Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userCritical long-range vector model in the UV
62
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study interacting critical UV regime of the long-range $O(N)$ vector model with quartic coupling. Analyzing CFT data within the scope of $epsilon$- and $1/N$-expansion, we collect evidence for the equivalence of this model and the critical IR limit of the cubic model coupled to a generalized free field $O(N)$ vector multiplet.
rate research
Read More
We use the background field method to systematically derive CFT data for the critical $phi^6$ vector model in three dimensions, and the Gross-Neveu model in dimensions $2leq d leq 4$. Specifically, we calculate the OPE coefficients and anomalous dimensions of various operators, up to next-to-leading order in the $1/N$ expansion.
We study the extent to which knot and link states (that is, states in 3d Chern-Simons theory prepared by path integration on knot and link complements) can or cannot be described by stabilizer states. States which are not classical mixtures of stabilizer states are known as magic states and play a key role in quantum resource theory. By implementing a particular magic monotone known as the mana we quantify the magic of knot and link states. In particular, for $SU(2)_k$ Chern-Simons theory we show that knot and link states are generically magical. For link states, we further investigate the mana associated to correlations between separate boundaries which characterizes the states long-range magic. Our numerical results suggest that the magic of a majority of link states is entirely long-range. We make these statements sharper for torus links.
We study finite $N$ aspects of the $O(m)times O(N-m)$ vector model with quartic interactions in general $2leq d leq 6$ spacetime dimensions. This model has recently been shown to display the phenomenon of persistent symmetry breaking at a perturbative Wilson-Fisher-like fixed point in $d=4-epsilon$ dimensions. The large rank limit of the bi-conical model displays a conformal manifold and a moduli space of vacua. We find a set of three double trace scalar operators that are respectively irrelevant, relevant and marginal deformations of the conformal manifold in general $d$. We calculate the anomalous dimensions of the single and multi-trace scalar operators to the first sub-leading order in the large rank expansion. The anomalous dimension of the marginal operator does not vanish in general, indicating that the conformal manifold is lifted at finite $N$. In the case of equal ranks we are able to derive explicitly the scaling dimensions of various operators as functions of only $d$.
We show how, upon heating the spin degrees of freedom of the Hubbard model to infinite temperature, the symmetries of the system allow the creation of steady-states with long-range correlations between $eta$-pairs. With induce this heating with either dissipation or periodic driving and evolve the system towards a nonequilibrium steady state, a process which melts all spin order in the system. The steady state is identical in both cases and displays distance-invariant off-diagonal $eta$-correlations. These correlations were first recognised in the superconducting eigenstates in Yangs seminal paper [Phys. Rev. Lett 63, 2144 (1989)], which are a subset of our steady states. We show that our results are a consequence of symmetry properties and entirely independent of the microscopic details of the model and the heating mechanism.
In the previous paper, we studied the random-mass Dirac fermion in one dimension by using the transfer-matrix methods and by introducing an imaginary vector potential in order to calculate the localization lengths. Especially we considered effects of the nonlocal but short-range correlations of the random mass. In this paper, we shall study effects of the long-range correlations of the random mass especially on the delocalization transition. The results depend on how randomness is introduced in the Dirac mass.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
