130 research outputs found
Efficient Learning of a One-dimensional Density Functional Theory
Density functional theory underlies the most successful and widely used
numerical methods for electronic structure prediction of solids. However, it
has the fundamental shortcoming that the universal density functional is
unknown. In addition, the computational result---energy and charge density
distribution of the ground state---is useful for electronic properties of
solids mostly when reduced to a band structure interpretation based on the
Kohn-Sham approach. Here, we demonstrate how machine learning algorithms can
help to free density functional theory from these limitations. We study a
theory of spinless fermions on a one-dimensional lattice. The density
functional is implicitly represented by a neural network, which predicts,
besides the ground-state energy and density distribution, density-density
correlation functions. At no point do we require a band structure
interpretation. The training data, obtained via exact diagonalization, feeds
into a learning scheme inspired by active learning, which minimizes the
computational costs for data generation. We show that the network results are
of high quantitative accuracy and, despite learning on random potentials,
capture both symmetry-breaking and topological phase transitions correctly.Comment: 5 pages, 3 figures; 4+ pages appendi
Infernal and Exceptional Edge Modes: Non-Hermitian Topology Beyond the Skin Effect
The classification of point gap topology in all local non-Hermitian symmetry
classes has been recently established. However, many entries in the resulting
periodic table have only been discussed in a formal setting and still lack a
physical interpretation in terms of their bulk-boundary correspondence. Here,
we derive the edge signatures of all two-dimensional phases with intrinsic
point gap topology. While in one dimension point gap topology invariably leads
to the non-Hermitian skin effect, non-Hermitian boundary physics is
significantly richer in two dimensions. We find two broad classes of
non-Hermitian edge states: (1) Infernal points, where a skin effect occurs only
at a single edge momentum, while all other edge momenta are devoid of edge
states. Under semi-infinite boundary conditions, the point gap thereby closes
completely, but only at a single edge momentum. (2) Non-Hermitian exceptional
point dispersions, where edge states persist at all edge momenta and furnish an
anomalous number of symmetry-protected exceptional points. Surprisingly, the
latter class of systems allows for a finite, non-extensive number of edge
states with a well defined dispersion along all generic edge terminations.
Instead, the point gap only closes along the real and imaginary eigenvalue
axes, realizing a novel form of non-Hermitian spectral flow.Comment: 6 pages, 3 figures, 13 pages supplementary materia
Infernal and exceptional edge modes: non-Hermitian topology beyond the skin effect
The classification of point gap topology in all local non-Hermitian (NH) symmetry classes has been recently established. However, many entries in the resulting periodic table have only been discussed in a formal setting and still lack a physical interpretation in terms of their bulk-boundary correspondence. Here, we derive the edge signatures of all two-dimensional phases with intrinsic point gap topology. While in one dimension point gap topology invariably leads to the NH skin effect, NH boundary physics is significantly richer in two dimensions. We find two broad classes of non-Hermitian edge states: (1) infernal points, where a skin effect occurs only at a single edge momentum, while all other edge momenta are devoid of edge states. Under semi-infinite boundary conditions, the point gap thereby closes completely, but only at a single edge momentum. (2) NH exceptional point dispersions, where edge states persist at all edge momenta and furnish an anomalous number of symmetry-protected exceptional points. Surprisingly, the latter class of systems allows for a finite, non-extensive number of edge states with a well defined dispersion along all generic edge terminations. Concomitantly, the point gap only closes along the real and imaginary eigenvalue axes, realizing a novel form of NH spectral flow
The Quartic Higgs Coupling at Hadron Colliders
The quartic Higgs self-coupling is the final measurement in the Higgs
potential needed to fully understand electroweak symmetry breaking. None of the
present or future colliders are known to be able to determine this parameter.
We study the chances of measuring the quartic self-coupling at hadron colliders
in general and at the VLHC in particular. We find the prospects challenging.Comment: 5 pages, 4 figure
Symmetry Indicators for Inversion-Symmetric Non-Hermitian Topological Band Structures
We characterize non-Hermitian band structures by symmetry indicator
topological invariants. Enabled by crystalline inversion symmetry, these
indicators allow us to short-cut the calculation of conventional non-Hermitian
topological invariants. In particular, we express the three-dimensional winding
number of point-gapped non-Hermitian systems, which is defined as an integral
over the whole Brillouin zone, in terms of symmetry eigenvalues at
high-symmetry momenta. Furthermore, for time-reversal symmetric non-Hermitian
topological insulators, we find that symmetry indicators characterize the
associated Chern-Simons form, whose evaluation usually requires a
computationally expensive choice of smooth gauge. In each case, we discuss the
non-Hermitian surface states associated with nontrivial symmetry indicators.Comment: 6 pages, 1 figure, supplement include
Symmetry breaking and spectral structure of the interacting Hatano-Nelson model
We study the Hatano-Nelson model, i.e., a one-dimensional non-Hermitian chain of spinless fermions with nearest-neighbor nonreciprocal hopping, in the presence of repulsive nearest-neighbor interactions. At half filling, we find two PT transitions, as the interaction strength increases. The first transition is marked by an exceptional point between the first and the second excited state in a finite-size system and is a first-order symmetry-breaking transition into a charge-density wave regime. Persistent currents characteristic of the Hatano-Nelson model abruptly vanish at the transition. The second transition happens at a critical interaction strength that scales with the system size and can thus only be observed in finite-size systems. It is characterized by a collapse of all energy eigenvalues onto the real axis. We further show that in a strong interaction regime, but away from half filling, the many-body spectrum shows point gaps with nontrivial winding numbers, akin to the topological properties of the single-particle spectrum of the Hatano-Nelson chain, which indicates the skin effect of extensive many-body eigenstates under open boundary conditions. Our results can be applied to other models such as the non-Hermitian Su-Schrieffer-Heeger-type model and contribute to an understanding of fermionic many-body systems with non-Hermitian Hamiltonians
A Hybrid Quantum-Classical Method for Electron-Phonon Systems
Interactions between electrons and phonons play a crucial role in quantum
materials. Yet, there is no universal method that would simultaneously
accurately account for strong electron-phonon interactions and electronic
correlations. By combining methods of the variational quantum eigensolver and
the variational non-Gaussian solver, we develop a hybrid quantum-classical
algorithm suitable for this type of correlated systems. This hybrid method
tackles systems with arbitrarily strong electron-phonon coupling without
increasing the number of required qubits and quantum gates, as compared to
purely electronic models. We benchmark the new method by applying it to the
paradigmatic Hubbard-Holstein model at half filling, and show that it correctly
captures the competition between charge density wave and antiferromagnetic
phases, quantitatively consistent with exact diagonalization.Comment: 8 pages, 4 figures; 4 pages Supplemental Materia
Discovery of Charge Order and Corresponding Edge State in Kagome Magnet FeGe
Kagome materials often host exotic quantum phases, including spin liquids, Chern gap, charge density wave, and superconductivity. Existing scanning microscopy studies of the kagome charge order have been limited to nonkagome surface layers. Here, we tunnel into the kagome lattice of FeGe to uncover features of the charge order. Our spectroscopic imaging identifies a 2×2 charge order in the magnetic kagome lattice, resembling that discovered in kagome superconductors. Spin mapping across steps of unit cell height demonstrates the existence of spin-polarized electrons with an antiferromagnetic stacking order. We further uncover the correlation between antiferromagnetism and charge order anisotropy, highlighting the unusual magnetic coupling of the charge order. Finally, we detect a pronounced edge state within the charge order energy gap, which is robust against the irregular shape fluctuations of the kagome lattice edges. We discuss our results with the theoretically considered topological features of the kagome charge order including unconventional magnetism and bulk-boundary correspondence
A hybrid quantum-classical method for electron-phonon systems
nteractions between electrons and phonons play a crucial role in quantum materials. Yet, there is no universal method that would simultaneously accurately account for strong electron-phonon interactions and electronic correlations. By combining methods of the variational quantum eigensolver and the variational non-Gaussian solver, we develop a hybrid quantum-classical algorithm suitable for this type of correlated systems. This hybrid method tackles systems with arbitrarily strong electron-phonon coupling without increasing the number of required qubits and quantum gates, as compared to purely electronic models. We benchmark our method by applying it to the paradigmatic Hubbard-Holstein model at half filling, and show that it correctly captures the competition between charge density wave and antiferromagnetic phases, quantitatively consistent with exact diagonalization
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