24 research outputs found
Detecting Fractional Chern Insulators in Optical Lattices through Quantized Displacement
The realization of interacting topological states of matter such as
fractional Chern insulators (FCIs) in cold atom systems has recently come
within experimental reach due to the engineering of optical lattices with
synthetic gauge fields providing the required topological band structures.
However, detecting their occurrence might prove difficult since transport
measurements akin to those in solid state systems are challenging to perform in
cold atom setups and alternatives have to be found. We show that for a FCI state realized in the lowest band of a Harper-Hofstadter model of
interacting bosons confined by a harmonic trapping potential, the fractionally
quantized Hall conductivity can be accurately determined by the
displacement of the atomic cloud under the action of a constant force which
provides a suitable experimentally measurable signal for detecting the
topological nature of the state. Using matrix-product state algorithms, we show
that, in both cylinder and square geometries, the movement of the particle
cloud in time under the application of a constant force field on top of the
confining potential is proportional to for an extended range of
field strengths.Comment: 5 pages, 6 figures, plus supplementary materia
Phase transitions and adiabatic preparation of a fractional Chern insulator in a boson cold atom model
We investigate the fate of hardcore bosons in a Harper-Hofstadter model which
was experimentally realized by Aidelsburger et al. [Nature Physics 11 , 162
(2015)] at half filling of the lowest band. We discuss the stability of an
emergent fractional Chern insulator (FCI) state in a finite region of the phase
diagram that is separated from a superfluid state by a first-order transition
when tuning the band topology following the protocol used in the experiment.
Since crossing a first-order transition is unfavorable for adiabatically
preparing the FCI state, we extend the model to stabilize a featureless
insulating state. The transition between this phase and the topological state
proves to be continuous, providing a path in parameter space along which an FCI
state could be adiabatically prepared. To further corroborate this statement,
we perform time-dependent DMRG calculations which demonstrate that the FCI
state may indeed be reached by adiabatically tuning a simple product state.Comment: 7 pages, 7 figures, published versio
Characterization of topological phases in models of interacting fermions
The concept of topology in condensed matter physics has led to the discovery of rich and exotic physics in recent years. Especially when strong correlations are included, phenomenons such as fractionalization and anyonic particle statistics can arise. In this thesis, we study several systems hosting topological phases of interacting fermions.
In the first part, we consider one-dimensional systems of parafermions, which are generalizations of Majorana fermions, in the presence of a Z_N charge symmetry. We classify the symmetry-protected topological (SPT) phases that can occur in these systems using the projective representations of the symmetries and find a finite number of distinct phases depending on the prime factorization of N. The different phases exhibit characteristic degeneracies in their entanglement spectrum (ES). Apart from these SPT phases, we report the occurrence of parafermion condensate phases for certain values of N. When including an additional Z_N symmetry, we find a non-Abelian group structure under the addition of phases.
In the second part of the thesis, we focus on two-dimensional lattice models of spinless fermions. First, we demonstrate the detection of a fractional Chern insulator (FCI) phase in the Haldane honeycomb model on an infinite cylinder by means of the density-matrix renormalization group (DMRG). We report the calculation of several quantities characterizing the topological order of the state, i.e., (i)~the Hall conductivity, (ii)~the spectral flow and level counting in the ES, (iii)~the topological entanglement entropy, and (iv)~the charge and topological spin of the quasiparticles. Since we have access to sufficiently large system sizes without band projection with DMRG, we are in addition able to investigate the transition from a metal to the FCI at small interactions which we find to be of first order.
In a further study, we consider a time-reversal symmetric model on the honeycomb lattice where a Chern insulator (CI) induced by next-nearest neighbor interactions has been predicted by mean field theory. However, various subsequent studies challenged this picture and it was still unclear whether the CI would survive quantum fluctuations. We therefore map out the phase diagram of the model as a function of the interactions on an infinite cylinder with DMRG and find evidence for the absence of the CI phase. However, we report the detection of two novel charge-ordered phases and corroborate the existence of the remaining phases that had been predicted in mean field theory. Furthermore, we characterize the transitions between the various phases by studying the behavior of correlation length and entanglement entropy at the phase boundaries. Finally, we develop an improvement to the DMRG algorithm for fermionic lattice models on cylinders. By using a real space representation in the direction along the cylinder and a real space representation in the perpendicular direction, we are able to use the momentum around the cylinder as conserved quantity to reduce computational costs. We benchmark the method by studying the interacting Hofstadter model and report a considerable speedup in computation time and a severely reduced memory usage
Phase diagram of the anisotropic triangular lattice Hubbard model
In a recent study [Phys. Rev. X 10, 021042 (2020)], we showed using
large-scale density matrix renormalization group (DMRG) simulations on infinite
cylinders that the triangular lattice Hubbard model has a chiral spin liquid
phase. In this work, we introduce hopping anisotropy in the model, making one
of the three distinct bonds on the lattice stronger or weaker compared with the
other two. We implement the anisotropy in two inequivalent ways, one which
respects the mirror symmetry of the cylinder and one which breaks this
symmetry. In the full range of anisotropy, from the square lattice to weakly
coupled one-dimensional chains, we find a variety of phases. Near the isotropic
limit we find the three phases identified in our previous work: metal, chiral
spin liquid, and 120 spiral order; we note that a recent paper suggests
the apparently metallic phase may actually be a Luther-Emery liquid, which
would also be in agreement with our results. When one bond is weakened by a
relatively small amount, the ground state quickly becomes the square lattice
N\'{e}el order. When one bond is strengthened, the story is much less clear,
with the phases that we find depending on the orientation of the anisotropy and
on the cylinder circumference. While our work is to our knowledge the first
DMRG study of the anisotropic triangular lattice Hubbard model, the overall
phase diagram we find is broadly consistent with that found previously using
other methods, such as variational Monte Carlo and dynamical mean field theory.Comment: v3: Added data regarding incommensurate spiral order using flux
insertion, 20 pages, 6 figures, plus 23 pages (35 figures) Supplemental
Material; v2: Slightly increased parameter space resolution for largest
cylinder; v1: 19 pages, 6 figures, plus 22 pages (34 figures) Supplemental
Materia
Topological phases in gapped edges of fractionalized systems
Recently, it has been proposed that exotic one-dimensional phases can be
realized by gapping out the edge states of a fractional topological insulator.
The low-energy edge degrees of freedom are described by a chain of coupled
parafermions. We introduce a classification scheme for the phases that can
occur in parafermionic chains. We find that the parafermions support both
topological symmetry fractionalized phases as well as phases in which the
parafermions condense. In the presence of additional symmetries, the phases
form a non-Abelian group. As a concrete example of the classification, we
consider the effective edge model for a fractional topological
insulator for which we calculate the entanglement spectra numerically and show
that all possible predicted phases can be realized.Comment: 11 pages, 7 figures, final versio
Interaction driven phases in the half-filled honeycomb lattice: an infinite density matrix renormalization group study
The emergence of the Haldane Chern insulator state due to strong short range
repulsive interactions in the half-filled fermionic spinless honeycomb lattice
model has been proposed and challenged with different methods and yet it still
remains controversial. In this work we revisit the problem using the infinite
density matrix renormalization group method and report numerical evidence
supporting i) the absence of the Chern insulator state, ii) two previously
unnoticed charge ordered phases and iii) the existence and stability of all the
non-topological competing orders that were found previously within mean field.
In addition, we discuss the nature of the corresponding phase transitions based
on our numerical data. Our work establishes the phase diagram of the
half-filled honeycomb lattice model tilting the balance towards the absence of
a Chern insulator phase for this model.Comment: 12 pages, 8 figures, published versio
Phase transitions and adiabatic preparation of a fractional Chern insulator in a boson cold-atom model
Charge excitation dynamics in bosonic fractional Chern insulators
The experimental realization of the Harper-Hofstadter model in ultra-cold
atomic gases has placed fractional states of matter in these systems within
reach---a fractional Chern insulator state (FCI) is expected to emerge for
sufficiently strong interactions when half-filling the lowest band. The
experimental setups naturally allow to probe the dynamics of this topological
state, yet little is known about its out-of-equilibrium properties. We explore,
using density matrix renormalization group (DMRG) simulations, the response of
the FCI state to spatially localized perturbations. After confirming the static
properties of the phase we show that the characteristic, gapless features are
clearly visible in the edge dynamics. We find that a local edge perturbation in
this model propagates chirally independent of the perturbation strength. This
contrasts the behavior of single particle models with counter-propagating edge
states, such as the non-interacting Harper-Hofstadter model, where the
chirality is manifest only for weak perturbations. Additionally, our
simulations show that there is inevitable density leakage from the first row of
sites into the bulk, preventing a naive chiral Luttinger theory interpretation
of the dynamics.Comment: 4+epsilon pages, 4 pages of supplementary material and a total of 8
figures. Published version with updated title, discussion, references, and
supplementary informatio
Characterization and stability of a fermionic \nu=1/3 fractional Chern insulator
Using the infinite density matrix renormalization group method on an infinite
cylinder geometry, we characterize the fractional Chern insulator state
in the Haldane honeycomb lattice model at filling of the lowest band
and check its stability. We investigate the chiral and topological properties
of this state through (i) its Hall conductivity, (ii) the topological
entanglement entropy, (iii) the charge spectral flow of the many body
entanglement spectrum, and (iv) the charge of the anyons. In contrast to
numerical methods restricted to small finite sizes, the infinite cylinder
geometry allows us to access and characterize directly the metal to fractional
Chern insulator transition. We find indications it is first order and no
evidence of other competing phases. Since our approach does not rely on any
band or subspace projection, we are able to prove the stability of the
fractional state in the presence of interactions exceeding the band gap, as has
been suggested in the literature. As a by-product we discuss the signatures of
Chern insulators within this technique.Comment: published versio