
rate research
Read More
For the simplest quantum field theory originating from a non-trivial fixed point of the renormalization group, the Lee-Yang model, we show that the operator space determined by the particle dynamics in the massive phase and that prescribed by conformal symmetry at criticality coincide.
The bootstrap determination of the geometrical correlation functions in the two-dimensional Potts model proposed in a paper [arXiv:1607.07224] was later shown in [arXiv:1809.02191] to be incorrect, the actual spectrum of the model being considerably more complex than initially conjectured. We provide in this paper a geometrical interpretation of the four-point functions built in [arXiv:1607.07224], and explain why the results obtained by these authors, albeit incorrect, appeared so close to those of their numerical simulations of the Potts model. Our strategy is based on a cluster expansion of correlation functions in RSOS minimal models, and a subsequent numerical and algebraic analysis of the corresponding $s$-channel spectrum, in full analogy with our early work on the Potts model [arXiv:1809.02191]. Remarkable properties of the lattice amplitudes are uncovered, which explain in particular the truncation of the spectrum of [arXiv:1809.02191] to the much simpler one of the RSOS models, and which will be used in a forthcoming paper to finally determine the geometric four-point functions of the Potts model itself.
We construct lattice parafermions - local products of order and disorder operators - in nearest-neighbor Z(N) models on regular isotropic planar lattices, and show that they are discretely holomorphic, that is they satisfy discrete Cauchy-Riemann equations, precisely at the critical Fateev-Zamolodchikov (FZ) integrable points. We generalize our analysis to models with anisotropic interactions, showing that, as long as the lattice is correctly embedded in the plane, such discretely holomorphic parafermions exist for particular values of the couplings which we identify as the anisotropic FZ points. These results extend to more general inhomogeneous lattice models as long as the covering lattice admits a rhombic embedding in the plane.
In $SU(N)$ gauge theory, it is argued recently that there exists a mixed anomaly between the CP symmetry and the 1-form $mathbb{Z}_N$ symmetry at $theta=pi$, and the anomaly matching requires CP to be spontaneously broken at $theta=pi$ if the system is in the confining phase. In this paper, we elaborate on this discussion by examining the large volume behavior of the partition functions of the $SU(N)/mathbb{Z}_N$ theory on $T^4$ a la t Hooft. The periodicity of the partition function in $theta$, which is not $2pi$ due to fractional instanton numbers, suggests the presence of a phase transition at $theta=pi$. We propose lattice simulations to study the distribution of the instanton number in $SU(N)/mathbb{Z}_N$ theories. A characteristic shape of the distribution is predicted when the system is in the confining phase. The measurements of the distribution may be useful in understanding the phase structure of the theory.
We investigate chiral zero modes and winding numbers at fixed points on $T^2/mathbb{Z}_N$ orbifolds. It is shown that the Atiyah-Singer index theorem for the chiral zero modes leads to a formula $n_+-n_-=(-V_++V_-)/2N$, where $n_{pm}$ are the numbers of the $pm$ chiral zero modes and $V_{pm}$ are the sums of the winding numbers at the fixed points on $T^2/mathbb{Z}_N$. This formula is complementary to our zero-mode counting formula on the magnetized orbifolds with non-zero flux background $M eq 0$, consistently with substituting $M = 0$ for the counting formula $n_+ - n_- = (2M - V_+ + V_-)/2N$.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
