356 citations · 706 across the 18 of their papers we have counts for
12 papers · 1 filter
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…
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…
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…
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…
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…