Corpus ID: 231924756

Stability of the bulk gap for frustration-free topologically ordered quantum lattice systems

@inproceedings{Nachtergaele2021StabilityOT,
title={Stability of the bulk gap for frustration-free topologically ordered quantum lattice systems},
author={B. Nachtergaele and Robert Sims and Amanda Young},
year={2021}
}
• Published 2021
• Physics, Mathematics
We prove that uniformly small short-range perturbations do not close the bulk gap above the ground state of frustration-free quantum spin systems that satisfy a standard local topological quantum order condition. In contrast with earlier results, we do not require a positive lower bound for finite-system Hamiltonians uniform in the system size. To obtain this result, we adapt the Bravyi-Hastings-Michalakis strategy to the GNS representation of the infinite-system ground state.
3 Citations
Block-diagonalization of infinite-volume lattice Hamiltonians with unbounded interactions
• Physics, Mathematics
• 2021
In this paper we extend the local iterative Lie-Schwinger block-diagonalization method – introduced in [DFPR3] for quantum lattice systems with bounded interactions in arbitrary dimension– to systemsExpand
Local stability of ground states in locally gapped and weakly interacting quantum spin systems
• Physics, Mathematics
• 2021
Based on a result by Yarotsky (J. Stat. Phys. 118, 2005), we prove that localized but otherwise arbitrary perturbations of weakly interacting quantum spin systems with uniformly gapped on-site termsExpand
Quasi-Locality Bounds for Quantum Lattice Systems. Part II. Perturbations of Frustration-Free Spin Models with Gapped Ground States
• Physics, Mathematics
• 2020
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 aExpand

References

SHOWING 1-10 OF 35 REFERENCES
Stability of Frustration-Free Hamiltonians
• Mathematics, Physics
• 2013
We prove stability of the spectral gap for gapped, frustration-free Hamiltonians under general, quasi-local perturbations. We present a necessary and sufficient condition for stability, which we callExpand
The Stability of Free Fermi Hamiltonians
Recent results have shown the stability of frustration-free Hamiltonians to weak local perturbations, assuming several conditions. In this paper, we prove the stability of free fermion HamiltoniansExpand
Automorphic equivalence within gapped phases in the bulk
• Physics, Mathematics
• 2019
We develop a new adiabatic theorem for unique gapped ground states which does not require the gap for local Hamiltonians. We instead require a gap in the bulk and a smoothness of expectation valuesExpand
Spectral gaps of frustration-free spin systems with boundary
• Physics, Mathematics
• 2018
In quantum many-body systems, the existence of a spectral gap above the ground state has far-reaching consequences. In this paper, we discuss "finite-size" criteria for having a spectral gap inExpand
Divide and conquer method for proving gaps of frustration free Hamiltonians
• Physics, Mathematics
• 2017
It is proved that for gapless models in any dimension, the spectral gap on regions of diameter $n$ is at most $o\left(\frac{\log(n)^{2+\epsilon}}{n}\right)$ for any positive $\ep silon$. Expand
Lie–Schwinger Block-Diagonalization and Gapped Quantum Chains
• Physics, Mathematics
• 2018
We study quantum chains whose Hamiltonians are perturbations by bounded interactions of short range of a Hamiltonian that does not couple the degrees of freedom located at different sites of theExpand
Topological quantum order: Stability under local perturbations
• Physics, Mathematics
• 2010
We study zero-temperature stability of topological phases of matter under weak time-independent perturbations. Our results apply to quantum spin Hamiltonians that can be written as a sum ofExpand
Local gap threshold for frustration-free spin systems
• Mathematics, Physics
• 2015
We improve Knabe's spectral gap bound for frustration-free translation-invariant local Hamiltonians in 1D. The bound is based on a relationship between global and local gaps. The global gap is theExpand
Improved local spectral gap thresholds for lattices of finite size
Knabe's theorem lower bounds the spectral gap of a one dimensional frustration-free local hamiltonian in terms of the local spectral gaps of finite regions. It also provides a local spectral gapExpand
Adiabatic theorem in the thermodynamic limit. Part II: Systems with a gap in the bulk
• Physics, Mathematics
• 2020
We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground stateExpand