27 research outputs found
Entropy dependence of correlations in one-dimensional SU(N) antiferromagnets
Motivated by the possibility to load multi-color fermionic atoms in optical
lattices, we study the entropy dependence of the properties of the
one-dimensional antiferromagnetic SU(N) Heisenberg model, the effective model
of the SU(N) Hubbard model with one particle per site (filling 1/N). Using
continuous-time world line Monte Carlo simulations for N=2 to 5, we show that
characteristic short-range correlations develop at low temperature as a
precursor of the ground state algebraic correlations. We also calculate the
entropy as a function of temperature, and we show that the first sign of
short-range order appears at an entropy per particle that increases with N and
already reaches 0.8k_B at N=4, in the range of experimentally accessible
values.Comment: 5 pages, 3 figures, 2 table
Competition between three-sublattice order and superfluidity in the quantum 3-state Potts model of ultracold bosons and fermions on a square optical lattice
We study a quantum version of the three-state Potts model that includes as
special cases the effective models of bosons and fermions on the square lattice
in the Mott insulating limit. It can be viewed as a model of quantum
permutations with amplitudes J_parallel and J_perp for identical and different
colors, respectively. For J_parallel=J_perp>0, it is equivalent to the SU(3)
Heisenberg model, which describes the Mott insulating phase of 3-color
fermions, while the parameter range J_perp<min(0,-J_parallel) can be realized
in the Mott insulating phase of 3-color bosonic atoms. Using linear flavor wave
theory, infinite projected entangled-pair states (iPEPS), and continuous-time
quantum Monte-Carlo simulations, we construct the full T=0 phase diagram, and
we explore the T>0 properties for J_perp<0. For dominant antiferromagnetic
J_parallel interactions, a three-sublattice long-range ordered stripe state is
selected out of the ground state manifold of the antiferromagnetic Potts model
by quantum fluctuations. Upon increasing |J_perp|, this state is replaced by a
uniform superfluid for J_perp<0, and by an exotic three-sublattice superfluid
followed by a two-sublattice superfluid for J_perp>0. The transition out of the
uniform superfluid (that can be realized with bosons) is shown to be a peculiar
type of Kosterlitz-Thouless transition with three types of elementary vortices
Emergent Potts order in the kagom\'e Heisenberg model
Motivated by the physical properties of Vesignieite
BaCuVO(OH), we study the Heisenberg model on the
kagom\'e lattice, that is proposed to describe this compound for and
. The nature of the classical ground state and the possible phase
transitions are investigated through analytical calculations and parallel
tempering Monte Carlo simulations. For and
, the ground states are not all related by an
Hamiltonian symmetry. Order appears at low temperature via the order by
disorder mechanism, favoring colinear configurations and leading to an emergent
Potts parameter. This gives rise to a finite temperature phase
transition. Effect of quantum fluctuations are studied through linear spin wave
approximation and high temperature expansions of the model. For
between and , the ground state goes
through a succession of semi-spiral states, possibly giving rise to multiple
phase transitions at low temperatures
TRIQS: A Toolbox for Research on Interacting Quantum Systems
We present the TRIQS library, a Toolbox for Research on Interacting Quantum
Systems. It is an open-source, computational physics library providing a
framework for the quick development of applications in the field of many-body
quantum physics, and in particular, strongly-correlated electronic systems. It
supplies components to develop codes in a modern, concise and efficient way:
e.g. Green's function containers, a generic Monte Carlo class, and simple
interfaces to HDF5. TRIQS is a C++/Python library that can be used from either
language. It is distributed under the GNU General Public License (GPLv3).
State-of-the-art applications based on the library, such as modern quantum
many-body solvers and interfaces between density-functional-theory codes and
dynamical mean-field theory (DMFT) codes are distributed along with it.Comment: 27 page
The kagome antiferromagnet: a chiral topological spin liquid ?
Inspired by the recent discovery of a new instability towards a chiral phase
of the classical Heisenberg model on the kagome lattice, we propose a specific
chiral spin liquid that reconciles different, well-established results
concerning both the classical and quantum models. This proposal is analyzed in
an extended mean-field Schwinger boson framework encompassing time reversal
symmetry breaking phases which allows both a classical and a quantum phase
description. At low temperatures, we find quantum fluctuations favor this
chiral phase, which is stable against small perturbations of second and third
neighbor interactions. For spin-1/2 this phase may be, beyond mean-field, a
chiral gapped spin liquid. Such a phase is consistent with Density Matrix
Renormalization Group results of Yan et al. (Science 322, 1173 (2011)).
Mysterious features of the low lying excitations of exact diagonalization
spectra also find an explanation in this framework. Moreover, thermal
fluctuations compete with quantum ones and induce a transition from this flux
phase to a planar zero flux phase at a non zero value of the renormalized
temperature (T/S^2), reconciling these results with those obtained for the
classical system.Comment: 4 pages, 4 figures, 1 tabl
Effect of perturbations on the kagome antiferromagnet at all temperatures
The ground state of the kagome Heisenberg antiferromagnet is now
recognized as a spin liquid, but its precise nature remains unsettled, even if
more and more clues point towards a gapless spin liquid. We use high
temperature series expansions (HTSE) to extrapolate the specific heat
and the magnetic susceptibility over the full temperature range,
using an improved entropy method with a self-determination of the ground state
energy per site . Optimized algorithms give the HTSE coefficients up to
unprecedented orders (20 in ) and as exact functions of the magnetic
field. Three extrapolations are presented for different low- behaviors of
: exponential (for a gapped system), linear or quadratic (for two
different types of gapless spin liquids). We study the effects of various
perturbations to the Heisenberg Hamiltonian: Ising anisotropy,
Dzyaloshinskii-Moriya interactions, second and third neighbor interactions, and
randomly distributed magnetic vacancies. We propose an experimental
determination of , which could be non zero, from measurements
under different magnetic fields.Comment: Main article of 7 pages and 5 figures, Supplemental Material of 42
page
Three-sublattice order in the SU(3) Heisenberg model on the square and triangular lattice
We present a numerical study of the SU(3) Heisenberg model of three-flavor
fermions on the triangular and square lattice by means of the density-matrix
renormalization group (DMRG) and infinite projected entangled-pair states
(iPEPS). For the triangular lattice we confirm that the ground state has a
three-sublattice order with a finite ordered moment which is compatible with
the result from linear flavor wave theory (LFWT). The same type of order has
recently been predicted also for the square lattice [PRL 105, 265301 (2010)]
from LFWT and exact diagonalization. However, for this case the ordered moment
cannot be computed based on LFWT due to divergent fluctuations. Our numerical
study clearly supports this three-sublattice order, with an ordered moment of
m=0.2-0.4 in the thermodynamic limit.Comment: Published version. 11 pages, 6 figure
Quantum Monte Carlo for correlated out-of-equilibrium nanoelectronic devices
International audienceWe present a simple, general purpose, quantum Monte-Carlo algorithm for out-of-equilibrium interacting nanoelectronics systems. It allows one to systematically compute the expansion of any physical observable (such as current or density) in powers of the electron-electron interaction coupling constant U. It is based on the out-of-equilibrium Keldysh Green's function formalism in real-time and corresponds to evaluating all the Feynman diagrams to a given order U n (up to n = 15 in the present work). A key idea is to explicitly sum over the Keldysh indices in order to enforce the unitarity of the time evolution. The coefficients of the expansion can easily be obtained for long time, stationary regimes, even at zero temperature. We then illustrate our approach with an application to the Anderson model, an archetype interacting mesoscopic system. We recover various results of the literature such as the spin susceptibility or the " Kondo ridge " in the current-voltage characteristics. In this case, we found the Monte-Carlo free of the sign problem even at zero temperature , in the stationary regime and in absence of particle-hole symmetry. The main limitation of the method is the lack of convergence of the expansion in U for large U , i.e. a mathematical property of the model rather than a limitation of the Monte-Carlo algorithm. Standard extrapolation methods of divergent series can be used to evaluate the series in the strong correlation regime