46 research outputs found
Entanglement Spectra of Interacting Fermions in Quantum Monte Carlo Simulations
In a recent article T. Grover [Phys. Rev. Lett. 111, 130402 (2013)]
introduced a simple method to compute Renyi entanglement entropies in the realm
of the auxiliary field quantum Monte Carlo algorithm. Here, we further develop
this approach and provide a stabilization scheme to compute higher order Renyi
entropies and an extension to access the entanglement spectrum. The method is
tested on systems of correlated topological insulators.Comment: 7+ pages, 5 figure
Phase diagram of the SU() antiferromagnet of spin on a square lattice
We investigate the ground state phase diagram of an SU()-symmetric
antiferromagnetic spin model on a square lattice where each site hosts an
irreducible representation of SU() described by a square Young tableau of
rows and columns. We show that negative sign free fermion Monte
Carlo simulations can be carried out for this class of quantum magnets at any
and even values of . In the large- limit, the saddle point
approximation favors a four-fold degenerate valence bond solid phase. In the
large -limit, the semi-classical approximation points to N\'eel state. On a
line set by in the versus phase diagram, we observe a
variety of phases proximate to the N\'eel state. At and we
observe the aforementioned four fold degenerate valence bond solid state. At
a two fold degenerate spin nematic state in which the C lattice
symmetry is broken down to C emerges. Finally at we observe a unique
ground state that pertains to a two-dimensional version of the
Affleck-Kennedy-Lieb-Tasaki state. For our specific realization, this symmetry
protected topological state is characterized by an SU(18), boundary
state, that has a dimerized ground state. These phases that are proximate to
the N\'eel state are consistent with the notion of monopole condensation of the
antiferromagnetic order parameter. In particular one expects spin disordered
states with degeneracy set by .Comment: 18 pages, 21 figures; adapted title to APS style and included minor
correction
Multicritical Nishimori point in the phase diagram of the +- J Ising model on a square lattice
We investigate the critical behavior of the random-bond +- J Ising model on a
square lattice at the multicritical Nishimori point in the T-p phase diagram,
where T is the temperature and p is the disorder parameter (p=1 corresponds to
the pure Ising model). We perform a finite-size scaling analysis of
high-statistics Monte Carlo simulations along the Nishimori line defined by
, along which the multicritical point lies. The
multicritical Nishimori point is located at p^*=0.89081(7), T^*=0.9528(4), and
the renormalization-group dimensions of the operators that control the
multicritical behavior are y_1=0.655(15) and y_2 = 0.250(2); they correspond to
the thermal exponent \nu= 1/y_2=4.00(3) and to the crossover exponent \phi=
y_1/y_2=2.62(6).Comment: 23 page
Fermionic quantum criticality in honeycomb and -flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
We numerically investigate the critical behavior of the Hubbard model on the
honeycomb and the -flux lattice, which exhibits a direct transition from a
Dirac semimetal to an antiferromagnetically ordered Mott insulator. We use
projective auxiliary-field quantum Monte Carlo simulations and a careful
finite-size scaling analysis that exploits approximately improved
renormalization-group-invariant observables. This approach, which is
successfully verified for the three-dimensional XY transition of the
Kane-Mele-Hubbard model, allows us to extract estimates for the critical
couplings and the critical exponents. The results confirm that the critical
behavior for the semimetal to Mott insulator transition in the Hubbard model
belongs to the Gross-Neveu-Heisenberg universality class on both lattices.Comment: 19 pages, 16 figures; v2: replaced Fig. 5, corrected typo in Uc for
the Kane-Mele-Hubbard model, 19 pages, 16 figure
Zero-temperature behavior of the random-anisotropy model in the strong-anisotropy limit
We consider the random-anisotropy model on the square and on the cubic
lattice in the strong-anisotropy limit. We compute exact ground-state
configurations, and we use them to determine the stiffness exponent at zero
temperature; we find and respectively
in two and three dimensions. These results show that the low-temperature phase
of the model is the same as that of the usual Ising spin-glass model. We also
show that no magnetic order occurs in two dimensions, since the expectation
value of the magnetization is zero and spatial correlation functions decay
exponentially. In three dimensions our data strongly support the absence of
spontaneous magnetization in the infinite-volume limit
The critical behavior of 3D Ising glass models: universality and scaling corrections
We perform high-statistics Monte Carlo simulations of three three-dimensional
Ising spin-glass models: the +-J Ising model for two values of the disorder
parameter p, p=1/2 and p=0.7, and the bond-diluted +-J model for
bond-occupation probability p_b = 0.45. A finite-size scaling analysis of the
quartic cumulants at the critical point shows conclusively that these models
belong to the same universality class and allows us to estimate the
scaling-correction exponent omega related to the leading irrelevant operator,
omega=1.0(1). We also determine the critical exponents nu and eta. Taking into
account the scaling corrections, we obtain nu=2.53(8) and eta=-0.384(9).Comment: 9 pages, published versio
The ALF (Algorithms for Lattice Fermions) project release 2.0. Documentation for the auxiliary-field quantum Monte Carlo code
The Algorithms for Lattice Fermions package provides a general code for the
finite-temperature and projective auxiliary-field quantum Monte Carlo
algorithm. The code is engineered to be able to simulate any model that can be
written in terms of sums of single-body operators, of squares of single-body
operators and single-body operators coupled to a bosonic field with given
dynamics. The package includes five pre-defined model classes: SU(N) Kondo,
SU(N) Hubbard, SU(N) t-V and SU(N) models with long range Coulomb repulsion on
honeycomb, square and N-leg lattices, as well as unconstrained lattice
gauge theories coupled to fermionic and matter. An implementation of the
stochastic Maximum Entropy method is also provided. One can download the code
from our Git instance at
https://git.physik.uni-wuerzburg.de/ALF/ALF/-/tree/ALF-2.0 and sign in to file
issues.Comment: 121 pages, 11 figures. v3: quick tutorial section added, typos
corrected, etc. Submission to SciPost. arXiv admin note: text overlap with
arXiv:1704.0013