Localization anisotropy and complex geometry in two-dimensional insulators

• URL: http://arxiv.org/abs/2002.01312v2
• Date: Tue, 17 Mar 2020 17:00:44 GMT
• Title: Localization anisotropy and complex geometry in two-dimensional insulators
• Authors: Bruno Mera
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The localization tensor is a measure of distinguishability between insulators and metals. This tensor is related to the quantum metric tensor associated with the occupied bands in momentum space. In two dimensions and in the thermodynamic limit, it defines a flat Riemannian metric over the twist-angle space, topologically a torus, which endows this space with a complex structure, described by a complex parameter $\tau$. It is shown that the latter is a physical observable related to the anisotropy of the system. The quantity $\tau$ and the Riemannian volume of the twist-angle space provide an invariant way to parametrize the flat quantum metric obtained in the thermodynamic limit. Moreover, if by changing the couplings of the theory, the system undergoes quantum phase transitions in which the gap closes, the complex structure $\tau$ is still well defined, although the metric diverges (metallic state), and it is fixed by the form of the Hamiltonian near the gap closing points. The Riemannian volume is responsible for the divergence of the metric at the phase transition.

Related papers

• Hilbert space geometry and quantum chaos [39.58317527488534]
  We consider the symmetric part of the QGT for various multi-parametric random matrix Hamiltonians. We find for a two-dimensional parameter space that, while the ergodic phase corresponds to the smooth manifold, the integrable limit marks itself as a singular geometry with a conical defect.
  arXiv  Detail & Related papers  (2024-11-18T19:00:17Z)
• On reconstruction of states from evolution induced by quantum dynamical semigroups perturbed by covariant measures [50.24983453990065]
  We show the ability to restore states of quantum systems from evolution induced by quantum dynamical semigroups perturbed by covariant measures. Our procedure describes reconstruction of quantum states transmitted via quantum channels and as a particular example can be applied to reconstruction of photonic states transmitted via optical fibers.
  arXiv  Detail & Related papers  (2023-12-02T09:56:00Z)
• Fluctuations, uncertainty relations, and the geometry of quantum state manifolds [0.0]
  The complete quantum metric of a parametrized quantum system has a real part and a symplectic imaginary part. We show that for a mixed quantum-classical system both real and imaginary parts of the quantum metric contribute to the dynamics.
  arXiv  Detail & Related papers  (2023-09-07T10:31:59Z)
• Complex dynamics approach to dynamical quantum phase transitions: the Potts model [0.0]
  This paper introduces complex dynamics methods to study dynamical quantum phase transitions in the one- and two-dimensional quantum 3-state Potts model. We show that special boundary conditions can alter the nature of the transitions, and verify the claim for the one-dimensional system by transfer matrix calculations. Our approach can be extended to multi-variable problems, higher dimensions, and approximate RG transformations expressed as rational functions.
  arXiv  Detail & Related papers  (2023-08-28T18:26:41Z)
• Quantifying measurement-induced quantum-to-classical crossover using an open-system entanglement measure [49.1574468325115]
  We study the entanglement of a single particle under continuous measurements. We find that the entanglement at intermediate time scales shows the same qualitative behavior as a function of the measurement strength.
  arXiv  Detail & Related papers  (2023-04-06T09:45:11Z)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• Local Noether theorem for quantum lattice systems and topological invariants of gapped states [0.0]
  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.
  arXiv  Detail & Related papers  (2022-01-04T19:44:36Z)
• Quantum Entanglement of Non-Hermitian Quasicrystals [7.371841894852217]
  We present a class of experimentally realizable models for non-Hermitian quasicrystal chains. We numerically determine the metal-insulator transition point. Inspired by entanglement spectrum, we further analytically prove that a duality exists between the two phase regions.
  arXiv  Detail & Related papers  (2021-12-26T16:17:04Z)
• Rectification induced by geometry in two-dimensional quantum spin lattices [58.720142291102135]
  We address the role of geometrical asymmetry in the occurrence of spin rectification in two-dimensional quantum spin chains. We show that geometrical asymmetry, along with inhomogeneous magnetic fields, can induce spin current rectification even in the XX model.
  arXiv  Detail & Related papers  (2020-12-02T18:10:02Z)
• Bulk detection of time-dependent topological transitions in quenched chiral models [48.7576911714538]
  We show that the winding number of the Hamiltonian eigenstates can be read-out by measuring the mean chiral displacement of a single-particle wavefunction. This implies that the mean chiral displacement can detect the winding number even when the underlying Hamiltonian is quenched between different topological phases.
  arXiv  Detail & Related papers  (2020-01-16T17:44:52Z)
• Probing chiral edge dynamics and bulk topology of a synthetic Hall system [52.77024349608834]
  Quantum Hall systems are characterized by the quantization of the Hall conductance -- a bulk property rooted in the topological structure of the underlying quantum states. Here, we realize a quantum Hall system using ultracold dysprosium atoms, in a two-dimensional geometry formed by one spatial dimension. We demonstrate that the large number of magnetic sublevels leads to distinct bulk and edge behaviors.
  arXiv  Detail & Related papers  (2020-01-06T16:59:08Z)

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

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.