16 research outputs found
Optimal Renormalization Group Transformation from Information Theory
Recently a novel real-space RG algorithm was introduced, identifying the
relevant degrees of freedom of a system by maximizing an information-theoretic
quantity, the real-space mutual information (RSMI), with machine learning
methods. Motivated by this, we investigate the information theoretic properties
of coarse-graining procedures, for both translationally invariant and
disordered systems. We prove that a perfect RSMI coarse-graining does not
increase the range of interactions in the renormalized Hamiltonian, and, for
disordered systems, suppresses generation of correlations in the renormalized
disorder distribution, being in this sense optimal. We empirically verify decay
of those measures of complexity, as a function of information retained by the
RG, on the examples of arbitrary coarse-grainings of the clean and random Ising
chain. The results establish a direct and quantifiable connection between
properties of RG viewed as a compression scheme, and those of physical objects
i.e. Hamiltonians and disorder distributions. We also study the effect of
constraints on the number and type of coarse-grained degrees of freedom on a
generic RG procedure.Comment: Updated manuscript with new results on disordered system
Universal higher-order bulk-boundary correspondence of triple nodal points
Triple nodal points are degeneracies of energy bands in momentum space at which three Hamiltonian eigenstates coalesce at a single eigenenergy. For spinless particles, the stability of a triple nodal point requires two ingredients: rotational symmetry of order three, four, or six; combined with mirror or space-time-inversion symmetry. However, despite ample studies of their classification, robust boundary signatures of triple nodal points have until now remained elusive. In this work, we first show that pairs of triple nodal points in semimetals and metals can be characterized by Stiefel-Whitney and Euler monopole invariants, of which the first one is known to facilitate higher-order topology. Motivated by this observation, we then combine symmetry indicators for corner charges and for the Stiefel-Whitney invariant in two dimensions with the classification of triple nodal points for spinless systems in three dimensions. The result is a complete higher-order bulk-boundary correspondence, where pairs of triple nodal points are characterized by fractional jumps of the hinge charge. We present minimal models of the various species of triple nodal points carrying higher-order topology, and illustrate the derived correspondence on Sc3AlC which becomes a higher-order triple-point metal in applied strain. The generalization to spinful systems, in particular to the WC-type triple-point material class, is briefly outlined
Triple nodal points characterized by their nodal-line structure in all magnetic space groups
We analyze triply degenerate nodal points [or triple points (TPs) for short] in energy bands of crystalline solids. Specifically, we focus on spinless band structures, i.e., when spin-orbit coupling is negligible, and consider TPs formed along high-symmetry lines in the momentum space by a crossing of three bands transforming according to a one-dimensional (1D) and a two-dimensional (2D) irreducible corepresentation (ICR) of the little cogroup. The result is a complete classification of such TPs in all magnetic space groups, including the nonsymmorphic ones, according to several characteristics of the nodal-line structure at and near the TP. We show that the classification of the presently studied TPs is exhausted by 13 magnetic point groups (MPGs) that can arise as the little cogroup of a high-symmetry line and which support both 1D and 2D spinless ICRs. For 10 of the identified MPGs, the TP characteristics are uniquely determined without further information; in contrast, for the 3 MPGs containing sixfold rotational symmetry, two types of TPs are possible, depending on the choice of the crossing ICRs. The classification result for each of the 13 MPGs is illustrated with first-principles calculations of a concrete material candidate
Multi-band nodal links in triple-point materials
We study a class of topological materials which in their momentum-space band
structure exhibit three-fold degeneracies known as triple points. Specifically,
we investigate and classify triple points occurring along high-symmetry lines
of -symmetric crystalline solids with negligible
spin-orbit coupling. By employing the recently discovered non-Abelian band
topology, we argue that a rotation-symmetry-breaking strain transforms a
certain class of triple points into multi-band nodal links. Although multi-band
nodal-line compositions were previously theoretically conceived, a practical
condensed-matter platform for their manipulation and inspection has hitherto
been missing. By reviewing the known triple-point materials in the considered
symmetry class, and by performing first-principles calculations to predict new
ones, we identify suitable candidates for the realization of multi-band nodal
links. In particular, we find that LiNaN is an ideal compound to study this
phenomenon, where the band nodes facilitate largely tunable density of states
and optical conductivity with doping and strain, respectively. The multi-band
linking is expected to equip the nodal rings with monopole charges, making such
triple-point materials a versatile platform to probe the non-Abelian band
topology.Comment: 4 pages (3 figures, 1 table) + 13 pages of Supplemental Material (13
figures, 3 tables) + reference
Symmetry and topology of hyperbolic Haldane models
Particles hopping on a two-dimensional hyperbolic lattice feature
unconventional energy spectra and wave functions that provide a largely
uncharted platform for topological phases of matter beyond the Euclidean
paradigm. Using real-space topological markers as well as Chern numbers defined
in the higher-dimensional momentum space of hyperbolic band theory, we
construct and investigate hyperbolic Haldane models, which are generalizations
of Haldane's honeycomb-lattice model to various hyperbolic lattices. We present
a general framework to characterize point-group symmetries in hyperbolic
tight-binding models, and use this framework to constrain the multiple first
and second Chern numbers in momentum space. We observe several topological gaps
characterized by first Chern numbers of value and . The momentum-space
Chern numbers respect the predicted symmetry constraints and agree with
real-space topological markers, indicating a direct connection to observables
such as the number of chiral edge modes. With our large repertoire of models,
we further demonstrate that the topology of hyperbolic Haldane models is
trivialized for lattices with strong negative curvature.Comment: main text (14 pages with 7 figures and 2 tables) + appendices (28
pages with 10 figures and 2 tables) + bibliography (2 pages
Simulating hyperbolic space on a circuit board
The Laplace operator encodes the behavior of physical systems at vastly different scales, describing heat flow, fluids, as well as electric, gravitational, and quantum fields. A key input for the Laplace equation is the curvature of space. Here we discuss and experimentally demonstrate that the spectral ordering of Laplacian eigenstates for hyperbolic (negatively curved) and flat two-dimensional spaces has a universally different structure. We use a lattice regularization of hyperbolic space in an electric-circuit network to measure the eigenstates of a ‘hyperbolic drum’, and in a time-resolved experiment we verify signal propagation along the curved geodesics. Our experiments showcase both a versatile platform to emulate hyperbolic lattices in tabletop experiments, and a set of methods to verify the effective hyperbolic metric in this and other platforms. The presented techniques can be utilized to explore novel aspects of both classical and quantum dynamics in negatively curved spaces, and to realise the emerging models of topological hyperbolic matter
Caloric vestibular stimulation modulates nociceptive evoked potentials
Vestibular stimulation has been reported to alleviate central pain. Clinical and physiological studies confirm pervasive interactions between vestibular signals and somatosensory circuits, including nociception. However, the neural mechanisms underlying vestibular-induced analgesia remain unclear, and previous clinical studies cannot rule out explanations based on alternative, non-specific effects such as distraction or placebo. To investigate how vestibular inputs influence nociception, we combined caloric vestibular stimulation (CVS) with psychophysical and electrocortical responses elicited by nociceptive-specific laser stimulation in humans (laser-evoked potentials, LEPs). Cold water CVS applied to the left ear resulted in significantly lower subjective pain intensity for experimental laser pain to the left hand immediately after CVS, relative both to before CVS and to 1 h after CVS. This transient reduction in pain perception was associated with reduced amplitude of all LEP components, including the early N1 wave reflecting the first arrival of nociceptive input to primary somatosensory cortex. We conclude that cold left ear CVS elicits a modulation of both nociceptive processing and pain perception. The analgesic effect induced by CVS could be mediated either by subcortical gating of the ascending nociceptive input, or by direct modulation of the primary somatosensory cortex
Non-Abelian Hyperbolic Band Theory from Supercells
Wave functions on periodic lattices are commonly described by Bloch band theory. Besides Abelian Bloch states labeled by a momentum vector, hyperbolic lattices support non-Abelian Bloch states that have so far eluded analytical treatments. By adapting the solid-state-physics notions of supercells and zone folding, we devise a method for the systematic construction of non-Abelian Bloch states. The method applies Abelian band theory to sequences of supercells, recursively built as symmetric aggregates of smaller cells, and enables a rapidly convergent computation of bulk spectra and eigenstates for both gapless and gapped tight-binding models. Our supercell method provides an efficient means of approximating the thermodynamic limit and marks a pivotal step toward a complete band-theoretic characterization of hyperbolic lattices