18,640 research outputs found
Phases of the generalized two-leg spin ladder: A view from the SU(4) symmetry
The zero-temperature phases of a generalized two-leg spin ladder with
four-spin exchanges are discussed by means of a low-energy field theory
approach starting from an SU(4) quantum critical point. The latter fixed point
is shown to be a rich multicritical point which unifies different competing
dimerized orders and a scalar chirality phase which breaks spontaneously the
time-reversal symmetry. The quantum phase transition between these phases is
governed by spin-singlet fluctuations and belongs to the Luttinger universality
class due to the existence of an exact U(1) self-duality symmetry.Comment: 5 pages, 1 figur
Exactly solvable Kitaev model in three dimensions
We introduce a spin-1/2 model in three dimensions which is a generalization
of the well-known Kitaev model on a honeycomb lattice. Following Kitaev, we
solve the model exactly by mapping it to a theory of non-interacting fermions
in the background of a static Z_2 gauge field. The phase diagram consists of a
gapped phase and a gapless one, similar to the two-dimensional case.
Interestingly, unlike in the two-dimensional model, in the gapless phase the
gap vanishes on a contour in the k space. Furthermore, we show that the flux
excitations of the gauge field, due to some local constraints, form loop like
structures; such loops exist on a lattice formed by the plaquettes in the
original lattice and is topologically equivalent to the pyrochlore lattice.
Finally, we derive a low-energy effective Hamiltonian that can be used to study
the properties of the excitations in the gapped phase.Comment: 9 pages, 7 figures; published version; a new section and more
references adde
Quasi-adiabatic Continuation of Quantum States: The Stability of Topological Ground State Degeneracy and Emergent Gauge Invariance
We define for quantum many-body systems a quasi-adiabatic continuation of
quantum states. The continuation is valid when the Hamiltonian has a gap, or
else has a sufficiently small low-energy density of states, and thus is away
from a quantum phase transition. This continuation takes local operators into
local operators, while approximately preserving the ground state expectation
values. We apply this continuation to the problem of gauge theories coupled to
matter, and propose a new distinction, perimeter law versus "zero law" to
identify confinement. We also apply the continuation to local bosonic models
with emergent gauge theories. We show that local gauge invariance is
topological and cannot be broken by any local perturbations in the bosonic
models in either continuous or discrete gauge groups. We show that the ground
state degeneracy in emergent discrete gauge theories is a robust property of
the bosonic model, and we argue that the robustness of local gauge invariance
in the continuous case protects the gapless gauge boson.Comment: 15 pages, 6 figure
Bulk and Edge excitations in a quantum Hall ferromagnet
In this article, we shall focus on the collective dynamics of the fermions in
a quantum Hall droplet. Specifically, we propose to look at the
quantum Hall ferromagnet. In this system, the electron spins are ordered in the
ground state due to the exchange part of the Coulomb interaction and the Pauli
exclusion principle. The low energy excitations are ferromagnetic magnons. To
provide a means for describing these magnons, we shall discuss a method of
introducing collective coordinates in the Hilbert space of many-fermion
systems. These collective coordinates are bosonic in nature. They map a part of
the fermionic Hilbert space into a bosonic Hilbert space. Using this technique,
we shall interpret the magnons as bosonic collective ex citations in the
Hilbert space of the many-electron Hall system. By considering a Hall droplet
of finite extent, we shall also obtain the effective Lagrangian governing the
spin collective excitations at the edge of the sample.Comment: Plain TeX 18 Pages Proceedings for the Y2K conference on strongly c
orrelated fermionic systems, Calcutta, Indi
Thermodynamics with density and temperature dependent particle masses and properties of bulk strange quark matter and strangelets
Thermodynamic formulas for investigating systems with density and/or
temperature dependent particle masses are generally derived from the
fundamental derivation equality of thermodynamics. Various problems in the
previous treatments are discussed and modified. Properties of strange quark
matter in bulk and strangelets at both zero and finite temperature are then
calculated based on the new thermodynamic formulas with a new quark mass
scaling, which indicates that low mass strangelets near beta equilibrium are
multi-quark states with an anti-strange quark, such as the pentaquark
(u^2d^2\bar{s}) for baryon nmber 1 and the octaquark (u^4d^3\bar{s}) for
dibaryon etc.Comment: 14 pages, 12 figures, Revtex4 styl
The Grassmannian Sigma Model in SU(2) Yang-Mills Theory
Spin-charge separation in pure SU(2) Yang-Mills theory was recently found to
involve the dynamics of an O(3) non-linear sigma model and, seemingly, a
Grassmannian non-linear sigma model. In this article we explicitly construct
the Grassmannian sigma model of the form appearing in the the spin-charge
separated SU(2) theory through a quaternionic decomposition of the manifold,
thus verifying its relevance in this context. The coupling between this model
and the O(3) non-linear sigma model is further commented upon.Comment: 11 pages, undergraduate research project; version published in J.
Phys.
Non-canonical statistics of finite quantum system
The canonical statistics describes the statistical properties of an open
system by assuming its coupling with the heat bath infinitesimal in comparison
with the total energy in thermodynamic limit. In this paper, we generally
derive a non-canonical distribution for the open system with a finite coupling
to the heat bath, which deforms the energy shell to effectively modify the
conventional canonical way. The obtained non-canonical distribution reflects
the back action of system on the bath, and thus depicts the statistical
correlations through energy fluctuations
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