Related papers: Local Noether theorem for quantum lattice systems and topological invariants of gapped states

Local Noether theorem for quantum lattice systems and topological invariants of gapped states

URL: http://arxiv.org/abs/2201.01327v3
Date: Mon, 29 Aug 2022 06:02:19 GMT
Title: Local Noether theorem for quantum lattice systems and topological invariants of gapped states
Authors: Anton Kapustin, Nikita Sopenko
Abstract summary: We study generalizations of the Berry phase for quantum lattice systems in arbitrary dimensions. A key role in these constructions is played by a certain differential graded Frechet-Lie algebra attached to any quantum lattice system.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We study generalizations of the Berry phase for quantum lattice systems in arbitrary dimensions. For a smooth family of gapped ground states in d dimensions, we define a closed (d+2)-form on the parameter space which generalizes the curvature of the Berry connection. Its cohomology class is a topological invariant of the family. When the family is equivariant under the action of a compact Lie group G, topological invariants take values in the equivariant cohomology of the parameter space. These invariants unify and generalize the Hall conductance and the Thouless pump. A key role in these constructions is played by a certain differential graded Frechet-Lie algebra attached to any quantum lattice system. As a by-product, we describe ambiguities in charge densities and conserved currents for arbitrary lattice systems with rapidly decaying interactions.

Related papers

Quantum channels, complex Stiefel manifolds, and optimization [45.9982965995401]
We establish a continuity relation between the topological space of quantum channels and the quotient of the complex Stiefel manifold. The established relation can be applied to various quantum optimization problems.
arXiv Detail & Related papers (2024-08-19T09:15:54Z)
Quantum Random Walks and Quantum Oscillator in an Infinite-Dimensional Phase Space [45.9982965995401]
We consider quantum random walks in an infinite-dimensional phase space constructed using Weyl representation of the coordinate and momentum operators. We find conditions for their strong continuity and establish properties of their generators.
arXiv Detail & Related papers (2024-06-15T17:39:32Z)
A Universal Kinematical Group for Quantum Mechanics [0.0]
In 1968, Dashen and Sharp obtained a certain singular Lie algebra of local densities and currents from canonical commutation relations in nonrelativistic quantum field theory. The corresponding Lie group is infinite dimensional: the natural semidirect product of an additive group of scalar functions with a group of diffeomorphisms.
arXiv Detail & Related papers (2024-04-28T18:46:24Z)
Bosonic Andreev bound state [0.0]
A general free bosonic system with a pairing term is described by a bosonic Bogoliubov-de Gennes (BdG) Hamiltonian. In fermionic BdG systems, a topological invariant of the whole particle (hole) bands can be nontrivial. In bosonic cases, the corresponding topological invariant is thought to be trivial owing to the stability of the bosonic ground state.
arXiv Detail & Related papers (2023-10-13T15:44:01Z)
Matter relative to quantum hypersurfaces [44.99833362998488]
We extend the Page-Wootters formalism to quantum field theory. By treating hypersurfaces as quantum reference frames, we extend quantum frame transformations to changes between classical and nonclassical hypersurfaces.
arXiv Detail & Related papers (2023-08-24T16:39:00Z)
Continuous percolation in a Hilbert space for a large system of qubits [58.720142291102135]
The percolation transition is defined through the appearance of the infinite cluster. We show that the exponentially increasing dimensionality of the Hilbert space makes its covering by finite-size hyperspheres inefficient. Our approach to the percolation transition in compact metric spaces may prove useful for its rigorous treatment in other contexts.
arXiv Detail & Related papers (2022-10-15T13:53:21Z)
Bridging the gap between topological non-Hermitian physics and open quantum systems [62.997667081978825]
We show how to detect a transition between different topological phases by measuring the response to local perturbations. Our formalism is exemplified in a 1D Hatano-Nelson model, highlighting the difference between the bosonic and fermionic cases.
arXiv Detail & Related papers (2021-09-22T18:00:17Z)
Novel quantum phases on graphs using abelian gauge theory [0.0]
We build a class of frustration-free and gapped Hamiltonians based on discrete abelian gauge groups. The resulting models have a ground state degeneracy that can be either a topological invariant or an extensive quantity. We analyze excitations and identify anyon-like excitations that account for the topological entanglement entropy.
arXiv Detail & Related papers (2021-04-14T13:46:10Z)
Particle on the sphere: group-theoretic quantization in the presence of a magnetic monopole [0.0]
We consider the problem of quantizing a particle on a 2-sphere. We construct the Hilbert space directly from the symmetry algebra. We show how the Casimir invariants of the algebra determine the bundle topology.
arXiv Detail & Related papers (2020-11-10T04:42:08Z)
Dynamical solitons and boson fractionalization in cold-atom topological insulators [110.83289076967895]
We study the $mathbbZ$ Bose-Hubbard model at incommensurate densities. We show how defects in the $mathbbZ$ field can appear in the ground state, connecting different sectors. Using a pumping argument, we show that it survives also for finite interactions.
arXiv Detail & Related papers (2020-03-24T17:31:34Z)
Localization anisotropy and complex geometry in two-dimensional insulators [0.0]
The localization tensor is a measure of distinguishability between insulators and metals. It is related to the quantum metric tensor associated with the occupied bands in momentum space.
arXiv Detail & Related papers (2020-02-04T14:29:57Z)

This list is automatically generated from the titles and abstracts of the papers in this site.