Quasiadiabatic continuation of quantum states: The stability of topological ground-state degeneracy and emergent gauge invariance

By M. B. Hastings, X. Wen. 2005

416 citations recorded by the source corpus.

We define for quantum many-body systems a quasiadiabatic continuation of quantum states. The continuation is valid when the Hamiltonian has a gap, or else has a sufficiently small low-energy density of states, and thus is away from a quantum phase transition. This continuation takes local operators into local operators, while approximately preserving the ground-state expectation values. We apply this continuation to the problem of gauge theories coupled to matter, and propose the distinction of perimeter law versus 'zero law' to identify confinement. We also apply the continuation to local bosonic models with emergent gauge theories. We show that local gauge invariance is topological and cannot be broken by any local perturbations in the bosonic models in either continuous or discrete gauge groups. We show that the ground-state degeneracy in emergent discrete gauge theories is a robust property of the bosonic model, and we argue that the robustness of local gauge invariance in the continuous case protects the gapless gauge boson.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/f95f47f3d5d56f8a012e36346d0bb55d963f94f0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Sergey Bravyi
2. Spyridon Michalakis
3. Hsin-Yuan Huang
4. Justyna P. Zwolak
5. John Preskill
6. Richard Kueng
7. M. B. Hastings
8. Daniel Loss

In Condensed Matter Physics

1. Sergey Bravyi
2. Spyridon Michalakis
3. Justyna P. Zwolak
4. Daniel Loss
5. David P. DiVincenzo
6. Richard Kueng
7. John Preskill
8. Hsin-Yuan Huang

Citations in the corpus

• Stability of Frustration-Free Hamiltonians (2011, methodology): “Nevertheless, here, we draw heavily from the methods developed in [5, 4], following the more succinct format of [4], which uses Hastings’ powerful quasi-adiabatic continuation [13].”
• Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems (2011, neutral): “In his 2004 paper [19] Hastings introduced a new technique, which he called ‘quasi-adiabatic continuation’ (see also [24]).”
• Schrieffer-Wolff transformation for quantum many-body systems (2011, methodology): “ states. It was recently shown explicitly that the Gell-Mann and Low theorem used in the derivation of Feynman-Dyson series fails for degenerate ground states [28]. Exact quasi-adiabatic continuation [29, 30] provides an alternative path to defining Heff via a unitary transformation starting from a fu”
• Generalized Symmetries in Condensed Matter (2022, neutral): “Perhaps surprisingly, the answer is ‘no’ (early discussions of the robustness of broken higher-form symmetries using different words include (34, 2, 35)).”
• Topological quantum order: Stability under local perturbations (2010, methodology): “For example, following [3], we can define string operators which have nontrivial action in the ground state subspace of the perturbed Hamiltonian and which have the correct commutation relations and expectation values.”