356 citations · 706 across the 18 of their papers we have counts for
18 papers
Algebras of order parameters in one-dimensional spin systems
Ameya Chavda, Clement Delcamp, Alex Turzillo +1
We study order parameters in one-dimensional quantum lattice models with finite invertible or non-invertible symmetry. We investigate what properties a string operator must satisfy…
Detection of 2D SPT phases under decoherence
Naren Manjunath, Alex Turzillo, Chong Wang
We propose a bulk order parameter for extracting symmetry-protected topological (SPT) invariants of quantum many-body mixed states on a two dimensional lattice using partial symmet…
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…
Symmetry Protected Topological Phases of Mixed States in the Doubled Space
Ruochen Ma, Alex Turzillo
The interplay of symmetry and topology in quantum many-body mixed states has recently garnered significant interest. In a phenomenon not seen in pure states, mixed states can exhib…
Duality and Stacking of Bosonic and Fermionic SPT Phases
Alex Turzillo, Minyoung You
We study the interplay of duality and stacking of bosonic and fermionic symmetry-protected topological phases in one spatial dimension. In general the classifications of bosonic an…
Symmetry Protected Topological Order in Open Quantum Systems
Caroline de Groot, Alex Turzillo, Norbert Schuch
We systematically investigate the robustness of symmetry protected topological (SPT) order in open quantum systems by studying the evolution of string order parameters and other pr…
Supersymmetric boundaries of one-dimensional phases of fermions beyond symmetry-protected topological states
Alex Turzillo, Minyoung You
It has recently been demonstrated that protected supersymmetry emerges on the boundaries of one-dimensional intrinsically fermionic symmetry protected trivial (SPT) phases. Here we…
Fermionic quantum cellular automata and generalized matrix product unitaries
Lorenzo Piroli, Alex Turzillo, Sujeet K. Shukla +1
We study matrix product unitary operators (MPUs) for fermionic one-dimensional (1D) chains. In stark contrast with the case of 1D qudit systems, we show that (i) fermionic MPUs do…
Symmetry-Enriched Quantum Spin Liquids in
Po-Shen Hsin, Alex Turzillo
We use the intrinsic one-form and two-form global symmetries of (3+1) bosonic field theories to classify quantum phases enriched by ordinary (-form) global symmetry. Differen…
Diagrammatic State Sums for 2D Pin-Minus TQFTs
Alex Turzillo
The two dimensional state sum models of Barrett and Tavares are extended to unoriented spacetimes. The input to the construction is an algebraic structure dubbed half twist algebra…
Free and Interacting Short-Range Entangled Phases of Fermions: Beyond the Ten-Fold Way
Yu-An Chen, Anton Kapustin, Alex Turzillo +1
We extend the periodic table of phases of free fermions in the ten-fold way symmetry classes to a classification of free fermionic phases protected by an arbitrary on-site unitary…
Fermionic Matrix Product States and One-Dimensional Short-Range Entangled Phases with Anti-Unitary Symmetries
Alex Turzillo, Minyoung You
We extend the formalism of Matrix Product States (MPS) to describe one-dimensional gapped systems of fermions with both unitary and anti-unitary symmetries. Additionally, systems w…
Spin Topological Field Theory and Fermionic Matrix Product States
Anton Kapustin, Alex Turzillo, Minyoung You
We study state-sum constructions of G-equivariant spin-TQFTs and their relationship to Matrix Product States. We show that in the Neveu-Schwarz, Ramond, and twisted sectors, the st…
Topological Field Theory and Matrix Product States
Anton Kapustin, Alex Turzillo, Minyoung You
It is believed that most (perhaps all) gapped phases of matter can be described at long distances by Topological Quantum Field Theory (TQFT). On the other hand, it has been rigorou…
Equivariant Topological Quantum Field Theory and Symmetry Protected Topological Phases
Anton Kapustin, Alex Turzillo
Short-range entangled topological phases of matter are closely connected to Topological Quantum Field Theory. We use this connection to classify bosonic Symmetry Protected Topologi…
Fermionic Symmetry Protected Topological Phases and Cobordisms
Anton Kapustin, Ryan Thorngren, Alex Turzillo +1
It has been proposed recently that interacting Symmetry Protected Topological (SPT) phases can be classified using cobordism theory. We test this proposal in the case of fermionic…
Dynamics of a first order transition to an absorbing state
Baptiste Néel, Ignacio Rondini, Alex Turzillo +2
A granular system confined in a quasi two-dimensional box that is vertically vibrated can transit to an absorbing state in which all particles bounce vertically in phase with the b…