Clement Delcamp
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View article: Twisted gauging and topological sectors in (2+1)d Abelian lattice gauge theories
Twisted gauging and topological sectors in (2+1)d Abelian lattice gauge theories Open
Given a two-dimensional quantum lattice model with an Abelian gauge theory interpretation, we investigate a duality operation that amounts to gauging its invertible 1-form symmetry, followed by gauging the resulting 0-form symmetry in a tw…
View article: Nonsemisimple noninvertible symmetry
Nonsemisimple noninvertible symmetry Open
We investigate the action of a non-semisimple, non-invertible symmetry on spin chains, whose topological defects encode the category of modules over the Taft algebra of dimension 4. Sacrificing Hermiticity, we construct several symmetric, …
View article: Entanglement and the density matrix renormalization group in the generalized Landau paradigm
Entanglement and the density matrix renormalization group in the generalized Landau paradigm Open
The fields of entanglement theory and tensor networks have recently emerged as central tools for characterizing quantum phases of matter. Here we determine the entanglement structure of ground states of gapped symmetric quantum lattice mod…
View article: Gauging Non-Invertible Symmetries in (2+1)d Topological Orders
Gauging Non-Invertible Symmetries in (2+1)d Topological Orders Open
We present practical and formal methods for gauging non-invertible symmetries in (2+1)d topological quantum field theories. Along the way, we generalize various aspects of invertible 0-form gauging, including symmetry fractionalization, di…
View article: Low-Depth Unitary Quantum Circuits for Dualities in One-Dimensional Quantum Lattice Models
Low-Depth Unitary Quantum Circuits for Dualities in One-Dimensional Quantum Lattice Models Open
A systematic approach to dualities in symmetric (1+1)d quantum lattice models has recently been proposed in terms of module categories over the symmetry fusion categories. By characterizing the nontrivial way in which dualities intertwine …
View article: Entanglement and the density matrix renormalisation group in the generalised Landau paradigm
Entanglement and the density matrix renormalisation group in the generalised Landau paradigm Open
The fields of entanglement theory and tensor networks have recently emerged as central tools for characterising quantum phases of matter. In this article, we determine the entanglement structure of ground states of gapped symmetric quantum…
View article: Symmetry topological field theory and non-abelian Kramers-Wannier dualities of generalised Ising models
Symmetry topological field theory and non-abelian Kramers-Wannier dualities of generalised Ising models Open
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 …
View article: Higher categorical symmetries and gauging in two-dimensional spin systems
Higher categorical symmetries and gauging in two-dimensional spin systems Open
We present a framework to systematically investigate higher categorical symmetries in two-dimensional spin systems. Though exotic, such generalised symmetries have been shown to naturally arise as dual symmetries upon gauging invertible sy…
View article: Report on 2301.01259v2
Report on 2301.01259v2 Open
We present a framework to systematically investigate higher categorical symmetries in two-dimensional spin systems.Though exotic, such generalised symmetries have been shown to naturally arise as dual symmetries upon gauging invertible sym…
View article: Dualities in One-Dimensional Quantum Lattice Models: Topological Sectors
Dualities in One-Dimensional Quantum Lattice Models: Topological Sectors Open
It has been a long-standing open problem to construct a general framework for relating the spectra of dual theories to each other. Here, we solve this problem for the case of one-dimensional quantum lattice models with symmetry-twisted bou…
View article: Report on scipost_202303_00011v1
Report on scipost_202303_00011v1 Open
We present a framework to systematically investigate higher categorical symmetries in two-dimensional spin systems.Though exotic, such generalised symmetries have been shown to naturally arise as dual symmetries upon gauging invertible sym…
View article: Low-depth unitary quantum circuits for dualities in one-dimensional quantum lattice models
Low-depth unitary quantum circuits for dualities in one-dimensional quantum lattice models Open
A systematic approach to dualities in symmetric (1+1)d quantum lattice models has recently been proposed in terms of module categories over the symmetry fusion categories. By characterizing the non-trivial way in which dualities intertwine…
View article: Dualities in One-Dimensional Quantum Lattice Models: Symmetric Hamiltonians and Matrix Product Operator Intertwiners
Dualities in One-Dimensional Quantum Lattice Models: Symmetric Hamiltonians and Matrix Product Operator Intertwiners Open
We present a systematic recipe for generating and classifying duality transformations in onedimensional quantum lattice systems. Our construction emphasizes the role of global symmetries, including those described by Abelian and non-Abelia…
View article: Higher categorical symmetries and gauging in two-dimensional spin systems
Higher categorical symmetries and gauging in two-dimensional spin systems Open
We present a framework to systematically investigate higher categorical symmetries in two-dimensional spin systems. Though exotic, such generalised symmetries have been shown to naturally arise as dual symmetries upon gauging invertible sy…
View article: Dualities in one-dimensional quantum lattice models: topological sectors
Dualities in one-dimensional quantum lattice models: topological sectors Open
It has been a long-standing open problem to construct a general framework for relating the spectra of dual theories to each other. Here, we solve this problem for the case of one-dimensional quantum lattice models with symmetry-twisted bou…
View article: A toy model for categorical charges
A toy model for categorical charges Open
We consider a higher gauge topological model in three spatial dimensions whose input datum is a 2-group encoding the mixing of a 0-form $\mathbb Z_2$- and 1-form $\mathbb Z_3$-symmetry. We study the excitation content of the theory on the …
View article: Crossing with the circle in Dijkgraaf–Witten theory and applications to topological phases of matter
Crossing with the circle in Dijkgraaf–Witten theory and applications to topological phases of matter Open
Given a fully extended topological quantum field theory, the “crossing with the circle” conditions establish that the dimension, or categorification thereof, of the quantum invariant assigned to a closed k-manifold Σ is equivalent to that …
View article: On the stability of topological order in tensor network states
On the stability of topological order in tensor network states Open
We construct a tensor network representation of the 3d toric code ground state that is stable to a generating set of uniform local tensor perturbations, including those that do not map to local operators on the physical Hilbert space. The …
View article: Dualities in one-dimensional quantum lattice models: symmetric Hamiltonians and matrix product operator intertwiners
Dualities in one-dimensional quantum lattice models: symmetric Hamiltonians and matrix product operator intertwiners Open
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 …
View article: On tensor network representations of the (3+1)d toric code
On tensor network representations of the (3+1)d toric code Open
We define two dual tensor network representations of the (3+1)d toric code ground state subspace. These two representations, which are obtained by initially imposing either family of stabilizer constraints, are characterized by different v…
View article: Tensor network approach to electromagnetic duality in (3+1)d topological gauge models
Tensor network approach to electromagnetic duality in (3+1)d topological gauge models Open
Given the Hamiltonian realisation of a topological (3+1)d gauge theory with finite group $G$, we consider a family of tensor network representations of its ground state subspace. This family is indexed by gapped boundary conditions encoded…
View article: Gauge Models of Topological Phases and Applications to Quantum Gravity
Gauge Models of Topological Phases and Applications to Quantum Gravity Open
In 2+1 dimensions, gravity is an SU(2) topological gauge theory that can be written as BF theory. In the condensed matter literature, the Hamiltonian realization of BF theory for finite groups is known as the Kitaev model. The correspondin…
View article: Dual loop quantizations of 3d gravity
Dual loop quantizations of 3d gravity Open
The loop quantization of 3d gravity consists in defining the Hilbert space of states satisfying the Gauß constraint and the flatness constraint. The Gauß constraint is enforced at the kinematical level by introducing spin networks which fo…
View article: Renormalization of tensor networks using graph-independent local truncations
Renormalization of tensor networks using graph-independent local truncations Open
We introduce an efficient algorithm for reducing bond dimensions in an\narbitrary tensor network without changing its geometry. The method is based on\na novel, quantitative understanding of local correlations in a network.\nTogether with …
View article: Towards a phase diagram for spin foams
Towards a phase diagram for spin foams Open
One of the most pressing issues for loop quantum gravity and spin foams is the construction of the continuum limit. In this paper, we propose a systematic coarse-graining scheme for three-dimensional lattice gauge models including spin foa…
View article: From 3D topological quantum field theories to 4D models with defects
From 3D topological quantum field theories to 4D models with defects Open
(2 + 1) dimensional topological quantum field theories (TQFTs) with defect excitations are by now quite well understood, while many questions are still open for (3 + 1) dimensional TQFTs. Here we propose a strategy to lift states and opera…
View article: From 3D TQFTs to 4D models with defects
From 3D TQFTs to 4D models with defects Open
(2+1) dimensional topological quantum field theories with defect excitations are by now quite well understood, while many questions are still open for (3+1) dimensional TQFTs. Here we propose a strategy to lift states and operators of a (2…