8 research outputs found
Fluctuation based interpretable analysis scheme for quantum many-body snapshots
Microscopically understanding and classifying phases of matter is at the
heart of strongly-correlated quantum physics. With quantum simulations, genuine
projective measurements (snapshots) of the many-body state can be taken, which
include the full information of correlations in the system. The rise of deep
neural networks has made it possible to routinely solve abstract processing and
classification tasks of large datasets, which can act as a guiding hand for
quantum data analysis. However, though proven to be successful in
differentiating between different phases of matter, conventional neural
networks mostly lack interpretability on a physical footing. Here, we combine
confusion learning with correlation convolutional neural networks, which yields
fully interpretable phase detection in terms of correlation functions. In
particular, we study thermodynamic properties of the 2D Heisenberg model,
whereby the trained network is shown to pick up qualitative changes in the
snapshots above and below a characteristic temperature where magnetic
correlations become significantly long-range. We identify the full counting
statistics of nearest neighbor spin correlations as the most important quantity
for the decision process of the neural network, which go beyond averages of
local observables. With access to the fluctuations of second-order correlations
-- which indirectly include contributions from higher order, long-range
correlations -- the network is able to detect changes of the specific heat and
spin susceptibility, the latter being in analogy to magnetic properties of the
pseudogap phase in high-temperature superconductors. By combining the confusion
learning scheme with transformer neural networks, our work opens new directions
in interpretable quantum image processing being sensible to long-range order.Comment: 15+3 page
Plasmons in Two-Dimensional Topological Insulators
We analyze collective excitations in models of two-dimensional topological
insulators using the random phase approximation. In a two-dimensional extension
of the Su-Schrieffer-Heeger model, edge plasmonic excitations with induced
charge-density distributions localized at the boundaries of the system are
found in the topologically non-trivial phase, dispersing similarly as
one-dimensional bulk plasmons in the conventional Su-Schrieffer-Heeger chain.
For two-dimensional bulk collective modes, we reveal regimes of enhanced
inter-band wave function correlations, leading to characteristic hardening and
softening of inter- and intra-band bulk plasmonic branches, respectively. In
the two-dimensional Haldane Chern insulator model, chiral, uni-directional edge
plasmons in nano-ribbon architectures are observed, which can be characterized
by an effective Coulomb interaction cross section. Bulk collective excitations
in the two-dimensional Haldane model are shown to be originated by
single-particle band structure details in different topological phases
Control of Plasmons in Doped Topological Insulators via Basis Atoms
Collective excitations in topologically non-trivial systems have attracted
considerable attention in recent years. Here we study plasmons in the
Su-Schrieffer-Heeger model whose low-energy electronic band is only partially
filled, such that the system is metallic. Using the random phase approximation,
we calculate the intra- and inter-band polarization functions and determine the
bulk plasmonic dispersion from the dielectric function within the random phase
approximation. We find that the sub-lattice basis states strongly affect the
polarization functions and therefore control the system's plasmonic
excitations. By varying the real-space separation of these local orbitals, one
can thus selectively enhance or suppress the plasmonic energies via a tunable
trade-off between intra-band and inter-band screening processes. Specifically,
this mechanism can be used to stabilize undamped high energy plasmons that have
already been reported in related models. We propose scenarios on how to control
and observe these effects in experiments
Parity effects and universal terms of O(1) in the entanglement near a boundary
In the presence of boundaries, the entanglement entropy in lattice models is
known to exhibit oscillations with the (parity of the) length of the subsystem,
which however decay to zero with increasing distance from the edge. We point
out in this article that, when the subsystem starts at the boundary and ends at
an impurity, oscillations of the entanglement (as well as of charge
fluctuations) appear which do not decay with distance, and which exhibit
universal features. We study these oscillations in detail for the case of the
XX chain with one modified link (a conformal defect) or two successive modified
links (a relevant defect), both numerically and analytically. We then
generalize our analysis to the case of extended (conformal) impurities, which
we interpret as SSH models coupled to metallic leads. In this context, the
parity effects can be interpreted in terms of the existence of non-trivial
topological phases
Topological Protection of Coherence in Noisy Open Quantum Systems
We consider topological protection mechanisms in dissipative quantum systems
in the presence of quenched disorder, with the intent to prolong coherence
times of qubits. The physical setting is a network of qubits and dissipative
cavities whose coupling parameters are tunable, such that topological edge
states can be stabilized. The evolution of a fiducial qubit is entirely
determined by a non-Hermitian Hamiltonian which thus emerges from a bona-fide
physical process. It is shown how even in the presence of disorder winding
numbers can be defined and evaluated in real space, as long as certain
symmetries are preserved. Hence we can construct the topological phase diagrams
of noisy open quantum models, such as the non-Hermitian disordered
Su-Schrieffer- Heeger dimer model and a trimer model that includes longer-range
couplings. In the presence of competing disorder parameters, interesting
re-entrance phenomena of topologically non-trivial sectors are observed. This
means that in certain parameter regions, increasing disorder drastically
increases the coherence time of the fiducial qubit
Bulk topological signatures of a quasicrystal
We show how measuring real space properties such as the charge density in a
quasiperiodic system can be used to gain insight into their topological
properties. In particular, for the Fibonacci chain, we show that the total
onsite charge oscillates when plotted in the appropriate coordinates, and the
number of oscillations is given by the Chern number of the gap in which the
Fermi level lies. We show that these oscillations have two distinct
interpretations, obtained by extrapolating results from the two extreme limits
of the Fibonacci chain -- the valence bond picture in the strong modulation
limit, and perturbation around the periodic chain in the weak modulation limit.
This effect is found to remain robust at moderate interactions, as well as in
the presence of disorder. We conclude that experimental measurement of the real
space charge distribution can yield information on topological properties in a
straightforward way.Comment: 8 pages, 6 figure
Quantifying hole-motion-induced frustration in doped antiferromagnets by Hamiltonian reconstruction
Unveiling the microscopic origins of quantum phases dominated by the interplay of spin and motional degrees of freedom constitutes one of the central challenges in strongly correlated many-body physics. When holes move through an antiferromagnetic spin background, they displace the positions of spins, which induces effective frustration in the magnetic environment. However, a concrete characterization of this effect in a quantum many-body system is still an unsolved problem. Here we present a Hamiltonian reconstruction scheme that allows for a precise quantification of hole-motion-induced frustration. We access non-local correlation functions through projective measurements of the many-body state, from which effective spin-Hamiltonians can be recovered after detaching the magnetic background from dominant charge fluctuations. The scheme is applied to systems of mixed dimensionality, where holes are restricted to move in one dimension, but SU(2) superexchange is two-dimensional. We demonstrate that hole motion drives the spin background into a highly frustrated regime, which can quantitatively be described by an effective J1–J2-type spin model. We exemplify the applicability of the reconstruction scheme to ultracold atom experiments by recovering effective spin-Hamiltonians of experimentally obtained 1D Fermi-Hubbard snapshots. Our method can be generalized to fully 2D systems, enabling promising microscopic perspectives on the doped Hubbard model
Quantifying hole-motion-induced frustration in doped antiferromagnets by Hamiltonian reconstruction
Abstract Unveiling the microscopic origins of quantum phases dominated by the interplay of spin and motional degrees of freedom constitutes one of the central challenges in strongly correlated many-body physics. When holes move through an antiferromagnetic spin background, they displace the positions of spins, which induces effective frustration in the magnetic environment. However, a concrete characterization of this effect in a quantum many-body system is still an unsolved problem. Here we present a Hamiltonian reconstruction scheme that allows for a precise quantification of hole-motion-induced frustration. We access non-local correlation functions through projective measurements of the many-body state, from which effective spin-Hamiltonians can be recovered after detaching the magnetic background from dominant charge fluctuations. The scheme is applied to systems of mixed dimensionality, where holes are restricted to move in one dimension, but SU(2) superexchange is two-dimensional. We demonstrate that hole motion drives the spin background into a highly frustrated regime, which can quantitatively be described by an effective J 1–J 2-type spin model. We exemplify the applicability of the reconstruction scheme to ultracold atom experiments by recovering effective spin-Hamiltonians of experimentally obtained 1D Fermi-Hubbard snapshots. Our method can be generalized to fully 2D systems, enabling promising microscopic perspectives on the doped Hubbard model