Related papers: Topological Defects on the Lattice I: The Ising mo…
We explore the connection between the transfer matrix formalism and discrete complex analysis approach to the two dimensional Ising model. We construct a discrete analytic continuation matrix, analyze its spectrum and establish a direct…
Dualities of quantum field theories are challenging to realize in lattice models of qubits. In this work, we explore one of the simplest dualities, T-duality of the compact boson CFT, and its realization in quantum spin chains. In the…
The Kramers-Wannier duality introduces a well-known non-invertible symmetry in the critical transverse-field Ising model. In this work, we extend this concept to a broad class of quantum lattice models induced from integrability, providing…
Investigating the interplay of dualities, generalized symmetries, and topological defects beyond theoretical models is an important challenge in condensed matter physics and quantum materials. A simple model exhibiting this physics is the…
We give a lattice theory treatment of certain one and two dimensional quantum field theories. In one dimension we construct a combinatorial version of a non-trivial field theory on the circle which is of some independent interest in itself…
The partition function of the two-dimensional Ising model is exactly obtained on a lattice with a twisted boundary condition. The continuum limit of the model off the critical temperature is found to give the mass-deformed Ising conformal…
The leading irrelevant perturbation, which controls the deviation of critical square lattice Ising model with periodic boundary conditions from its continuous CFT analog is identified. An explicit expression for the coupling constant in…
We construct defect networks in pure Yang-Mills theory in two dimensions using a refinement of the lattice approach. The refinement preserves the locality properties of individual defects, and is compatible with solvability of the theory…
Topological defect lines (TDLs) in two-dimensional conformal field theories (CFTs) are standard examples of generalized symmetries in quantum field theory. Integrable lattice incarnations of these TDLs, such as those provided by…
Crystalline symmetries give rise to topological invariants that can distinguish quantum phases of matter. Understanding these in strongly interacting systems is an ongoing research direction requiring non-perturbative methods. Recent…
Conformal field theory finds applications across diverse fields, from statistical systems at criticality to quantum gravity through the AdS/CFT correspondence. These theories are subject to strong constraints, enabling a systematic…
We study the dynamics of topological defects in continuum theories governed by a free energy minimization principle, building on our recently developed framework [Romano J, Mahault B and Golestanian R 2023 J. Stat. Mech.: Theory Exp.…
We consider two disordered lattice models on the square lattice: on the medial lattice the random field Ising model at T=0 and on the direct lattice the random bond Potts model in the large-q limit at its transition point. The interface…
The self-duality of the transverse-field Ising model is an archetype for dualities that, alongside symmetry and topology, are used as an organizing principle throughout modern physics. This duality, however, is not exact. The original and…
A realistic material may possess defects, which often bring the material new properties that have practical applications. The boundary defects of a two-dimensional topologically ordered system are thought of as an alternative way of…
Strongly interacting models often possess "dualities" subtler than a one-to-one mapping of energy levels. The maps can be non-invertible, as apparent in the canonical example of Kramers and Wannier. We analyse an algebraic structure common…
We describe discrete symmetries of two-dimensional Yang-Mills theory with gauge group $G$ associated to outer automorphisms of $G$, and their corresponding defects. We show that the gauge theory partition function with defects can be…
We consider the topological defect lines commuting with the spectral flow and the $\mathcal{N}=(4,4)$ superconformal symmetry in two dimensional non-linear sigma models on K3. By studying their fusion with boundary states, we derive a…
Spin networks appear in a number of areas, for instance in lattice gauge theories and in quantum gravity. They describe the contraction of intertwiners according to the underlying network. We show that a certain generating function of…
We demonstrate the semiclassical nature of symmetry twist defects that differ from quantum deconfined anyons in a true topological phase by examining non-abelian crystalline defects in an abelian lattice model. An underlying non-dynamical…