Related papers: Tensor Renormalization Group Calculations of Parti…
An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square…
In this thesis, we present a novel method combining energy-based finite-size scaling with tensor network renormalization (TNR) to study phase transitions in lattice models. This approach effectively calculates running coupling constants and…
We compute the exact partition function of the 2D Ising Model at critical temperature but with nonzero magnetic field at the boundary. The model describes a renormalization group flow between the free and fixed conformal boundary conditions…
We construct local generalizations of 3-state Potts models with exotic critical points. We analytically show that these are described by non-diagonal modular invariant partition functions of products of $Z_3$ parafermion or $u(1)_6$…
Field theories with combinatorial non-local interactions such as tensor invariants are interesting candidates for describing a phase transition from discrete quantum-gravitational to continuum geometry. In the so-called cyclic-melonic…
By formulating the renormalization group as a quantum channel acting on density matrices in Quantum Field Theories (QFTs), we show that ground-state expectation values of observables supported on slow momentum modes can be approximated by…
Two replicas of a 2D Ising model are coupled by frustrated spin-spin interactions. It is known that this inter-layer coupling is marginal and that the bulk critical behavior belongs to the Ashkin-Teller (AT) universality class, as the…
In the group field theory approach to quantum gravity, continuous spacetime geometry is expected to emerge via phase transition. However, understanding the phase diagram and finding fixed points under the renormalization group flow remains…
We initiate a numerical conformal bootstrap study of CFTs with $S_n \ltimes (S_Q)^n$ global symmetry. These include CFTs that can be obtained as coupled replicas of two-dimensional critical Potts models. Particular attention is paid to the…
The novel concept of entanglement renormalization and its corresponding tensor network renormalization technique have been highly successful in developing a controlled real space renormalization group (RG) scheme. Numerically approximate…
We propose a scheme to perform tensor network based finite-size scaling analysis for two-dimensional classical models. In the tensor network representation of the partition function, we use higher-order tensor renormalization group (HOTRG)…
We formulate rational conformal field theory in terms of a symmetric special Frobenius algebra A and its representations. A is an algebra in the modular tensor category of Moore-Seiberg data of the underlying chiral CFT. The multiplication…
We determine the spaces of states of the two-dimensional $O(n)$ and $Q$-state Potts models with generic parameters $n,Q\in \mathbb{C}$ as representations of their known symmetry algebras. While the relevant representations of the conformal…
The renormalization of composite operators is a fundamental aspect of quantum field theory, relevant for the description of phase transitions and high energy phenomenology. We calculate the anomalous dimensions of a large set of operators…
Renormalization group and Coulomb gas mappings are used to derive theoretical predictions for the corrections to the exactly known asymptotic fractal masses of the hull, external perimeter, singly connected bonds and total mass of the…
We investigate the multi-particle states of the (1+1)-dimensional Ising model using a spectroscopy scheme based on the tensor renormalization group method. We start by computing the finite-volume energy spectrum of the model from the…
We study the scaling of the traces of the integer powers of the partially transposed reduced density matrix and of the entanglement negativity for two spin blocks as function of their length and separation in the critical Ising chain. For…
We consider the universality class of the two-dimensional Tricritical Ising Model. The scaling form of the free-energy naturally leads to the definition of universal ratios of critical amplitudes which may have experimental relevance. We…
We find the cross-over behavior for the spin-spin correlation function for the 2D Ising and 3-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation approach of the perturbation series…
Conformal symmetry, emerging at critical points, can be lost when renormalization group fixed points collide. Recently, it was proposed that after collisions, real fixed points transition into the complex plane, becoming complex fixed…