166 research outputs found
The geometric order of stripes and Luttinger liquids
It is argued that the electron stripes as found in correlated oxides have to
do with an unrecognized form of order. The manifestation of this order is the
robust property that the charge stripes are at the same time anti-phase
boundaries in the spin system. We demonstrate that the quantity which is
ordering is sublattice parity, referring to the geometric property of a
bipartite lattice that it can be subdivided in two sublattices in two different
ways. Re-interpreting standard results of one dimensional physics, we
demonstrate that the same order is responsible for the phenomenon of
spin-charge separation in strongly interacting one dimensional electron
systems. In fact, the stripe phases can be seen from this perspective as the
precise generalization of the Luttinger liquid to higher dimensions. Most of
this paper is devoted to a detailed exposition of the mean-field theory of
sublattice parity order in 2+1 dimensions. Although the quantum-dynamics of the
spin- and charge degrees of freedom is fully taken into account, a perfect
sublattice parity order is imposed. Due to novel order-out-of-disorder physics,
the sublattice parity order gives rise to full stripe order at long wavelength.
This adds further credibility to the notion that stripes find their origin in
the microscopic quantum fluctuations and it suggests a novel viewpoint on the
relationship between stripes and high Tc superconductivity.Comment: 29 pages, 14 figures, 1 tabl
Field induced d_x^2-y^2+id_xy state in d-density-wave metals
We argue that the d_{xy} component of the order parameter can be generated to
form the d_x^2-y^2+id_xy-density wave state by the external magnetic field. The
driving force for this transition is the coupling of the magnetic field with
the orbital magnetism. The fully gapped particle spectrum and the magnetically
active collective mode of the condensate are discussed as a possible signature
of the d+id' density wave state.Comment: 5 pages, 2 color figure
Systematic Density Expansion of the Lyapunov Exponents for a Two-dimensional Random Lorentz Gas
We study the Lyapunov exponents of a two-dimensional, random Lorentz gas at
low density. The positive Lyapunov exponent may be obtained either by a direct
analysis of the dynamics, or by the use of kinetic theory methods. To leading
orders in the density of scatterers it is of the form
, where and are
known constants and is the number density of scatterers expressed
in dimensionless units. In this paper, we find that through order
, the positive Lyapunov exponent is of the form
. Explicit numerical values of the new constants
and are obtained by means of a systematic analysis. This takes into
account, up to , the effects of {\it all\/} possible
trajectories in two versions of the model; in one version overlapping scatterer
configurations are allowed and in the other they are not.Comment: 12 pages, 9 figures, minor changes in this version, to appear in J.
Stat. Phy
Hidden order in bosonic gases confined in one dimensional optical lattices
We analyze the effective Hamiltonian arising from a suitable power series
expansion of the overlap integrals of Wannier functions for confined bosonic
atoms in a 1d optical lattice. For certain constraints between the coupling
constants, we construct an explicit relation between such an effective bosonic
Hamiltonian and the integrable spin- anisotropic Heisenberg model. Therefore
the former results to be integrable by construction. The field theory is
governed by an anisotropic non linear -model with singlet and triplet
massive excitations; such a result holds also in the generic non-integrable
cases. The criticality of the bosonic system is investigated. The schematic
phase diagram is drawn. Our study is shedding light on the hidden symmetry of
the Haldane type for one dimensional bosons.Comment: 5 pages; 1 eps figure. Revised version, to be published in New. J.
Phy
Geometry and the Hidden Order of Luttinger Liquids: the Universality of Squeezed Space
We present the case that Luttinger liquids are characterized by a form of
hidden order which is similar, but distinct in some crucial regards, to the
hidden order characterizing spin-1 Heisenberg chains. We construct a string
correlator for the Luttinger liquid which is similar to the string correlator
constructed by den Nijs and Rommelse for the spin chain. From a geometric
prespective on the so-called `squeezed space' construction, we demonstrate that
the physics at long wavelength can be reformulated in terms of a gauge
theory. Peculiarly, the normal spin chain lives at infinite gauge coupling
where it is characterized by deconfinement. We identify the microscopic
conditions required for confinement thereby identifying a novel phase of the
spin-chain. We demonstrate that the Luttinger liquid can be approached in the
same general framework. The difference from the spin chain is that the gauge
sector is critical in the sense that the Luttinger liquid is at the phase
boundary where the local symmetry emerges. We evaluate the string
correlator analytically and show that the squeezed space structure is present
both for the strongly coupled Hubbard model and the non-interacting fermion
gas. These structures are hard-wired in the mathematical structure of
bosonization and this becomes obvious by considering string correlators.
Numerical results are presented for the string correlator using a non-abelian
version of the density matrix renormalization group algorithm, confirming in
detail the expectations following from the theory. We conclude with some
observations regarding the generalization of bosonization to higher dimensions.Comment: 24 pages, 14 eps figures, Revtex
Impurity induced resonant state in a pseudogap state of a high temperature superconductor
We predict a resonance impurity state generated by the substitution of one Cu
atom with a nonmagnetic atom, such as Zn, in the pseudogap state of a high-T_c
superconductor. The precise microscopic origin of the pseudogap is not
important for this state to be formed, in particular this resonance will be
present even in the absence of superconducting fluctuations in the normal
state. In the presence of superconducting fluctuations, we predict the
existence of a counterpart impurity peak on a symmetric bias.
The nature of impurity resonance is similar to the previously studied
resonance in the d-wave superconducting state.Comment: 4 pages, 2 figure
Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
In this work, we illustrate how a Jordan-Wigner transformation combined with
symmetry considerations enables a direct solution of Kitaev's model on the
honeycomb lattice. We (i) express the p-wave type fermionic ground states of
this system in terms of the original spins, (ii) adduce that symmetry alone
dictates the existence of string and planar brane type correlators and their
composites, (iii) compute the value of such non-local correlators by employing
the Jordan-Wigner transformation, (iv) affirm that the spectrum is
inconsequential to the existence of topological quantum order and that such
information is encoded in the states themselves, and (v) express the anyonic
character of the excitations in this system and the local symmetries that it
harbors in terms of fermions.Comment: 14 pages, 7 figure
Quasiparticle States around a Nonmagnetic Impurity in D-Density-Wave State of High- Cuprates
Recently Chakravarty {\em et al.} proposed an ordered -density wave (DDW)
state as an explanation of the pseudogap phase in underdoped high-temperature
cuprates. We study the competition between the DDW and superconducting ordering
based on an effective mean-field Hamiltonian. We are mainly concerned with the
effect of the DDW ordering on the electronic state around a single nonmagnetic
impurity. We find that a single subgap resonance peak appears in the local
density of state around the impurity. In the unitary limit, the position of
this resonance peak is always located at with respect to the Fermi
energy. This result is dramatically different from the case of the pure
superconducting state for which the impurity resonant energy is approximately
pinned at the Fermi level. This can be used to probe the existence of the DDW
ordering in cuprates.Comment: 4 pages, 4 figure
Mechanism of pseudogap probed by a local impurity
The response to a local strong non-magnetic impurity in the pseudogap phase
is examined in two distinctly different scenarios: phase-fluctuation (PF) of
pairing field and d-density-wave (DDW) order. In the PF scenario, the resonance
state is generally double-peaked near the Fermi level, and is abruptly
broadened by vortex fluctuations slightly above the transition temperature. In
the DDW scenario, the resonance is single-peaked and remains sharp up to
gradual intrinsic thermal broadening, and the resonance energy is analytically
determined to be at minus of the chemical potential.Comment: 4 pages, 2 figure
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