1,162 research outputs found
Pacifying the Fermi-liquid: battling the devious fermion signs
The fermion sign problem is studied in the path integral formalism. The
standard picture of Fermi liquids is first critically analyzed, pointing out
some of its rather peculiar properties. The insightful work of Ceperley in
constructing fermionic path integrals in terms of constrained world-lines is
then reviewed. In this representation, the minus signs associated with
Fermi-Dirac statistics are self consistently translated into a geometrical
constraint structure (the {\em nodal hypersurface}) acting on an effective
bosonic dynamics. As an illustrative example we use this formalism to study
1+1-dimensional systems, where statistics are irrelevant, and hence the sign
problem can be circumvented. In this low-dimensional example, the structure of
the nodal constraints leads to a lucid picture of the entropic interaction
essential to one-dimensional physics. Working with the path integral in
momentum space, we then show that the Fermi gas can be understood by analogy to
a Mott insulator in a harmonic trap. Going back to real space, we discuss the
topological properties of the nodal cells, and suggest a new holographic
conjecture relating Fermi liquids in higher dimensions to soft-core bosons in
one dimension. We also discuss some possible connections between mixed
Bose/Fermi systems and supersymmetry.Comment: 28 pages, 5 figure
Mottness collapse and statistical quantum criticality
We forward here the case that the anomalous electron states found in cuprate
superconductors and related systems are rooted in a deeply non-classical
fermion sign structure. The collapse of Mottness as advocated by Phillips and
supported by recent DCA results on the Hubbard model is setting the necessary
microscopic conditions. The crucial insight is due to Weng who demonstrated
that in the presence of Mottness the fundamental workings of quantum statistics
changes and we will elaborate on the effects of this Weng statistics with an
emphasis on characterizing these further using numerical methods. The pseudogap
physics of the underdoped regime appears as a consequence of the altered
statistics and the profound question is how to connect this by a continuous
quantum phase transition to the overdoped regime ruled by normal Fermi-Dirac
statistics. Proof of principle follows from
Ceperley's constrained path integral formalism where states can be explicitly
constructed showing a merger of
Fermi-Dirac sign structure and scale invariance of the quantum dynamics.Comment: 27 pages, 4 figures, submitted to theme issue of Phil. Trans. R. Soc.
Extended Bloch theorem for topological lattice models with open boundaries
While the Bloch spectrum of translationally invariant noninteracting lattice
models is trivially obtained by a Fourier transformation, diagonalizing the
same problem in the presence of open boundary conditions is typically only
possible numerically or in idealized limits. Here we present exact analytic
solutions for the boundary states in a number of lattice models of current
interest, including nodal-line semimetals on a hyperhoneycomb lattice,
spin-orbit coupled graphene, and three-dimensional topological insulators on a
diamond lattice, for which no previous exact finite-size solutions are
available in the literature. Furthermore, we identify spectral mirror symmetry
as the key criterium for analytically obtaining the entire (bulk and boundary)
spectrum as well as the concomitant eigenstates, and exemplify this for Chern
and insulators with open boundaries of co-dimension one. In the
case of the two-dimensional Lieb lattice, we extend this further and show how
to analytically obtain the entire spectrum in the presence of open boundaries
in both directions, where it has a clear interpretation in terms of bulk, edge,
and corner states
Topological superconductivity of spin-3/2 carriers in a three-dimensional doped Luttinger semimetal
We investigate topological Cooper pairing, including gapless Weyl and fully
gapped class DIII superconductivity, in a three-dimensional doped Luttinger
semimetal. The latter describes effective spin-3/2 carriers near a quadratic
band touching and captures the normal-state properties of the 227 pyrochlore
iridates and half-Heusler alloys. Electron-electron interactions may favor
non--wave pairing in such systems, including even-parity -wave pairing.
We argue that the lowest energy -wave pairings are always of complex (e.g.,
) type, with nodal Weyl quasiparticles. This implies scaling of the density of states (DoS) at low energies in the clean
limit, or over a wide critical region in the presence of
disorder. The latter is consistent with the -dependence of the penetration
depth in the half-Heusler compound YPtBi. We enumerate routes for experimental
verification, including specific heat, thermal conductivity, NMR relaxation
time, and topological Fermi arcs. Nucleation of any -wave pairing also
causes a small lattice distortion and induces an -wave component; this gives
a route to strain-engineer exotic pairings. We also consider odd-parity,
fully gapped -wave superconductivity. For hole doping, a gapless Majorana
fluid with cubic dispersion appears at the surface. We invent a generalized
surface model with -fold dispersion to simulate a bulk with winding number
. Using exact diagonalization, we show that disorder drives the surface
into a critically delocalized phase, with universal DoS and multifractal
scaling consistent with the conformal field theory (CFT) SO(), where
counts replicas. This is contrary to the naive expectation of
a surface thermal metal, and implies that the topology tunes the surface
renormalization group to the CFT in the presence of disorder.Comment: Published Version in PRB (Editors' Suggestion): 49 Pages, 17 Figures,
3 Table
Geometric phases and competing orders in two dimensions
We discuss the problem of characterizing "quantum disordered" ground states,
obtained upon loss of antiferromagnetic order on general lattices in two
spatial dimensions, with arbitrary electronic band structure. A key result is
the response in electron bilinears to the skyrmion density in the local
antiferromagnetic order, induced by geometric phases. We also discuss the
connection to topological terms obtained under situations where the electronic
spectrum has a Dirac form.Comment: 36 pages, 5 figure
Vortices in quantum droplets: Analogies between boson and fermion systems
The main theme of this review is the many-body physics of vortices in quantum
droplets of bosons or fermions, in the limit of small particle numbers. Systems
of interest include cold atoms in traps as well as electrons confined in
quantum dots. When set to rotate, these in principle very different quantum
systems show remarkable analogies. The topics reviewed include the structure of
the finite rotating many-body state, universality of vortex formation and
localization of vortices in both bosonic and fermionic systems, and the
emergence of particle-vortex composites in the quantum Hall regime. An overview
of the computational many-body techniques sets focus on the configuration
interaction and density-functional methods. Studies of quantum droplets with
one or several particle components, where vortices as well as coreless vortices
may occur, are reviewed, and theoretical as well as experimental challenges are
discussed.Comment: Review article, 53 pages, 53 figure
Using Gap Symmetry and Structure to Reveal the Pairing Mechanism in Fe-based Superconductors
I review theoretical ideas and implications of experiments for the gap
structure and symmetry of the Fe-based superconductors. Unlike any other class
of unconventional superconductors, one has in these systems the possibility to
tune the interactions by small changes in pressure, doping or disorder. Thus,
measurements of order parameter evolution with these parameters should enable a
deeper understanding of the underlying interactions. I briefly review the
"standard paradigm" for -wave pairing in these systems, and then focus on
developments in the past several years which have challenged this picture. I
discuss the reasons for the apparent close competition between pairing in s-
and d-wave channels, particularly in those systems where one type of Fermi
surface pocket -- hole or electron -- is missing. Observation of a transition
between - and -wave symmetry, possibly via a time reversal symmetry
breaking "" state, would provide an importantconfirmation of these ideas.
Several proposals for detecting these novel phases are discussed, including the
appearance of order parameter collective modes in Raman and optical
conductivities. Transitions between two different types of -wave states,
involving various combinations of signs on Fermi surface pockets, can also
proceed through a -breaking "" state. I discuss recent work
that suggests pairing may take place away from the Fermi level over a
surprisingly large energy range, as well as the effect of glide plane symmetry
of the Fe-based systems on the superconductivity, including various exotic,
time and translational invariance breaking pair states that have been proposed.
Finally, I address disorder issues, and the various ways systematic
introduction of disorder can (and cannot) be used to extract information on gap
symmetry and structure.Comment: 41 pp., Published in special focus issue of Comptes Rendus Physique
(Paris) on recent progress in Fe-based Superconductivity. Full issue with 10
review articles available at
http://www.sciencedirect.com/science/journal/16310705/17/1-
- …