267 research outputs found
Fermionic projected entangled-pair states and topological phases
We study fermionic matrix product operator algebras and identify the
associated algebraic data. Using this algebraic data we construct fermionic
tensor network states in two dimensions that have non-trivial
symmetry-protected or intrinsic topological order. The tensor network states
allow us to relate physical properties of the topological phases to the
underlying algebraic data. We illustrate this by calculating defect properties
and modular matrices of supercohomology phases. Our formalism also captures
Majorana defects as we show explicitly for a class of
symmetry-protected and intrinsic topological phases. The tensor networks states
presented here are well-suited for numerical applications and hence open up new
possibilities for studying interacting fermionic topological phases.Comment: Published versio
Fermionic matrix product states and one-dimensional topological phases
We develop the formalism of fermionic matrix product states (fMPS) and show how irreducible fMPS fall in two different classes, related to the different types of simple Z(2) graded algebras, which are physically distinguished by the absence or presence of Majorana edge modes. The local structure of fMPS with Majorana edge modes also implies that there is always a twofold degeneracy in the entanglement spectrum. Using the fMPS formalism, we make explicit the correspondence between the Z(8) classification of time-reversal-invariant spinless superconductors and the modulo 8 periodicity in the representation theory of real Clifford algebras. Studying fMPS with general onsite unitary and antiunitary symmetries allows us to define invariants that label symmetry-protected phases of interacting fermions. The behavior of these invariants under stacking of fMPS is derived, which reveals the group structure of such interacting phases. We also consider spatial symmetries and show how the invariant phase factor in the partition function of reflection-symmetric phases on an unorientable manifold appears in the fMPS framework
Chiroptical studies on brevianamide B : vibrational and electronic circular dichroism confronted
Chiroptical spectroscopy, such as electronic circular dichroism (ECD) and vibrational circular dichroism (VCD) are highly sensitive techniques to probe molecular conformation, configuration, solvation and aggregation. Here we report the application of these techniques to study the fungal metabolite brevianamide B. Comparison of the experimental ECD and VCD spectra with the density functional theory (DFT) simulated counterparts establishes that VCD is the more reliable technique to assign absolute configuration due to the larger functional and dispersion dependence of computed ECD spectra. Despite a low amount of available material, and a relatively unusual example of using VCD carbonyl multiplets, the absolute configuration could be reliably predicted, strengthening the case for application of VCD in the study of complex natural products. Spectral and crystallographic evidence for or against the formation of a dimeric aggregate is discussed; in solution the VCD spectra strongly suggest only monomeric species are present
Mapping topological to conformal field theories through strange correlators
We extend the concept of strange correlators, defined for symmetry-protected
phases in [You et al., Phys. Rev. Lett. 112, 247202 (2014)], to topological
phases of matter by taking the inner product between string-net ground states
and product states. The resulting two-dimensional partition functions are shown
to be either critical or symmetry broken, as the corresponding transfer
matrices inherit all matrix product operator symmetries of the string-net
states. For the case of critical systems, those non-local matrix product
operator symmetries are the lattice remnants of topological conformal defects
in the field theory description. Following [Aasen et al., J. Phys. A 49, 354001
(2016)], we argue that the different conformal boundary conditions can be
obtained by applying the strange correlator concept to the different
topological sectors of the string-net obtained from Ocneanu's tube algebra.
This is demonstrated by calculating the conformal field theory spectra on the
lattice in the different topological sectors for the Fibonacci/hard-hexagon and
Ising string-net. Additionally, we provide a complementary perspective on
symmetry-preserving real-space renormalization by showing how known tensor
network renormalization methods can be understood as the approximate truncation
of an exactly coarse-grained strange correlator
Projected seniority-two orbital optimization of the Antisymmetric Product of one-reference orbital Geminal
We present a new, non-variational orbital-optimization scheme for the
Antisymmetric Product of one-reference orbital Geminal wave function. Our
approach is motivated by the observation that an orbital-optimized
seniority-zero configuration interaction (CI) expansion yields similar results
to an orbital-optimized seniority-zero-plus-two CI expansion [J. Chem. Phys.,
135, 044119 (2011)]. A numerical analysis is performed for the C, LiF and
CH molecules as well as for the symmetric stretching of hypothetical
(linear) hydrogen chains. For these test cases, the proposed
orbital-optimization protocol yields similar results to its variational orbital
optimization counterpart, but prevents symmetry-breaking of molecular orbitals
in most cases.Comment: 7 pages, 2 figure
Matrix product operators for symmetry-protected topological phases: Gauging and edge theories
Projected entangled pair states (PEPS) provide a natural ansatz for the
ground states of gapped, local Hamiltonians in which global characteristics of
a quantum state are encoded in properties of local tensors. We develop a
framework to describe on-site symmetries, as occurring in systems exhibiting
symmetry-protected topological (SPT) quantum order, in terms of virtual
symmetries of the local tensors expressed as a set of matrix product operators
(MPOs) labeled by distinct group elements. These MPOs describe the possibly
anomalous symmetry of the edge theory, whose local degrees of freedom are
concretely identified in a PEPS. A classification of SPT phases is obtained by
studying the obstructions to continuously deforming one set of MPOs into
another, recovering the results derived for fixed-point models [X. Chen et al.,
Phys. Rev. B 87, 155114 (2013)]. Our formalism accommodates perturbations away
from fixed point models, opening the possibility of studying phase transitions
between different SPT phases. We also demonstrate that applying the recently
developed quantum state gauging procedure to a SPT PEPS yields a PEPS with
topological order determined by the initial symmetry MPOs. The MPO framework
thus unifies the different approaches to classifying SPT phases, via
fixed-points models, boundary anomalies, or gauging the symmetry, into the
single problem of classifying inequivalent sets of matrix product operator
symmetries that are defined purely in terms of a PEPS.Comment: 16 + 19 pages, 13 figures; v2 substantial changes to all sections,
new appendices added; v3 published versio
Method For Making 2-Electron Response Reduced Density Matrices Approximately N-representable
In methods like geminal-based approaches or coupled cluster that are solved
using the projected Schr\"odinger equation, direct computation of the
2-electron reduced density matrix (2-RDM) is impractical and one falls back to
a 2-RDM based on response theory. However, the 2-RDMs from response theory are
not -representable. That is, the response 2-RDM does not correspond to an
actual physical -electron wave function. We present a new algorithm for
making these non--representable 2-RDMs approximately -representable, i.e.
it has the right symmetry and normalization and it fulfills the -, - and
-conditions. Next to an algorithm which can be applied to any 2-RDM, we have
also developed a 2-RDM optimization procedure specifically for seniority-zero
2-RDMs. We aim to find the 2-RDM with the right properties that is the closest
(in the sense of the Frobenius norm) to the non-N-representable 2-RDM by
minimizing the square norm of the difference between the initial 2-RDM and the
targeted 2-RDM under the constraint that the trace is normalized and the 2-RDM,
- and -matrices are positive semidefinite, i.e. their eigenvalues are
non-negative. Our method is suitable for fixing non-N-respresentable 2-RDMs
which are close to being N-representable. Through the N-representability
optimization algorithm we add a small correction to the initial 2-RDM such that
it fulfills the most important N-representability conditions.Comment: 13 pages, 8 figure
Resurgence of superconductivity and the role of dxy hole band in FeSeTe
Iron-chalcogenide superconductors display rich phenomena caused by orbital-dependent band shifts and electronic correlations. Additionally, they are potential candidates for topological superconductivity due to the band inversion between the Fe d bands and the chalcogen p band. Here we present a detailed study of the electronic structure of the nematic superconductors FeSeTe (0 < x < 0.4) using angle-resolved photoemission spectroscopy to understand the role of orbital-dependent band shifts, electronic correlations and the chalcogen band. We assess the changes in the effective masses using a three-band low energy model, and the band renormalization via comparison with DFT band structure calculations. The effective masses decrease for all three-hole bands inside the nematic phase, followed by a strong increase for the band with d orbital character. Interestingly, this nearly-flat d band becomes more correlated as it shifts towards the Fermi level with increasing Te concentrations and as the second superconducting dome emerges. Our findings suggests that the d hole band, which is very sensitive to the chalcogen height, could be involved in promoting an additional pairing channel and increasing the density of states to stabilize the second superconducting dome in FeSeTe. This simultaneous shift of the d hole band and enhanced superconductivity is in contrast with FeSeS
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