• Corpus ID: 239050054

On adiabatic cycles of quantum spin systems

@inproceedings{Shiozaki2021OnAC,
  title={On adiabatic cycles of quantum spin systems},
  author={Ken Shiozaki},
  year={2021}
}
  • K. Shiozaki
  • Published 20 October 2021
  • Physics, Mathematics
Motivated by the Ω-spectrum proposal of unique gapped ground states by Kitaev [1], we study adiabatic cycles in gapped quantum spin systems from various perspectives. We give a few exactly solvable models in one and two spatial dimensions and discuss how nontrivial adiabatic cycles are detected. For one spatial dimension, we study the adiabatic cycle in detail with the matrix product state and show that the symmetry charge can act on the space of matrices without changing the physical states… 

Figures from this paper

Adiabatic paths of Hamiltonians, symmetries of topological order, and automorphism codes
The recent “honeycomb code” is a fault-tolerant quantum memory defined by a sequence of checks which implements a nontrivial automorphism of the toric code. We argue that a general framework to
Flow of (higher) Berry curvature and bulk-boundary correspondence in parametrized quantum systems
This paper is concerned with the physics of parametrized gapped quantum many-body systems, which can be viewed as a generalization of conventional topological phases of matter. In such systems,
Higher Berry Phase of Fermions and Index Theorem
When a quantum field theory is trivially gapped, its infrared fixed point is an invertible field theory. The partition function of the invertible field theory records the response to various background

References

SHOWING 1-10 OF 42 REFERENCES
Symmetry protection of topological phases in one-dimensional quantum spin systems
We discuss the characterization and stability of the Haldane phase in integer spin chains on the basis of simple, physical arguments. We find that an odd-S Haldane phase is a topologically nontrivial
Classification of gapped symmetric phases in one-dimensional spin systems
Quantum many-body systems divide into a variety of phases with very different physical properties. The questions of what kinds of phases exist and how to identify them seem hard, especially for
Classifying quantum phases using matrix product states and projected entangled pair states
We give a classification of gapped quantum phases of one-dimensional systems in the framework of matrix product states (MPS) and their associated parent Hamiltonians, for systems with unique as well
Classification of Interacting Topological Floquet Phases in One Dimension
Periodic driving of a quantum system can enable new topological phases with no analog in static systems. In this paper we systematically classify one-dimensional topological and symmetry-protected
Topological phases of fermions in one dimension
In this paper we show how the classification of topological phases in insulators and superconductors is changed by interactions, in the case of one-dimensional systems. We focus on the
Floquet topological phases with symmetry in all dimensions
Periodically driven Floquet systems can host dynamical phases, including a range of exotic topological phases that have no static analogs. This work presents a homotopy approach to the study of
Instanton effects in lattice models of bosonic symmetry-protected topological states
Bosonic symmetry-protected topological (SPT) states are gapped disordered phases of matter possessing symmetry-preserving boundary excitations. It has been proposed that, at long wavelengths, the
Braiding statistics approach to symmetry-protected topological phases
We construct a 2D quantum spin model that realizes an Ising paramagnet with gapless edge modes protected by Ising symmetry. This model provides an example of a "symmetry-protected topological phase."
Periodic table for topological insulators and superconductors
Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a
Symmetric Finite-Time Preparation of Cluster States via Quantum Pumps
It has recently been established that cluster-like states – states that are in the same symmetry-protected topological phase as the cluster state – provide a family of resource states that can be
...
1
2
3
4
5
...