Efficient algorithm to compute the Berry conductivity

Dauphin, Alexandre; Müller, Markus; Martín-Delgado, M. A.

doi:10.1088/1367-2630/16/7/073016

Cited by 4 publications

(3 citation statements)

References 85 publications

(180 reference statements)

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“…In general, the critical mesh size M c is controlled by the proximity of the cyclic path φ ∈ [0, 2π] to gap closing points (see, e.g., Ref. [35]): the latter can be seen as sources of Berry-type curvature, in the sense that the field strength F (φ) is concentrated at such points in the limit of an infinitesimal mesh M → ∞. Here, the relevant gap is the purity gap.…”

Section: E Measurement Of ∆ϕ E and "Purity Adiabaticity" Requirementmentioning

confidence: 99%

Probing the Topology of Density Matrices

et al. 2018

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The mixedness of a quantum state is usually seen as an adversary to topological quantization of observables. For example, exact quantization of the charge transported in a so-called Thouless adiabatic pump is lifted at any finite temperature in symmetry-protected topological insulators. Here, we show that certain directly observable many-body correlators preserve the integrity of topological invariants for mixed Gaussian quantum states in one dimension. Our approach relies on the expectation value of the many-body momentum-translation operator and leads to a physical observable-the "ensemble geometric phase" (EGP)-which represents a bona fide geometric phase for mixed quantum states, in the thermodynamic limit. In cyclic protocols, the EGP provides a topologically quantized observable that detects encircled spectral singularities ("purity-gap" closing points) of density matrices. While we identify the many-body nature of the EGP as a key ingredient, we propose a conceptually simple, interferometric setup to directly measure the latter in experiments with mesoscopic ensembles of ultracold atoms.

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Section: E Measurement Of ∆ϕ E and "Purity Adiabaticity" Requirementmentioning

confidence: 99%

Probing the Topology of Density Matrices

et al. 2018

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“…Therefore, these new results open the way towards the characterization of fermion quantum phases of matter with topological phases protected by symmetry in thermal states, or more general density matrices. Note that other studies on thermal effects and related issues in topological systems have been recently carried out [43][44][45][46][47][48][49][50][51][52].…”

Section: Introductionmentioning

confidence: 99%

Symmetry-protected topological phases at finite temperature

2015

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We have applied the recently developed theory of topological Uhlmann numbers to a representative model of a topological insulator in two dimensions, the Qi-Wu-Zhang model. We have found a stable symmetry-protected topological (SPT) phase under external thermal fluctuations in two-dimensions. A complete phase diagram for this model is computed as a function of temperature and coupling constants in the original Hamiltonian. It shows the appearance of large stable phases of matter with topological properties compatible with thermal fluctuations or external noise and the existence of critical lines separating abruptly trivial phases from topological phases. These novel critical temperatures represent thermal topological phase transitions. The initial part of the paper comprises a self-contained explanation of the Uhlmann geometric phase needed to understand the topological properties that it may acquire when applied to topological insulators and superconductors.Contents arXiv:1502.01355v2 [cond-mat.str-el] 30 Jun 2015

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“…A direct generalization of the algorithm would be the study of the transverse conductivity with partially filled bands [79]. When the Fermi energy lies in an energy band, it is still possible to distinguish the contribution from the geometrical phase to the conductivity, often called Berry conductivity.…”

Section: Discussionmentioning

confidence: 99%

Efficient algorithm to compute the second Chern number in four dimensional systems

Mochol-Grzelak

Dauphin

Celi

et al. 2018

Quantum Sci. Technol.

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Topological insulators are exotic material that possess conducting surface states protected by the topology of the system. They can be classified in terms of their properties under discrete symmetries and are characterized by topological invariants. The latter has been measured experimentally for several models in one, two and three dimensions in both condensed matter and quantum simulation platforms. The recent progress in quantum simulation opens the road to the simulation of higher dimensional Hamiltonians and in particular of the 4D quantum Hall effect. These systems are characterized by the second Chern number, a topological invariant that appears in the quantization of the transverse conductivity for the non-linear response to both external magnetic and electric fields. This quantity cannot always be computed analytically and there is therefore a need of an algorithm to compute it numerically. In this work, we propose an efficient algorithm to compute the second Chern number in 4D systems. We construct the algorithm with the help of lattice gauge theory and discuss the convergence to the continuous gauge theory. We benchmark the algorithm on several relevant models, including the 4D Dirac Hamiltonian and the 4D quantum Hall effect and verify numerically its rapid convergence. * alexandre.dauphin@icfo.eu arXiv:1803.07003v2 [cond-mat.quant-gas]

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Efficient algorithm to compute the Berry conductivity

Cited by 4 publications

References 85 publications

Probing the Topology of Density Matrices

Probing the Topology of Density Matrices

Symmetry-protected topological phases at finite temperature

Efficient algorithm to compute the second Chern number in four dimensional systems

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