5,123 research outputs found
Quantum phase transitions of metals in two spatial dimensions: I. Ising-nematic order
We present a renormalization group theory for the onset of Ising-nematic
order in a Fermi liquid in two spatial dimensions. This is a quantum phase
transition, driven by electron interactions, which spontaneously reduces the
point-group symmetry from square to rectangular. The critical point is
described by an infinite set of 2+1 dimensional local field theories, labeled
by points on the Fermi surface. Each field theory contains a real scalar field
representing the Ising order parameter, and fermionic fields representing a
time-reversed pair of patches on the Fermi surface. We demonstrate that the
field theories obey compatibility constraints required by our redundant
representation of the underlying degrees of freedom. Scaling forms for the
response functions are proposed, and supported by computations by up to three
loops. Extensions of our results to other transitions of two-dimensional Fermi
liquids with broken point-group and/or time-reversal symmetry are noted. Our
results extend also to the problem of a Fermi surface coupled to a U(1) gauge
field.Comment: 46 pages, 11 figures; paper II is arXiv:1005.1288 ; (v3) added
results for off-critical behavior; (v4+v5) added clarifications, including
new appendi
Thermodynamics of an one-dimensional ideal gas with fractional exclusion statistics
We show that the particles in the Calogero-Sutherland Model obey fractional
exclusion statistics as defined by Haldane. We construct anyon number densities
and derive the energy distribution function. We show that the partition
function factorizes in the form characteristic of an ideal gas. The virial
expansion is exactly computable and interestingly it is only the second virial
coefficient that encodes the statistics information.Comment: 10pp, REVTE
Coordinate Representation of the Two-Spinon wavefunction and Spinon Interaction
By deriving and studying the coordinate representation for the two-spinon
wavefunction, we show that spinon excitations in the Haldane-Shastry model
interact. The interaction is given by a short-range attraction and causes a
resonant enhancement in the two-spinon wavefunction at short separations
between the spinons. We express the spin susceptibility for a finite lattice in
terms of the resonant enhancement, given by the two-spinon wavefunction at zero
separation. In the thermodynamic limit, the spinon attraction turns into the
square-root divergence in the dynamical spin susceptibility.Comment: 19 pages, 5 .eps figure
Breakdown of Luttinger liquid state in one-dimensional frustrated spinless fermion model
Haldane hypothesis about the universality of Luttinger liquid (LL) behavior
in conducting one-dimensional (1D) fermion systems is checked numerically for
spinless fermion model with next-nearest-neighbor interactions. It is shown
that for large enough interactions the ground state can be gapless (metallic)
due to frustrations but not be LL. The exponents of correlation functions for
this unusual conducting state are found numerically by finite-size method.Comment: 3 pages, 4 figures, RevTe
The effect of host heterogeneity and parasite intragenomic interactions on parasite population structure
Understanding the processes that shape the genetic structure of parasite populations and the functional consequences of different parasite genotypes is critical for our ability to predict how an infection can spread through a host population and for the design of effective vaccines to combat infection and disease. Here, we examine how the genetic structure of parasite populations responds to host genetic heterogeneity. We consider the well-characterized molecular specificity of major histocompatibility complex binding of antigenic peptides to derive deterministic and stochastic models. We use these models to ask, firstly, what conditions favour the evolution of generalist parasite genotypes versus specialist parasite genotypes? Secondly, can parasite genotypes coexist in a population? We find that intragenomic interactions between parasite loci encoding antigenic peptides are pivotal in determining the outcome of evolution. Where parasite loci interact synergistically (i.e. the recognition of additional antigenic peptides has a disproportionately large effect on parasite fitness), generalist parasite genotypes are favoured. Where parasite loci act multiplicatively (have independent effects on fitness) or antagonistically (have diminishing effects on parasite fitness), specialist parasite genotypes are favoured. A key finding is that polymorphism is not stable and that, with respect to functionally important antigenic peptides, parasite populations are dominated by a single genotype
String order and adiabatic continuity of Haldane chains and band insulators
The ground state of spin-1 Haldane chains is characterized by the so-called
string order. We show that the same hidden order is also present in ordinary
one-dimensional band insulators. We construct a family of Hamiltonians which
connects adiabatically band insulators to two topologically non-equivalent spin
models, the Haldane chain and the antiferromagnetic spin-1/2 ladder. We observe
that the localized spin-1/2 edge-state characteristic of spin-1 chains is
smoothly connected to a surface-bound state of band insulators and its
emergence is not related to any bulk phase transition. Furthermore, we show
that the string order is absent in any dimensions higher than one.Comment: 6 pages, 7 figures. Appendix about charge string orders added.
Version as publishe
Non-perturbative behavior of the quantum phase transition to a nematic Fermi fluid
We discuss shape (Pomeranchuk) instabilities of the Fermi surface of a
two-dimensional Fermi system using bosonization. We consider in detail the
quantum critical behavior of the transition of a two dimensional Fermi fluid to
a nematic state which breaks spontaneously the rotational invariance of the
Fermi liquid. We show that higher dimensional bosonization reproduces the
quantum critical behavior expected from the Hertz-Millis analysis, and verify
that this theory has dynamic critical exponent . Going beyond this
framework, we study the behavior of the fermion degrees of freedom directly,
and show that at quantum criticality as well as in the the quantum nematic
phase (except along a set of measure zero of symmetry-dictated directions) the
quasi-particles of the normal Fermi liquid are generally wiped out. Instead,
they exhibit short ranged spatial correlations that decay faster than any
power-law, with the law and we
verify explicitely the vanishing of the fermion residue utilizing this
expression. In contrast, the fermion auto-correlation function has the behavior
. In this regime we also find that, at
low frequency, the single-particle fermion density-of-states behaves as
, where is larger
than the free Fermi value, N(0), and is a constant. These results confirm
the non-Fermi liquid nature of both the quantum critical theory and of the
nematic phase.Comment: 20 pages, 2 figures, 1 table; new version with minor changes; new
subsection 3C2 added with an explicit calculation of the quasiparticle
residue at the nematic transition; minor typos corrected, new references;
general beautification of the text and figure
Critical exponents of the degenerate Hubbard model
We study the critical behaviour of the \SUN{} generalization of the
one-dimensional Hubbard model with arbitrary degeneracy . Using the
integrability of this model by Bethe Ansatz we are able to compute the spectrum
of the low-lying excitations in a large but finite box for arbitrary values of
the electron density and of the Coulomb interaction. This information is used
to determine the asymptotic behaviour of correlation functions at zero
temperature in the presence of external fields lifting the degeneracy. The
critical exponents depend on the system parameters through a
dressed charge matrix implying the relevance of the interaction of charge- and
spin-density waves.Comment: 18 page
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