Related papers: Quantum operations for Kramers-Wannier duality
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…
Non-invertible Kramers-Wannier (KW) duality symmetries are constructed for the transverse-field Ising model (TFIM) at the self-dual point under various boundary conditions (BCs), as long as the resultant Hamiltonian commutes with the ${\rm…
The Kramers-Wannier self-duality of critical quantum chains is examined from the perspective of model wave functions. We demonstrate, using the transverse-field Ising chain and the $3$-state Potts chain as examples, that the symmetry…
We explore non-invertible symmetries in two-dimensional lattice models with subsystem $\mathbb Z_2$ symmetry. We introduce a subsystem $\mathbb Z_2$-gauging procedure, called the subsystem Kramers-Wannier transformation, which generalizes…
We relate two classical dualities in low-dimensional quantum field theory: Kramers-Wannier duality of the Ising and related lattice models in $2$ dimensions, with electromagnetic duality for finite gauge theories in $3$ dimensions. The…
We give an explicit operator representation (via a sequential circuit and projection to symmetry subspaces) of Kramers-Wannier duality transformation in higher-dimensional subsystem symmetric models generalizing the construction in the 1D…
We realize a broad class of code constructions, including Kramers-Wannier duality, tensor product, and check product, as quantum processes consisting of ancilla initialization, local unitaries, and projective measurements. Using…
Non-invertible symmetries of quantum field theories and many-body systems generalize the concept of symmetries by allowing non-invertible operations in addition to more ordinary invertible ones described by groups. The aim of this paper is…
For a class of two-dimensional Euclidean lattice field theories admitting topological lines encoded into a spherical fusion category, we explore aspects of their realisations as boundary theories of a three-dimensional topological quantum…
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 explore the relationship between complexity and duality in quantum systems, focusing on how local and non-local operators evolve under time evolution. We find that non-local operators, which are dual to local operators under specific…
The study of entanglement in quantum field theories provides insight into universal properties which are typically challenging to extract by means of local observables. However, calculations of quantities related to entanglement in gauge…
We present a systematic recipe for generating and classifying duality transformations in one-dimensional quantum lattice systems. Our construction emphasizes the role of global symmetries, including those described by (non)-abelian groups…
The Kramers-Wannier duality is shown to hold for all the even number spin correlation functions of the two dimensional square lattice Ising model in the sense that the high temperature $(T>T_{c})$ expressions for these correlation functions…
The notion of duality -- that a given physical system can have two different mathematical descriptions -- is a key idea in modern theoretical physics. Establishing a duality in lattice statistical mechanics models requires the construction…
We show for any oriented surface, possibly with a boundary, how to generalize Kramers-Wannier duality to the world of quantum groups. The generalization is motivated by quantization of Poisson-Lie T-duality from the string theory.…
We present a new combinatorial approach to the Ising model incorporating arbitrary bond weights on planar graphs. In contrast to existing methodologies, the exact free energy is expressed as the determinant of a set of ordered and…
The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a…
The Kramers-Wannier transformation of the 1+1d transverse-field Ising model exchanges the paramagnetic and ferromagnetic phases and, at criticality, manifests as a non-invertible symmetry. Extending such self-duality symmetries beyond…
We present a detailed study of the finite one-dimensional quantum Ising chain in a transverse field in the presence of boundary magnetic fields coupled with the order-parameter spin operator. We consider two magnetic fields located at the…