Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userBootstrapping Heisenberg Magnets and their Cubic Instability
109
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study the critical $O(3)$ model using the numerical conformal bootstrap. In particular, we use a recently developed cutting-surface algorithm to efficiently map out the allowed space of CFT data from correlators involving the leading $O(3)$ singlet $s$, vector $phi$, and rank-2 symmetric tensor $t$. We determine their scaling dimensions to be $(Delta_{s}, Delta_{phi}, Delta_{t}) = (0.518942(51), 1.59489(59), 1.20954(23))$, and also bound various OPE coefficients. We additionally introduce a new ``tip-finding algorithm to compute an upper bound on the leading rank-4 symmetric tensor $t_4$, which we find to be relevant with $Delta_{t_4} < 2.99056$. The conformal bootstrap thus provides a numerical proof that systems described by the critical $O(3)$ model, such as classical Heisenberg ferromagnets at the Curie transition, are unstable to cubic anisotropy.
rate research
Read More
We study the conformal bootstrap for a 4-point function of fermions $langlepsipsipsipsirangle$ in 3D. We first introduce an embedding formalism for 3D spinors and compute the conformal blocks appearing in fermion 4-point functions. Using these results, we find general bounds on the dimensions of operators appearing in the $psi times psi$ OPE, and also on the central charge $C_T$. We observe features in our bounds that coincide with scaling dimensions in the Gross-Neveu models at large $N$. We also speculate that other features could coincide with a fermionic CFT containing no relevant scalar operators.
We study the conformal bootstrap constraints for 3D conformal field theories with a $mathbb{Z}_2$ or parity symmetry, assuming a single relevant scalar operator $epsilon$ that is invariant under the symmetry. When there is additionally a single relevant odd scalar $sigma$, we map out the allowed space of dimensions and three-point couplings of such Ising-like CFTs. If we allow a second relevant odd scalar $sigma$, we identify a feature in the allowed space compatible with 3D $mathcal{N}=1$ superconformal symmetry and conjecture that it corresponds to the minimal $mathcal{N}=1$ supersymmetric extension of the Ising CFT. This model has appeared in previous numerical bootstrap studies, as well as in proposals for emergent supersymmetry on the boundaries of topological phases of matter. Adding further constraints from 3D $mathcal{N}=1$ superconformal symmetry, we isolate this theory and use the numerical bootstrap to compute the leading scaling dimensions $Delta_{sigma} = Delta_{epsilon} - 1 = .58444(22)$ and three-point couplings $lambda_{sigmasigmaepsilon} = 1.0721(2)$ and $lambda_{epsilonepsilonepsilon} = 1.67(1)$. We additionally place bounds on the central charge and use the extremal functional method to estimate the dimensions of the next several operators in the spectrum. Based on our results we observe the possible exact relation $lambda_{epsilonepsilonepsilon}/lambda_{sigmasigmaepsilon} = tan(1)$.
We use numerical bootstrap techniques to study correlation functions of a traceless symmetric tensors of $O(N)$ with two indexes $t_{ij}$. We obtain upper bounds on operator dimensions for all the relevant representations and several values of $N$. We discover several families of kinks, which do not correspond to any known model and we discuss possible candidates. We then specialize to the case $N=4$, which has been conjectured to describe a phase transition in the antiferromagnetic real projective model $ARP^{3}$. Lattice simulations provide strong evidence for the existence of a second order phase transition, while an effective field theory approach does not predict any fixed point. We identify a set of assumptions that constrain operator dimensions to a closed region overlapping with the lattice prediction. The region is still present after pushing the numerics in the single correlator case or when considering a mixed system involving $t$ and the lowest dimension scalar singlet.
We estimate thermal one-point functions in the 3d Ising CFT using the operator product expansion (OPE) and the Kubo-Martin-Schwinger (KMS) condition. Several operator dimensions and OPE coefficients of the theory are known from the numerical bootstrap for flat-space four-point functions. Taking this data as input, we use a thermal Lorentzian inversion formula to compute thermal one-point coefficients of the first few Regge trajectories in terms of a small number of unknown parameters. We approximately determine the unknown parameters by imposing the KMS condition on the two-point functions $langle sigmasigma rangle$ and $langle epsilonepsilon rangle$. As a result, we estimate the one-point functions of the lowest-dimension $mathbb Z_2$-even scalar $epsilon$ and the stress-energy tensor $T_{mu u}$. Our result for $langle sigmasigma rangle$ at finite-temperature agrees with Monte-Carlo simulations within a few percent, inside the radius of convergence of the OPE.
Consider at a finite temperature T a superfluid moving with a velocity v relative to the thermal bath or its normal component. From Landaus argument there exists a critical v_c (T) beyond which excitations can be spontaneously generated and the system becomes unstable. Identifying the final state induced by such an instability has been an outstanding open question. Using holographic duality we perform dynamical simulations of evolutions from initial unstable states, and find that the system settles to a homogenous superfluid state with a final velocity below the critical velocity. The dynamical evolution process appears to be highly chaotic, exhibiting transient turbulence. Nevertheless we are able to identify from the simulations a universal physical mechanism for the reduction of superfluid velocity, in terms of spontaneous nucleation of solitons. We also derive a simple analytic formula which relates the final velocity to the number of solitons nucleated during the evolution.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
