## 8 Citations

### Classification of equivariant approximately locality-preserving unitaries on spin chains

- Mathematics
- 2021

We extend the classification of approximately locality-preserving unitaries (ALPUs) on spin chains recently obtained by [1] to take a local symmetry action of a finite symmetry group G into account.…

### Automorphic equivalence within gapped phases in the bulk

- PhysicsJournal of Functional Analysis
- 2020

### Stability of the spectral gap and ground state indistinguishability for a decorated AKLT model

- Mathematics, Physics
- 2022

. We use cluster expansions to establish local indistiguishability of the ﬁnite-volume ground states for the AKLT model on decorated hexagonal lattices with decoration parameter at least 5. Our…

### A classification of invertible phases of bosonic quantum lattice systems in one dimension

- MathematicsJournal of Mathematical Physics
- 2021

We study invertible states of 1d bosonic quantum lattice systems. We show that every invertible 1d state is in a trivial phase: after tensoring with some unentangled ancillas it can be disentangled…

### On ℤ2-indices for ground states of fermionic chains

- MathematicsReviews in Mathematical Physics
- 2020

For parity-conserving fermionic chains, we review how to associate [Formula: see text]-indices to ground states in finite systems with quadratic and higher-order interactions as well as to quasifree…

### M ay 2 01 9 On Z 2-indices for ground states of fermionic chains

- Mathematics
- 2019

For parity-conserving fermionic chains, we review how to associate Z2-indices to ground states in finite systems with quadratic and higher-order interactions as well as to quasifree ground states on…

### Quasi-Locality Bounds for Quantum Lattice Systems. Part II. Perturbations of Frustration-Free Spin Models with Gapped Ground States

- MathematicsAnnales Henri Poincaré
- 2021

We study the stability with respect to a broad class of perturbations of gapped ground-state phases of quantum spin systems defined by frustration-free Hamiltonians. The core result of this work is a…

### The Split and Approximate Split Property in 2D Systems: Stability and Absence of Superselection Sectors

- MathematicsCommunications in Mathematical Physics
- 2022

The split property of a pure state for a certain cut of a quantum spin system can be understood as the entanglement between the two subsystems being weak. From this point of view, we may say that if…

## References

SHOWING 1-10 OF 19 REFERENCES

### The Split Property and the Symmetry Breaking¶of the Quantum Spin Chain

- Physics
- 2001

Abstract: We consider the relationship between the symmetry breaking and the split property of pure states of quantum spin chains. We obtain a representation theoretic condition implying that the…

### Spectral gap, and split property in quantum spin chains

- Mathematics
- 2010

In this article, we consider a class of ground states with spectral gap for quantum spin chains on an integer lattice and we prove that the factorization lemma of Hastings [“Topology and phases in…

### Topological Phase Transition and Z_{2} Index for S=1 Quantum Spin Chains.

- MathematicsPhysical review letters
- 2018

By using the index, this work provides the first rigorous proof of the existence of a "topological" phase transition, which cannot be characterized by any conventional order parameters, between the Affleck-Kennedy-Lieb-Tasaki (AKLT) model and trivial models.

### BOUNDEDNESS OF ENTANGLEMENT ENTROPY AND SPLIT PROPERTY OF QUANTUM SPIN CHAINS

- Physics
- 2011

We show that boundedness of entanglement entropy for pure states of bipartite quantum spin systems implies split property of subsystems. As a corollary, in one-dimensional quantum spin chains, we…

### Entanglement spectrum of a topological phase in one dimension

- Physics
- 2010

We show that the Haldane phase of S=1 chains is characterized by a double degeneracy of the entanglement spectrum. The degeneracy is protected by a set of symmetries (either the dihedral group of…

### On Gapped Phases with a Continuous Symmetry and Boundary Operators

- Mathematics
- 2014

We discuss the role of compact symmetry groups, G, in the classification of gapped ground state phases of quantum spin systems. We consider two representations of G on infinite subsystems. First, in…

### A $${{\mathbb {Z}}}_2$$-Index of Symmetry Protected Topological Phases with Time Reversal Symmetry for Quantum Spin Chains

- Physics, MathematicsCommunications in Mathematical Physics
- 2019

We introduce a ${\mathbb Z}_2$-index for time reversal invariant Hamiltonians with unique gapped ground state on quantum spin chains. We show this is an invariant of a $C^1$-classification of gapped…

### Stability of gapped ground state phases of spins and fermions in one dimension

- PhysicsJournal of Mathematical Physics
- 2018

We investigate the persistence of spectral gaps of one-dimensional frustration free quantum lattice systems under weak perturbations and with open boundary conditions. Assuming the interactions of…

### Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems

- Mathematics
- 2009

We prove Lieb-Robinson bounds for systems defined on infinite dimensional Hilbert spaces and described by unbounded Hamiltonians. In particular, we consider harmonic and certain anharmonic lattice…

### Lieb–Schultz–Mattis Type Theorems for Quantum Spin Chains Without Continuous Symmetry

- MathematicsCommunications in Mathematical Physics
- 2019

We prove that a quantum spin chain with half-odd-integral spin cannot have a unique ground state with a gap, provided that the interaction is short ranged, translation invariant, and possesses…