40 citations · 262 across the 25 of their papers we have counts for
24 papers
Non-abelian quantum double models from iterated gauging
David Blanik, José Garre-Rubio
We reconstruct all (2+1)D quantum double models of finite groups from their boundary symmetries through the repeated application of a gauging procedure, extending the existing cons…
From gauging to duality in one-dimensional quantum lattice models
Bram Vancraeynest-De Cuiper, José Garre-Rubio, Frank Verstraete +3
Gauging and duality transformations, two of the most useful tools in many-body physics, are shown to be equivalent up to constant depth quantum circuits in the case of one-dimensio…
Two-Dimensional Bialgebras and Quantum Groups: Algebraic Structures and Tensor Network Realizations
José Garre-Rubio, András Molnár, Germán Sierra
We introduce a framework to define coalgebra and bialgebra structures on two-dimensional (2D) square lattices, extending the algebraic theory of Hopf algebras and quantum groups be…
A simple mechanism for unstable degeneracies in local Hamiltonians
Jose Garre Rubio
If a local Hamiltonian eigenstate is mapped to another state by local operators commuting with the Hamiltonian terms, the latter is also an eigenstate. This basic observation impli…
Gauging Quantum Phases: A Matrix Product State Approach
David Blanik, José Garre-Rubio, Norbert Schuch
Utilizing the framework of matrix product states, we investigate gauging as a method for exploring quantum phases of matter. Specifically, we describe how symmetry-protected topolo…
Detection of 2D SPT Order with Partial Symmetries
Alex Turzillo, Naren Manjunath, Jose Garre-Rubio
A method of using partial symmetries to distinguish two dimensional symmetry protected topological (SPT) phases of on-site, unitary symmetries is proposed. This novel order paramet…
MPS Stability and the Intersection Property
José Garre-Rubio, Alex Turzillo, András Molnár
We identify a property of the local tensors of matrix product states (MPS) that guarantees that their parent Hamiltonians satisfy the intersection property. The intersection proper…
Internal structure of gauge-invariant Projected Entangled Pair States
David Blanik, José Garre-Rubio, András Molnár +1
Projected entangled pair states (PEPS) are very useful in the description of strongly correlated systems, partly because they allow encoding symmetries, either global or local (gau…
Systematic construction of stabilizer codes via gauging abelian boundary symmetries
Bram Vancraeynest-De Cuiper, José Garre-Rubio
We propose a systematic framework to construct a (d+1)-dimensional stabilizer model from an initial generic d-dimensional abelian symmetry. Our approach builds upon the iterative g…
Fractional domain wall statistics in spin chains with anomalous symmetries
Jose Garre Rubio, Norbert Schuch
We study the statistics of domain wall excitations in quantum spin chains. We focus on systems with finite symmetry groups represented by matrix product unitaries (MPUs), i.e. fini…
Emergent (2+1)D topological orders from iterative (1+1)D gauging
Jose Garre Rubio
Gauging introduces gauge fields in order to localize an existing global symmetry, resulting in a dual global symmetry on the gauge fields that can be gauged again. By iterating the…
Gauging quantum states with non-anomalous matrix product operator symmetries
José Garre Rubio, Ilya Kull
Gauging a global symmetry of a system amounts to introducing new degrees of freedom whose transformation rule makes the overall system observe a local symmetry. In quantum systems…
Complete characterization of non-Abelian topological phase transitions and detection of anyon splitting with projected entangled pair states
Wen-Tao Xu, Jose Garre-Rubio, Norbert Schuch
It is well-known that many topological phase transitions of intrinsic Abelian topological phases are accompanied by condensation and confinement of anyons. However, for non-Abelian…
Matrix Product Operator Algebras II: Phases of Matter for 1D Mixed States
Alberto Ruiz-de-Alarcón, José Garre-Rubio, András Molnár +1
The classification of topological phases of matter is fundamental to understand and characterize the properties of quantum materials. In this paper we study phases of matter in one…
Matrix product operator algebras I: representations of weak Hopf algebras and projected entangled pair states
Andras Molnar, Alberto Ruiz de Alarcón, José Garre-Rubio +3
Matrix Product Operators (MPOs) are tensor networks representing operators acting on 1D systems. They model a wide variety of situations, including communication channels with memo…
Fractionalization of subsystem symmetries in two dimensions
David T. Stephen, Arpit Dua, José Garre-Rubio +2
The fractionalization of global symmetry charges is a striking hallmark of topological quantum order. Here, we discuss the fractionalization of subsystem symmetries in two-dimensio…
Classifying phases protected by matrix product operator symmetries using matrix product states
José Garre-Rubio, Laurens Lootens, András Molnár
We classify the different ways in which matrix product states (MPSs) can stay invariant under the action of matrix product operator (MPO) symmetries. This is achieved through a loc…
String order parameters for symmetry fractionalization in an enriched toric code
José Garre-Rubio, Mohsin Iqbal, David T. Stephen
We study a simple model of symmetry-enriched topological order obtained by decorating a toric code model with lower-dimensional symmetry-protected topological states. We show that…
Subsystem symmetry enriched topological order in three dimensions
David T. Stephen, José Garre-Rubio, Arpit Dua +1
We introduce a model of three-dimensional (3D) topological order enriched by planar subsystem symmetries. The model is constructed starting from the 3D toric code, whose ground sta…
Symmetries in topological tensor network states: classification, construction and detection
José Garre-Rubio
This thesis contributes to the understanding of symmetry-enriched topological phases focusing on their descriptions in terms of tensor network states. The Projected Entangled Pair…
Local order parameters for symmetry fractionalization
José Garre-Rubio, Sofyan Iblisdir
We propose a family of order parameters to detect the symmetry fractionalization class of anyons in 2D topological phases. This fractionalization class accounts for the projective,…
Mathematical open problems in Projected Entangled Pair States
J. Ignacio Cirac, José Garre-Rubio, David Pérez-García
Projected Entangled Pair States (PEPS) are used in practice as an efficient parametrization of the set of ground states of quantum many body systems. The aim of this paper is to pr…
Normal projected entangled pair states generating the same state
Andras Molnar, José Garre-Rubio, David Pérez-García +2
Tensor networks are generated by a set of small rank tensors and define many-body quantum states in a succinct form. The corresponding map is not one-to-one: different sets of tens…
Symmetry reduction induced by anyon condensation: a tensor network approach
José Garre-Rubio, Sofyan Iblisdir, David Pérez-García
Topological ordered phases are related to changes in the properties of their quasi-particle excitations (anyons). We study these relations in the framework of projected entanglemen…