53 research outputs found
Formation of Electronic Nematic Phase in Interacting Systems
We study the formation of an electronic nematic phase characterized by a
broken point-group symmetry in interacting fermion systems within the weak
coupling theory. As a function of interaction strength and chemical potential,
the phase transition between the isotropic Fermi liquid and nematic phase is
first order at zero temperature and becomes second order at a finite
temperature. The transition is present for all typical, including quasi-2D,
electronic dispersions on the square lattice and takes place for arbitrarily
small interaction when at van Hove filling, thus suppressing the Lifshitz
transition. In connection with the formation of the nematic phase, we discuss
the origin of the first order transition and competition with other broken
symmetry states.Comment: revtex4, 6 pages, 6 figures; revised introduction, updated reference
Presymplectic current and the inverse problem of the calculus of variations
The inverse problem of the calculus of variations asks whether a given system
of partial differential equations (PDEs) admits a variational formulation. We
show that the existence of a presymplectic form in the variational bicomplex,
when horizontally closed on solutions, allows us to construct a variational
formulation for a subsystem of the given PDE. No constraints on the
differential order or number of dependent or independent variables are assumed.
The proof follows a recent observation of Bridges, Hydon and Lawson and
generalizes an older result of Henneaux from ordinary differential equations
(ODEs) to PDEs. Uniqueness of the variational formulation is also discussed.Comment: v2: 17 pages, no figures, BibTeX; minor corrections, close to
published versio
Numerical indications on the semiclassical limit of the flipped vertex
We introduce a technique for testing the semiclassical limit of a quantum
gravity vertex amplitude. The technique is based on the propagation of a
semiclassical wave packet. We apply this technique to the newly introduced
"flipped" vertex in loop quantum gravity, in order to test the intertwiner
dependence of the vertex. Under some drastic simplifications, we find very
preliminary, but surprisingly good numerical evidence for the correct classical
limit.Comment: 4 pages, 8 figure
Supercurrent in Nodal Superconductors
In recent years, a number of nodal superconductors have been identified;
d-wave superconductors in high T_c cuprates, CeCoIn, and
\kappa-(ET)_2Cu(NCS)_2, 2D f-wave superconductor in Sr_2RuO_4 and hybrid
s+g-wave superconductor in YNi_2B_2C. In this work we conduct a theoretical
study of nodal superconductors in the presence of supercurrent. For simplicity,
we limit ourselves to d-wave and 2D f-wave superconductors. We compute the
quasiparticle density of states and the temperature dependence of the depairing
critical current in nodal superconductors, both of which are accessible
experimentally.Comment: revtex4, 6 pages, 7 figures; fixed typos, updated references, trimmed
introductio
Strong-field molecular alignment for quantum logic and quantum control
We discuss an approach to quantum control based on initial adiabatic tuning of the field-free Hamiltonian by a strong laser field to optimize the system for the desired transitions induced by the control laser pulse. As an illustration, we describe single-qubit, two-qubit, and some qudit logical gates within rotational and vibrational states of a diatomic molecule. Gate operations use resonant Raman transitions, and the prior adjustment of the Hamiltonian is done by a strong nonresonant aligning field.Peer reviewed: YesNRC publication: Ye
Comments on Microcausality, Chaos, and Gravitational Observables
Observables in gravitational systems must be non-local so as to be invariant
under diffeomorphism gauge transformations. But at the classical level some
such observables can nevertheless satisfy an exact form of microcausality. This
property is conjectured to remain true at all orders in the semiclassical
expansion, though with limitations at finite or . We
also discuss related issues concerning observables in black hole spacetimes and
comment on the senses in which they do and do not experience the form of chaos
identified by Shenker and Stanford. In particular, in contrast to the situation
in a reflecting cavity, this chaos does not afflict observables naturally
associated with Hawking radiation for evaporating black holes.Comment: 16 pages, 1 figure; references adde
Dual Computations of Non-abelian Yang-Mills on the Lattice
In the past several decades there have been a number of proposals for
computing with dual forms of non-abelian Yang-Mills theories on the lattice.
Motivated by the gauge-invariant, geometric picture offered by dual models and
successful applications of duality in the U(1) case, we revisit the question of
whether it is practical to perform numerical computation using non-abelian dual
models. Specifically, we consider three-dimensional SU(2) pure Yang-Mills as an
accessible yet non-trivial case in which the gauge group is non-abelian. Using
methods developed recently in the context of spin foam quantum gravity, we
derive an algorithm for efficiently computing the dual amplitude and describe
Metropolis moves for sampling the dual ensemble. We relate our algorithms to
prior work in non-abelian dual computations of Hari Dass and his collaborators,
addressing several problems that have been left open. We report results of spin
expectation value computations over a range of lattice sizes and couplings that
are in agreement with our conventional lattice computations. We conclude with
an outlook on further development of dual methods and their application to
problems of current interest.Comment: v1: 18 pages, 7 figures, v2: Many changes to appendix, minor changes
throughout, references and figures added, v3: minor corrections, 22 page
Intertwiner dynamics in the flipped vertex
We continue the semiclassical analysis, started in a previous paper, of the
intertwiner sector of the flipped vertex spinfoam model. We use independently
both a semi-analytical and a purely numerical approach, finding the correct
behavior of wave packet propagation and physical expectation values. In the
end, we show preliminary results about correlation functions.Comment: 12 pages, 7 figure
Van Hove singularity and spontaneous Fermi surface symmetry breaking in Sr3Ru2O7
The most salient features observed around a metamagnetic transition in
Sr3Ru2O7 are well captured in a simple model for spontaneous Fermi surface
symmetry breaking under a magnetic field, without invoking a putative quantum
critical point. The Fermi surface symmetry breaking happens in both a majority
and a minority spin band but with a different magnitude of the order parameter,
when either band is tuned close to van Hove filling by the magnetic field. The
transition is second order for high temperature T and changes into first order
for low T. The first order transition is accompanied by a metamagnetic
transition. The uniform magnetic susceptibility and the specific heat
coefficient show strong T dependence, especially a log T divergence at van Hove
filling. The Fermi surface instability then cuts off such non-Fermi liquid
behavior and gives rise to a cusp in the susceptibility and a specific heat
jump at the transition temperature.Comment: 11 pages, 4 figure
Coupling a Point-Like Mass to Quantum Gravity with Causal Dynamical Triangulations
We present a possibility of coupling a point-like, non-singular, mass
distribution to four-dimensional quantum gravity in the nonperturbative setting
of causal dynamical triangulations (CDT). In order to provide a point of
comparison for the classical limit of the matter-coupled CDT model, we derive
the spatial volume profile of the Euclidean Schwarzschild-de Sitter space glued
to an interior matter solution. The volume profile is calculated with respect
to a specific proper-time foliation matching the global time slicing present in
CDT. It deviates in a characteristic manner from that of the pure-gravity
model. The appearance of coordinate caustics and the compactness of the mass
distribution in lattice units put an upper bound on the total mass for which
these calculations are expected to be valid. We also discuss some of the
implementation details for numerically measuring the expectation value of the
volume profiles in the framework of CDT when coupled appropriately to the
matter source.Comment: 26 pages, 9 figures, updated published versio
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