25 research outputs found
Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
We study the ground state properties of the critical Lipkin-Meshkov-Glick
model. Using the Holstein-Primakoff boson representation, and the continuous
unitary transformation technique, we compute explicitly the finite-size scaling
exponents for the energy gap, the ground state energy, the magnetization, and
the spin-spin correlation functions. Finally, we discuss the behavior of the
two-spin entanglement in the vicinity of the phase transition.Comment: 4 pages, published versio
Finite-size scaling exponents and entanglement in the two-level BCS model
We analyze the finite-size properties of the two-level BCS model. Using the
continuous unitary transformation technique, we show that nontrivial scaling
exponents arise at the quantum critical point for various observables such as
the magnetization or the spin-spin correlation functions. We also discuss the
entanglement properties of the ground state through the concurrence which
appears to be singular at the transition.Comment: 4 pages, 3 figures, published versio
Emergent Fermions and Anyons in the Kitaev Model
We study the gapped phase of the Kitaev model on the honeycomb lattice using
perturbative continuous unitary transformations. The effective low-energy
Hamiltonian is found to be an extended toric code with interacting anyons.
High-energy excitations are emerging free fermions which are composed of
hardcore bosons with an attached string of spin operators. The excitation
spectrum is mapped onto that of a single particle hopping on a square lattice
in a magnetic field. We also illustrate how to compute correlation functions in
this framework. The present approach yields analytical perturbative results in
the thermodynamical limit without using the Majorana or the Jordan-Wigner
fermionization initially proposed to solve this problem.Comment: 4 pages, 5 figures, published versio
Perturbative study of the Kitaev model with spontaneous time-reversal symmetry breaking
We analyze the Kitaev model on the triangle-honeycomb lattice whose ground
state has recently been shown to be a chiral spin liquid. We consider two
perturbative expansions: the isolated-dimer limit containing Abelian anyons and
the isolated-triangle limit. In the former case, we derive the low-energy
effective theory and discuss the role played by multi-plaquette interactions.
In this phase, we also compute the spin-spin correlation functions for any
vortex configuration. In the isolated-triangle limit, we show that the
effective theory is, at lowest nontrivial order, the Kitaev honeycomb model at
the isotropic point. We also compute the next-order correction which opens a
gap and yields non-Abelian anyons.Comment: 7 pages, 4 figures, published versio
Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model
We analyze the finite-size scaling exponents in the Lipkin-Meshkov-Glick
model by means of the Holstein-Primakoff representation of the spin operators
and the continuous unitary transformations method. This combination allows us
to compute analytically leading corrections to the ground state energy, the
gap, the magnetization, and the two-spin correlation functions. We also present
numerical calculations for large system size which confirm the validity of this
approach. Finally, we use these results to discuss the entanglement properties
of the ground state focusing on the (rescaled) concurrence that we compute in
the thermodynamical limit.Comment: 20 pages, 9 figures, published versio
Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model
We establish a relation between several entanglement properties in the
Lipkin-Meshkov-Glick model, which is a system of mutually interacting spins
embedded in a magnetic field. We provide analytical proofs that the single-copy
entanglement and the global geometric entanglement of the ground state close to
and at criticality behave as the entanglement entropy. These results are in
deep contrast to what is found in one- dimensional spin systems where these
three entanglement measures behave differently.Comment: 4 pages, 2 figures, published versio
Bound states in two-dimensional spin systems near the Ising limit: A quantum finite-lattice study
We analyze the properties of low-energy bound states in the transverse-field
Ising model and in the XXZ model on the square lattice. To this end, we develop
an optimized implementation of perturbative continuous unitary transformations.
The Ising model is studied in the small-field limit which is found to be a
special case of the toric code model in a magnetic field. To analyze the XXZ
model, we perform a perturbative expansion about the Ising limit in order to
discuss the fate of the elementary magnon excitations when approaching the
Heisenberg point.Comment: 21 pages, 18 figures, published versio
Perturbative approach to an exactly solved problem: the Kitaev honeycomb model
We analyze the gapped phase of the Kitaev honeycomb model perturbatively in
the isolated-dimer limit. Our analysis is based on the continuous unitary
transformations method which allows one to compute the spectrum as well as
matrix elements of operators between eigenstates, at high order. The starting
point of our study consists in an exact mapping of the original honeycomb spin
system onto a square-lattice model involving an effective spin and a hardcore
boson. We then derive the low-energy effective Hamiltonian up to order 10 which
is found to describe an interacting-anyon system, contrary to the order 4
result which predicts a free theory. These results give the ground-state energy
in any vortex sector and thus also the vortex gap, which is relevant for
experiments. Furthermore, we show that the elementary excitations are emerging
free fermions composed of a hardcore boson with an attached spin- and phase-
operator string. We also focus on observables and compute, in particular, the
spin-spin correlation functions. We show that they admit a multi-plaquette
expansion that we derive up to order 6. Finally, we study the creation and
manipulation of anyons with local operators, show that they also create
fermions, and discuss the relevance of our findings for experiments in optical
lattices.Comment: 28 pages, 25 figure
Finite-size scaling exponents in the interacting boson model
We investigate the finite-size scaling exponents for the critical point at
the shape phase transition from U(5) (spherical) to O(6) (deformed
-unstable) dynamical symmetries of the Interacting Boson Model, making
use of the Holstein-Primakoff boson expansion and the continuous unitary
transformation technique. We compute exactly the leading order correction to
the ground state energy, the gap, the expectation value of the -boson number
in the ground state and the transition probability from the ground state
to the first excited state, and determine the corresponding finite-size scaling
exponents.Comment: 4 pages, 3 figures, published versio
Robustness of a perturbed topological phase
We investigate the stability of the topological phase of the toric code model in the presence of a uniform magnetic field by means of variational and high-order series expansion approaches. We find that when this perturbation is strong enough, the system undergoes a topological phase transition whose first- or second-order nature depends on the field orientation. When this transition is of second order, it is in the Ising universality class except for a special line on which the critical exponent driving the closure of the gap varies continuously, unveiling a new topological universality class. © 2011 American Physical Society