Results 1  10
of
19
Anyons in an exactly solved model and beyond
, 2005
"... A spin 1/2 system on a honeycomb lattice is studied. The interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength. The model is solved exactly by a reduction to free fermions in a static Z2 gauge f ..."
Abstract

Cited by 30 (2 self)
 Add to MetaCart
(Show Context)
A spin 1/2 system on a honeycomb lattice is studied. The interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength. The model is solved exactly by a reduction to free fermions in a static Z2 gauge field. A phase diagram in the parameter space is obtained. One of the phases has an energy gap and carries excitations that are Abelian anyons. The other phase is gapless, but acquires a gap in the presence of magnetic field. In the latter case excitations are nonAbelian anyons whose braiding rules coincide with those of conformal blocks for the Ising model. We also consider a general theory of free fermions with a gapped spectrum, which is characterized by a spectral Chern number ν. The Abelian and nonAbelian phases of the original model correspond to ν = 0 and ν = ±1, respectively. The anyonic properties of excitation depend on ν mod 16, whereas ν itself governs edge thermal transport. The paper also provides mathematical background on anyons as well as an elementary theory of Chern number for quasidiagonal matrices.
Stability of relativistic matter with magnetic
, 1997
"... Abstract. We give a proof of stability of relativistic matter with magnetic fields all the way up to the critical value of the nuclear charge Zα = 2/π. 1. ..."
Abstract

Cited by 15 (6 self)
 Add to MetaCart
(Show Context)
Abstract. We give a proof of stability of relativistic matter with magnetic fields all the way up to the critical value of the nuclear charge Zα = 2/π. 1.
States and Flux Configurations of the TwoDimensional FalicovKimball Model
 Theory of Electronic Diamagnetism in TwoDimensional Lattices, Phys
"... The FalicovKimball model is a lattice model of itinerant spinless fermions ("electrons") interacting by an onsite potential with classical particles ("ions"). We continue the investigations of the crystalline ground states that appear for various filling of electrons and ions f ..."
Abstract

Cited by 12 (0 self)
 Add to MetaCart
(Show Context)
The FalicovKimball model is a lattice model of itinerant spinless fermions ("electrons") interacting by an onsite potential with classical particles ("ions"). We continue the investigations of the crystalline ground states that appear for various filling of electrons and ions for large coupling. We investigate the model for square as well as triangular lattices. New ground states are found and the effects of a magnetic flux on the structure of the phase diagram are studied. The flux phase problem where one has to find the optimal flux configurations and the nuclei configurations is also solved in some cases. Finally we consider a model where the fermions are replaced by hardcore bosons. This model also has crystalline ground states. Therefore their existence does not require the Pauli principle, but only the onsite hardcore constraint for the itinerant particles. KEY WORDS: angular lattice. FalicovKimball model; hardcore bosons; flux phase; tri1.
Reflection positivity and phase transitions in lattice spin models, Methods of contemporary mathematical statistical physics
 Lecture Notes in Math
, 1970
"... ..."
(Show Context)
Recent developments in quantum mechanics with magnetic fields
 Proc. of Symposia in Pure Math. Vol 76 Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon’s 60th Birthday Part
, 2006
"... We present a review on the recent developments concerning rigorous mathematical results on Schrödinger operators with magnetic fields. This paper is dedicated to the sixtieth birthday of Barry Simon. ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
(Show Context)
We present a review on the recent developments concerning rigorous mathematical results on Schrödinger operators with magnetic fields. This paper is dedicated to the sixtieth birthday of Barry Simon.
A simple proof of HardyLiebThirring inequalities
 Comm. Math. Phys
"... Abstract. We give a short and unified proof of HardyLiebThirring inequalities for moments of eigenvalues of fractional Schrödinger operators. The proof covers the optimal parameter range. It is based on a recent inequality by Solovej, Sørensen, and Spitzer. Moreover, we prove that any nonmagnetic ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
Abstract. We give a short and unified proof of HardyLiebThirring inequalities for moments of eigenvalues of fractional Schrödinger operators. The proof covers the optimal parameter range. It is based on a recent inequality by Solovej, Sørensen, and Spitzer. Moreover, we prove that any nonmagnetic LiebThirring inequality implies a magnetic LiebThirring inequality (with possibly a larger constant). 1. Introduction and
Discrete random electromagnetic Laplacians
 in the Mathematical Physics Preprint Archive, mp arc@math.utexas.edu
, 1995
"... We consider discrete random magnetic Laplacians in the plane and discrete random electromagnetic Laplacians in higher dimensions. The existence of these objects relies on a theorem of FeldmanMoore which was generalized by Lind to the nonabelian case. For example, it allows to realize ergodic Schrod ..."
Abstract

Cited by 5 (4 self)
 Add to MetaCart
We consider discrete random magnetic Laplacians in the plane and discrete random electromagnetic Laplacians in higher dimensions. The existence of these objects relies on a theorem of FeldmanMoore which was generalized by Lind to the nonabelian case. For example, it allows to realize ergodic Schrodinger operators with stationary independent magnetic fields on discrete two dimensional lattices including also nonperiodic situations like Penrose lattices. The theorem is generalized here to higher dimensions. The Laplacians obtained from the electromagnetic vector potential are elements of a von Neumann algebra constructed from the underlying dynamical system respectively from the ergodic equivalence relation. They generalize Harper operators which correspond to constant magnetic fields. For independent identically distributed magnetic fields and special Anderson models, we compute the density of states using a random walk expansion. Mathematics subject classification: 28D15, 47A10, 47A3...
REMARKS ON EIGENVALUE ESTIMATES AND SEMIGROUP DOMINATION
, 2009
"... We present an overview over recent results concerning semiclassical spectral estimates for magnetic Schrödinger operators. We discuss how the constants in magnetic and nonmagnetic eigenvalue bounds are related and we prove, in an abstract setting, that any nonmagnetic LiebThirringtype inequalit ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
(Show Context)
We present an overview over recent results concerning semiclassical spectral estimates for magnetic Schrödinger operators. We discuss how the constants in magnetic and nonmagnetic eigenvalue bounds are related and we prove, in an abstract setting, that any nonmagnetic LiebThirringtype inequality implies a magnetic LiebThirringtype inequality with possibly a larger constant.