A Theorem on Extensive Spectral Degeneracy for Systems with Higher Symmetries in General Dimensions

• URL: http://arxiv.org/abs/2208.11690v1
• Date: Wed, 24 Aug 2022 17:50:52 GMT
• Title: A Theorem on Extensive Spectral Degeneracy for Systems with Higher Symmetries in General Dimensions
• Authors: Zohar Nussinov, Gerardo Ortiz
• Abstract summary: We establish lower bounds on the spectral degeneracy of quantum systems with higher Gauge Like symmetries. We exploit the effects of modified boundary conditions. We briefly discuss why, in spite of the proven large degeneracy associated with infrared-ultraviolet mixing, some systems may still exhibit conventional physical behaviors.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We establish, in the spirit of the Lieb-Schultz-Mattis theorem, lower bounds on the spectral degeneracy of quantum systems with higher (Gauge Like) symmetries with rather generic physical boundary conditions in an arbitrary number of spatial dimensions. Contrary to applying twists or equivalent adiabatic operations, we exploit the effects of modified boundary conditions. When a general choice of boundary geometry is immaterial in approaching the thermodynamic limit, systems that exhibit non-commuting Gauge Like symmetries, such as the orbital compass model, must have an exponential (in the size of the boundary) degeneracy of each of their spectral levels. We briefly discuss why, in spite of the proven large degeneracy associated with infrared-ultraviolet mixing, some systems may still exhibit conventional physical behaviors, i.e., of those of systems with non-extensive degeneracies, due to entropic "order by disorder" type effects.

Related papers

• Gapless Floquet topology [40.2428948628001]
  We study the existence of topological edge zero- and pi-modes despite the lack of bulk gaps in the quasienergy spectrum. We numerically study the effect of interactions, which give a finite lifetime to the edge modes in the thermodynamic limit with the decay rate consistent with Fermi's Golden Rule.
  arXiv  Detail & Related papers  (2024-11-04T19:05:28Z)
• Topological Order in the Spectral Riemann Surfaces of Non-Hermitian Systems [44.99833362998488]
  We show topologically ordered states in the complex-valued spectra of non-Hermitian systems. These arise when the distinctive exceptional points in the energy surfaces of such models are annihilated. We illustrate the characteristics of the topologically protected states in a non-Hermitian two-band model.
  arXiv  Detail & Related papers  (2024-10-24T10:16:47Z)
• Non-chiral non-Bloch invariants and topological phase diagram in non-unitary quantum dynamics without chiral symmetry [26.179241616332387]
  We identify the non-Bloch topological phase diagram of a one-dimensional (1D) non-Hermitian system without chiral symmetry. We find that such topological invariants can distinguish topologically distinct gapped phases. Our work provides a useful platform to study the interplay among topology, symmetries and the non-Hermiticity.
  arXiv  Detail & Related papers  (2024-07-26T03:29:30Z)
• Non-Hermitian skin effect in arbitrary dimensions: non-Bloch band theory and classification [0.0]
  Non-Hermitian skin effect (NHSE) is a distinctive phenomenon in non-Hermitian systems. NHSE is characterized by a significant accumulation of eigenstates at system boundaries. We present a geometry-adaptive non-Bloch band theory in arbitrary dimensions.
  arXiv  Detail & Related papers  (2024-07-01T13:49:53Z)
• Non-Bloch band theory for non-Hermitian continuum systems [1.2845309023495566]
  We generalize the non-Bloch band theory to non-Hermitian continuum systems. We show that the appropriate discretization of continuum systems into lattice models requires matching the hopping range of the latter to the number of boundary conditions. Our theory serves as a useful toolbox for investigating the rich non-Bloch physics in non-Hermitian continuum systems.
  arXiv  Detail & Related papers  (2023-10-12T17:57:24Z)
• Geometry-dependent skin effect and anisotropic Bloch oscillations in a non-Hermitian optical lattice [5.593595192885069]
  geometry-dependent skin effect (GDSE) refers to that the localization of extensive eigenstates depends on the system's geometry under open boundary conditions. In this paper, we demonstrate the emergence of GDSE in a two-dimensional $sp$ optical ladder lattice with on-site atom loss. Our results reveal that the GDSE has an intrinsic anisotropic bulk dynamics independent of boundary conditions, and offer its realization and detection in quantum systems.
  arXiv  Detail & Related papers  (2023-04-07T18:00:07Z)
• Edge states, Majorana fermions and topological order in superconducting wires with generalized boundary conditions [0.0]
  We study the properties of one-dimensional topological superconductors under the influence of generic boundary conditions. In particular, we investigate the resilience of the long-distance, edge-to-edge quantum mutual information and squashed entanglement.
  arXiv  Detail & Related papers  (2022-07-04T14:05:03Z)
• Point-gap topology with complete bulk-boundary correspondence in dissipative quantum systems [0.0]
  The spectral and dynamical properties of dissipative quantum systems are investigated from a topological point of view. We find anomalous skin modes with exponential amplification even though the quantum system is purely dissipative.
  arXiv  Detail & Related papers  (2020-10-28T10:15:40Z)
• 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)
• Quantum Geometric Confinement and Dynamical Transmission in Grushin Cylinder [68.8204255655161]
  We classify the self-adjoint realisations of the Laplace-Beltrami operator minimally defined on an infinite cylinder. We retrieve those distinguished extensions previously identified in the recent literature, namely the most confining and the most transmitting.
  arXiv  Detail & Related papers  (2020-03-16T11:37:23Z)
• 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.