526 research outputs found
A Class of Parameter Dependent Commuting Matrices
We present a novel class of real symmetric matrices in arbitrary dimension
, linearly dependent on a parameter . The matrix elements satisfy a set
of nontrivial constraints that arise from asking for commutation of pairs of
such matrices for all , and an intuitive sufficiency condition for the
solvability of certain linear equations that arise therefrom. This class of
matrices generically violate the Wigner von Neumann non crossing rule, and is
argued to be intimately connected with finite dimensional Hamiltonians of
quantum integrable systems.Comment: Latex, Added References, Typos correcte
Superconductivity in CoO Layers and the Resonating Valence Bond Mean Field Theory of the Triangular Lattice t-J model
Motivated by the recent discovery of superconductivity in two dimensional
CoO layers, we present some possibly useful results of the RVB mean field
theory applied to the triangular lattice. Away from half filling, the order
parameter is found to be complex, and yields a fully gapped quasiparticle
spectrum. The sign of the hopping plays a crucial role in the analysis, and we
find that superconductivity is as fragile for one sign as it is robust for the
other. NaCoOHO is argued to belong to the robust case, by
comparing the LDA Fermi surface with an effective tight binding model. The high
frequency Hall constant in this system is potentially interesting, since it is
pointed out to increase linearly with temperature without saturation for T
T.Comment: Published in Physical Review B, total 1 tex + 9 eps files. Erratum
added as separate tex file on November 7, 2003, a numerical factor corrected
in the erratum on Dec 3, 200
Including a phase in the Bethe equations of the Hubbard model
We compute the Bethe equations of generalized Hubbard models, and study their
thermodynamical limit. We argue how they can be connected to the ones found in
the context of AdS/CFT correspondence, in particular with the so-called
dressing phase problem. We also show how the models can be interpreted, in
condensed matter physics, as integrable multi-leg Hubbard models.Comment: 30 page
The Origin of Degeneracies and Crossings in the 1d Hubbard Model
The paper is devoted to the connection between integrability of a finite
quantum system and degeneracies of its energy levels. In particular, we analyze
in detail the energy spectra of finite Hubbard chains. Heilmann and Lieb
demonstrated that in these systems there are crossings of levels of the same
parameter independent symmetry. We show that this apparent violation of the
Wigner-von Neumann noncrossing rule follows directly from the existence of
nontrivial conservation laws and is a characteristic signature of quantum
integrability. The energy spectra of Hubbard chains display many instances of
permanent (at all values of the coupling) twofold degeneracies that cannot be
explained by parameter independent symmetries. We relate these degeneracies to
the different transformation properties of the conserved currents under spatial
reflections and the particle-hole transformation and estimate the fraction of
doubly degenerate states. We also discuss multiply degenerate eigenstates of
the Hubbard Hamiltonian. The wave functions of many of these states do not
depend on the coupling, which suggests the existence of an additional parameter
independent symmetry.Comment: 25 pages, 12 figure
Magnetization plateaux in an extended Shastry-Sutherland model
We study an extended two-dimensional Shastry-Sutherland model in a magnetic
field where besides the usual Heisenberg exchanges of the Shastry-Sutherland
model two additional SU(2) invariant couplings are included. Perturbative
continous unitary transformations are used to determine the leading order
effects of the additional couplings on the pure hopping and on the long-range
interactions between the triplons which are the most relevant terms for small
magnetization. We then compare the energy of various magnetization plateaux in
the classical limit and we discuss the implications for the two-dimensional
quantum magnet SrCu(BO).Comment: 8 pages, Proceedings of the HFM2008 Conferenc
Fermionic R-Operator and Integrability of the One-Dimensional Hubbard Model
We propose a new type of the Yang-Baxter equation (YBE) and the decorated
Yang-Baxter equation (DYBE). Those relations for the fermionic R-operator were
introduced recently as a tool to treat the integrability of the fermion models.
Using the YBE and the DYBE for the XX fermion model, we construct the fermionic
R-operator for the one-dimensional (1D) Hubbard model. It gives another proof
of the integrability of the 1D Hubbard model. Furthermore a new approach to the
SO(4) symmetry of the 1D Hubbard model is discussed.Comment: 25 page
Quantum spin models with exact dimer ground states
Inspired by the exact solution of the Majumdar-Ghosh model, a family of
one-dimensional, translationally invariant spin hamiltonians is constructed.
The exchange coupling in these models is antiferromagnetic, and decreases
linearly with the separation between the spins. The coupling becomes
identically zero beyond a certain distance. It is rigorously proved that the
dimer configuration is an exact, superstable ground state configuration of all
the members of the family on a periodic chain. The ground state is two-fold
degenerate, and there exists an energy gap above the ground state. The
Majumdar-Ghosh hamiltonian with two-fold degenerate dimer ground state is just
the first member of the family.
The scheme of construction is generalized to two and three dimensions, and
illustrated with the help of some concrete examples. The first member in two
dimensions is the Shastry-Sutherland model. Many of these models have
exponentially degenerate, exact dimer ground states.Comment: 10 pages, 8 figures, revtex, to appear in Phys. Rev.
Extremely Correlated Quantum Liquids
We formulate the theory of an extremely correlated electron liquid,
generalizing the standard Fermi liquid. This quantum liquid has specific
signatures in various physical properties, such as the Fermi surface volume and
the narrowing of electronic bands by spin and density correlation functions.
We use Schwinger's source field idea to generate equations for the Greens
function for the Hubbard operators. A local (matrix) scale transformation in
the time domain to a quasiparticle Greens function, is found to be optimal.
This transformation allows us to generate vertex functions that are guaranteed
to reduce to the bare values for high frequencies, i.e. are ``asymptotically
free''. The quasiparticles are fractionally charged objects, and we find an
exact Schwinger Dyson equation for their Greens function. We find a hierarchy
of equations for the vertex functions, and further we obtain Ward identities so
that systematic approximations are feasible.
An expansion in terms of the density of holes measured from the Mott Hubbard
insulating state follows from the nature of the theory. A systematic
presentation of the formalism is followed by some preliminary explicit
calculations.Comment: 40 pages, typos remove
Raman Scattering and Anomalous Current Algebra: Observation of Chiral Bound State in Mott Insulators
Recent experiments on inelastic light scattering in a number of insulating
cuprates [1] revealed a new excitation appearing in the case of crossed
polarizations just below the optical absorption threshold. This observation
suggests that there exists a local exciton-like state with an odd parity with
respect to a spatial reflection. We present the theory of high energy large
shift Raman scattering in Mott insulators and interpret the experiment [1] as
an evidence of a chiral bound state of a hole and a doubly occupied site with a
topological magnetic excitation. A formation of these composites is a crucial
feature of various topological mechanisms of superconductivity. We show that
inelastic light scattering provides an instrument for direct measurements of a
local chirality and anomalous terms in the electronic current algebra.Comment: 18 pages, TeX, C Version 3.
Striped phase in a quantum XY-model with ring exchange
We present quantum Monte Carlo results for a square-lattice S=1/2 XY-model
with a standard nearest-neighbor coupling J and a four-spin ring exchange term
K. Increasing K/J, we find that the ground state spin-stiffness vanishes at a
critical point at which a spin gap opens and a striped bond-plaquette order
emerges. At still higher K/J, this phase becomes unstable and the system
develops a staggered magnetization. We discuss the quantum phase transitions
between these phases.Comment: 4 pages, 4 figures. v2: only minor change
- …