159 research outputs found
Renyi Entropies of Interacting Fermions from Determinantal Quantum Monte Carlo Simulations
Entanglement measures such as the entanglement entropy have become an
indispensable tool to identify the fundamental character of ground states of
interacting quantum many-body systems. For systems of interacting spin or
bosonic degrees of freedom much recent progress has been made not only in the
analytical description of their respective entanglement entropies but also in
their numerical classification. Systems of interacting fermionic degrees of
freedom however have proved to be more difficult to control, in particular with
regard to the numerical understanding of their entanglement properties. Here we
report a generalization of the replica technique for the calculation of Renyi
entropies to the framework of determinantal Quantum Monte Carlo simulations --
the numerical method of choice for unbiased, large-scale simulations of
interacting fermionic systems. We demonstrate the strength of this approach
over a recent alternative proposal based on a decomposition in free fermion
Green's functions by studying the entanglement entropy of one-dimensional
Hubbard systems both at zero and finite temperatures.Comment: 11 pages, 10 figure
Topological Order and Quantum Criticality
In this chapter we discuss aspects of the quantum critical behavior that
occurs at a quantum phase transition separating a topological phase from a
conventionally ordered one. We concentrate on a family of quantum lattice
models, namely certain deformations of the toric code model, that exhibit
continuous quantum phase transitions. One such deformation leads to a
Lorentz-invariant transition in the 3D Ising universality class. An alternative
deformation gives rise to a so-called conformal quantum critical point where
equal-time correlations become conformally invariant and can be related to
those of the 2D Ising model. We study the behavior of several physical
observables, such as non-local operators and entanglement entropies, that can
be used to characterize these quantum phase transitions. Finally, we briefly
consider the role of thermal fluctuations and related phase transitions, before
closing with a short overview of field theoretical descriptions of these
quantum critical points.Comment: 24 pages, 7 figures, chapter of the book "Understanding Quantum Phase
Transitions", edited by Lincoln D. Carr (CRC Press / Taylor and Francis,
2010); v2: updated reference
Spin-Peierls Instability of Three-Dimensional Spin Liquids with Majorana Fermi Surfaces
Three-dimensional (3D) variants of the Kitaev model can harbor gapless spin
liquids with a Majorana Fermi surface on certain tricoordinated lattice
structures such as the recently introduced hyperoctagon lattice. Here we
investigate Fermi surface instabilities arising from additional spin exchange
terms (such as a Heisenberg coupling) which introduce interactions between the
emergent Majorana fermion degrees of freedom. We show that independent of the
sign and structure of the interactions, the Majorana surface is always
unstable. Generically the system spontaneously doubles its unit cell at
exponentially small temperatures and forms a spin liquid with line nodes.
Depending on the microscopics further symmetries of the system can be broken at
this transition. These spin-Peierls instabilities of a 3D spin liquid are
closely related to BCS instabilities of fermions.Comment: 7 pages, 3 figure
Optimized ensemble Monte Carlo simulations of dense Lennard-Jones fluids
We apply the recently developed adaptive ensemble optimization technique to
simulate dense Lennard-Jones fluids and a particle-solvent model by
broad-histogram Monte Carlo techniques. Equilibration of the simulated fluid is
improved by sampling an optimized histogram in radial coordinates that shifts
statistical weight towards the entropic barriers between the shells of the
liquid. Interstitial states in the vicinity of these barriers are identified
with unprecedented accuracy by sharp signatures in the quickly converging
histogram and measurements of the local diffusivity. The radial distribution
function and potential of mean force are calculated to high precision.Comment: 4.2 pages, 6 figure
Finite-temperature phase diagram of the Heisenberg-Kitaev model
We discuss the finite-temperature phase diagram of the Heisenberg-Kitaev
model on the hexagonal lattice, which has been suggested to describe the
spin-orbital exchange of the effective spin-1/2 momenta in the Mott insulating
Iridate Na2IrO3. At zero-temperature this model exhibits magnetically ordered
states well beyond the isotropic Heisenberg limit as well as an extended
gapless spin liquid phase around the highly anisotropic Kitaev limit. Using a
pseudofermion functional renormalization group (RG) approach, we extract both
the Curie-Weiss scale and the critical ordering scale (for the magnetically
ordered states) from the RG flow of the magnetic susceptibility. The
Curie-Weiss scale switches sign -- indicating a transition of the dominant
exchange from antiferromagnetic to ferromagnetic -- deep in the magnetically
ordered regime. For the latter we find no significant frustration, i.e. a
substantial suppression of the ordering scale with regard to the Curie-Weiss
scale. We discuss our results in light of recent experimental susceptibility
measurements for Na2IrO3.Comment: 4+e pages, 5 figure
A R\'enyi entropy perspective on topological order in classical toric code models
Concepts of information theory are increasingly used to characterize
collective phenomena in condensed matter systems, such as the use of
entanglement entropies to identify emergent topological order in interacting
quantum many-body systems. Here we employ classical variants of these concepts,
in particular R\'enyi entropies and their associated mutual information, to
identify topological order in classical systems. Like for their quantum
counterparts, the presence of topological order can be identified in such
classical systems via a universal, subleading contribution to the prevalent
volume and boundary laws of the classical R\'enyi entropies. We demonstrate
that an additional subleading contribution generically arises for all
R\'enyi entropies with when driving the system towards a
phase transition, e.g. into a conventionally ordered phase. This additional
subleading term, which we dub connectivity contribution, tracks back to partial
subsystem ordering and is proportional to the number of connected parts in a
given bipartition. Notably, the Levin-Wen summation scheme -- typically used to
extract the topological contribution to the R\'enyi entropies -- does not fully
eliminate this additional connectivity contribution in this classical context.
This indicates that the distillation of topological order from R\'enyi
entropies requires an additional level of scrutiny to distinguish topological
from non-topological contributions. This is also the case for quantum
systems, for which we discuss which entropies are sensitive to these
connectivity contributions. We showcase these findings by extensive numerical
simulations of a classical variant of the toric code model, for which we study
the stability of topological order in the presence of a magnetic field and at
finite temperatures from a R\'enyi entropy perspective.Comment: 17 pages, 19 figure
Perturbed vortex lattices and the stability of nucleated topological phases
We study the stability of nucleated topological phases that can emerge when
interacting non-Abelian anyons form a regular array. The studies are carried
out in the context of Kitaev's honeycomb model, where we consider three
distinct types of perturbations in the presence of a lattice of Majorana mode
binding vortices -- spatial anisotropy of the vortices, dimerization of the
vortex lattice and local random disorder. While all the nucleated phases are
stable with respect to weak perturbations of each kind, strong perturbations
are found to result in very different behavior. Anisotropy of the vortices
stabilizes the strong-pairing like phases, while dimerization can recover the
underlying non-Abelian phase. Local random disorder, on the other hand, can
drive all the nucleated phases into a gapless thermal metal state. We show that
all these distinct behavior can be captured by an effective staggered
tight-binding model for the Majorana modes. By studying the pairwise
interactions between the vortices, i.e. the amplitudes for the Majorana modes
to tunnel between vortex cores, the locations of phase transitions and the
nature of the resulting states can be predicted. We also find that due to
oscillations in the Majorana tunneling amplitude, lattices of Majorana modes
may exhibit a Peierls-like instability, where a dimerized configuration is
favored over a uniform lattice. As the nature of the nucleated phases depends
only on the Majorana tunneling, our results apply also to other system
supporting localized Majorana mode arrays, such as Abrikosov lattices in p-wave
superconductors, Wigner crystals in Moore-Read fractional quantum Hall states
or arrays of topological nanowires.Comment: 13 pages, 4 pages of appendices, 24 figures. Published versio
Optimized parallel tempering simulations of proteins
We apply a recently developed adaptive algorithm that systematically improves
the efficiency of parallel tempering or replica exchange methods in the
numerical simulation of small proteins. Feedback iterations allow us to
identify an optimal set of temperatures/replicas which are found to concentrate
at the bottlenecks of the simulations. A measure of convergence for the
equilibration of the parallel tempering algorithm is discussed. We test our
algorithm by simulating the 36-residue villin headpiece sub-domain HP-36
wherewe find a lowest-energy configuration with a root-mean-square-deviation of
less than 4 Angstroem to the experimentally determined structure.Comment: 22 pages, 7 figure
Quantum spin liquids in frustrated spin-1 diamond antiferromagnets
Motivated by the recent synthesis of the spin-1 A-site spinel NiRhO, we investigate the classical to quantum crossover of a
frustrated - Heisenberg model on the diamond lattice upon varying the
spin length . Applying a recently developed pseudospin functional
renormalization group (pf-FRG) approach for arbitrary spin- magnets, we find
that systems with reside in the classical regime where the
low-temperature physics is dominated by the formation of coplanar spirals and a
thermal (order-by-disorder) transition. For smaller local moments =1 or
=1/2 we find that the system evades a thermal ordering transition and forms
a quantum spiral spin liquid where the fluctuations are restricted to
characteristic momentum-space surfaces. For the tetragonal phase of
NiRhO, a modified -- exchange
model is found to favor a conventionally ordered N\'eel state (for arbitrary
spin ) even in the presence of a strong local single-ion spin anisotropy and
it requires additional sources of frustration to explain the experimentally
observed absence of a thermal ordering transition.Comment: 11 pages, 14 figure
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