[Show abstract][Hide abstract] ABSTRACT: We investigate the phase diagram of spinless fermions with nearest and
next-nearest neighbour density-density interactions on the honeycomb lattice at
half-filling. Using Exact Diagonalization techniques of the full Hamiltonian
and constrained subspaces, combined with a careful choice of finite-size
clusters, we determine the different charge orderings that occur for large
interactions. In this regime we find a two-sublattice N\'eel-like state, a
charge modulated state with a tripling of the unit cell, a zig-zag phase and a
novel charge ordered states with a 12 site unit cells we call N\'eel domain
wall crystal, as well as a region of phase separation for attractive
interactions. A sizeable region of the phase diagram is classically degenerate,
but it remains unclear whether an order-by-disorder mechanism will lift the
degeneracy. For intermediate repulsion we find evidence for a Kekul\'e or
plaquette bond-order wave phase. We also investigate the possibility of a
spontaneous Chern insulator phase (dubbed topological Mott insulator), as
previously put forward by several mean-field studies. Although we are unable to
detect convincing evidence for this phase based on energy spectra and order
parameters, we find an enhancement of current-current correlations with the
expected spatial structure compared to the non-interacting situation. While for
the studied $t{-}V_1{-}V_2$ model the phase transition to the putative
topological Mott insulator is preempted by the phase transitions to the various
ordered states, our findings might hint at the possibility for a topological
Mott insulator in an enlarged Hamiltonian parameter space, where the competing
phases are suppressed.
Physical Review B 05/2015; 92(8). DOI:10.1103/PhysRevB.92.085146 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We investigate the quantum phases of hard-core bosonic atoms in an extended
Hubbard model where particles interact via soft-shoulder potentials in one
dimension. Using a combination of field-theoretical methods and strong-coupling
perturbation theory, we demonstrate that the low-energy phase can be a
conformal cluster Luttinger liquid (CLL) phase with central charge $c=1$, where
the microscopic degrees of freedom correspond to mesoscopic ensembles of
particles. Using numerical density-matrix-renormalization-group methods, we
demonstrate that the CLL phase, first predicted in [Phys. Rev. Lett. 111,
165302 (2013)], is separated from a conventional Tomonaga-Luttinger liquid by
an exotic critical point with central charge $c=3/2$. The latter is expression
of an emergent conformal supersymmetry, which is not present in the original
Hamiltonian. We discuss the observability of the CLL phase in realistic
experimental settings with weakly-dressed Rydberg atoms confined to optical
lattices. Using quantum Monte-Carlo simulations, we show that the typical
features of CLLs are stable up to comparatively high temperatures. Using exact
diagonalizations and quantum trajectory methods, we provide a protocol for
adiabatic state preparation as well as quantitative estimates on the effects of
particle losses.
Physical Review B 02/2015; 92(4). DOI:10.1103/PhysRevB.92.045106 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Quantum trajectories and superoperator algorithms implemented within the
matrix product state (MPS) framework are powerful tools to simulate the
real-time dynamics of open dissipative quantum systems. As for the unitary
case, the reachable time-scales as well as system sizes are limited by the
(possible) build-up of entanglement entropy. The aforementioned methods
constitute complementary approaches how Lindblad master equations can be
integrated relying either on a quasi-exact representation of the full density
matrix or a stochastic unraveling of the density matrix in terms of pure
states. In this work, we systematically benchmark both methods by studying the
dynamics of a Bose-Hubbard chain in the presence of local as well as global
dephasing. The build-up as well as system-size scaling of entanglement entropy
strongly depends on the method and the parameter regime and we discuss the
applicability of the methods for these cases as well as study the distribution
of observables and time discretization errors that can become a limiting factor
for global dissipation.
[Show abstract][Hide abstract] ABSTRACT: We study the phase diagram of the spin-1 quantum bilinear-biquadratic antiferromagnet on the kagome lattice using exact diagonalization and the density matrix renormalization group algorithm. The SU(3)-symmetric point of this model Hamiltonian is a spontaneously trimerized state whose qualitative nature persists even at the Heisenberg point, a finding that contrasts previous proposals. We report the ground state energy per site of the Heisenberg model to be −1.410(2) and establish the presence of a spin gap.
Physical Review B 06/2014; 91(10). DOI:10.1103/PhysRevB.91.100407 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study a dissipative Bose-Hubbard chain subject to an engineered bath using
a superoperator approach based on matrix product operators. The dissipation is
engineered to stabilize a BEC condensate wave function in its steady state. We
then characterize the steady state emerging from the interplay between
incompatible Hamiltonian and dissipative dynamics. While it is expected that
interactions lead to this competition, even the kinetic energy in an open
boundary condition setup competes with the dissipation, leading to a
non-trivial steady state. We also present results for the transient dynamics
and probe the relaxation time revealing the closing of the dissipative gap in
the thermodynamic limit.
Physical Review A 05/2014; 90(3). DOI:10.1103/PhysRevA.90.033612 · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study the momentum space entanglement spectra of bosonic and fermionic
formulations of the spin-1/2 XXZ chain with analytical methods and exact
diagonalization. We investigate the behavior of the entanglement gaps, present
in both partitions, across quantum phase transitions in the XXZ chain. In both
cases, finite size scaling reveals that the entanglement gap closure does not
occur at the physical transition points. For bosons, we find that the
entanglement gap observed in [Thomale et al., Phys. Rev. Lett. 105, 116805
(2010)] depends on the scaling dimension of the conformal field theory as
varied by the XXZ anisotropy. For fermions, the infinite entanglement gap
present at the XX point persists well past the phase transition at the
Heisenberg point. We elaborate on how these shifted transition points in the
entanglement spectra may in fact support the numerical study of the physical
transitions in the momentum space density matrix renormalization group.
[Show abstract][Hide abstract] ABSTRACT: Signal propagation in the non equilibirum evolution after quantum quenches
has recently attracted much experimental and theoretical interest. A key
question arising in this context is what principles, and which of the
properties of the quench, determine the characteristic propagation velocity.
Here we investigate such issues for a class of quench protocols in one of the
central paradigms of interacting many-particle quantum systems, the spin-1/2
Heisenberg XXZ chain. We consider quenches from a variety of initial thermal
density matrices to the same final Hamiltonian using matrix product state
methods. The spreading velocities are observed to vary substantially with the
initial density matrix. However, we achieve a striking data collapse when the
spreading velocity is considered to be a function of the excess energy. Using
the fact that the XXZ chain is integrable, we present an explanation of the
observed velocities in terms of "excitations" in an appropriately defined
generalized Gibbs ensemble.
[Show abstract][Hide abstract] ABSTRACT: Motivated by recent developments in conformal field theory (CFT), we devise a
Quantum Monte Carlo (QMC) method to calculate the moments of the partially
transposed reduced density matrix at finite temperature. These are used to
construct scale invariant combinations that are related to the negativity, a
true measure of entanglement for two intervals embedded in a chain. These
quantities can serve as witnesses of criticality. In particular, we study
several scale invariant combinations of the moments for the 1D hard-core boson
model. For two adjacent intervals unusual finite size corrections are present,
showing parity effects that oscillate with a filling dependent period. These
are more pronounced in the presence of boundaries. For large chains we find
perfect agreement with CFT. Oppositely, for disjoint intervals corrections are
more severe and CFT is recovered only asymptotically. Furthermore, we provide
evidence that their exponent is the same as that governing the corrections of
the mutual information. Additionally we study the 1D Bose-Hubbard model in the
superfluid phase. Remarkably, the finite-size effects are smaller and QMC data
are already in impressive agreement with CFT at moderate large sizes.
Physical Review B 12/2013; 90(6). DOI:10.1103/PhysRevB.90.064401 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We present evidence for Majorana edge states in a number conserving theory describing a system of spinless fermions on two wires that are coupled by pair hopping. Our analysis is based on a combination of a qualitative low energy approach and numerical techniques using the density matrix renormalization group. In addition, we discuss an experimental realization of pair-hopping interactions in cold atom gases confined in optical lattices.
[Show abstract][Hide abstract] ABSTRACT: We clarify the existence of several magnetization plateaux for the kagome $S=1/2$ antiferromagnetic Heisenberg model in a magnetic field. Using approximate or exact localized magnon eigenstates, we are able to describe in a similar manner the plateau states that occur for magnetization per site $m=1/3$, 5/9, and 7/9 of the saturation value. These results are confirmed using large-scale Exact Diagonalization on lattices up to 63 sites.
Physical Review B 10/2013; 88(14):144416. DOI:10.1103/PhysRevB.88.144416 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study the phase diagram of interacting electrons in a dispersionless Chern band as a function of their filling. We find hierarchy multiplets of incompressible states at fillings ν=1/3, 2/5, 3/7, 4/9, 5/9, 4/7, 3/5 as well as ν=1/5, 2/7. These are accounted for by an analogy to Haldane pseudopotentials extracted from an analysis of the two-particle problem. Important distinctions to standard fractional quantum Hall physics are striking: in the absence of particle-hole symmetry in a single band, an interaction-induced single-hole dispersion appears, which perturbs and eventually destabilizes incompressible states as ν increases. For this reason, the nature of the state at ν=2/3 is hard to pin down, while ν=5/7, 4/5 do not seem to be incompressible in our system.
[Show abstract][Hide abstract] ABSTRACT: We study the entanglement spectrum (ES) of the Bose-Hubbard model on the two-dimensional square lattice at unit filling, both in the Mott insulating and in the superfluid phase. In the Mott phase, we demonstrate that the ES is dominated by the physics at the boundary between the two subsystems. On top of the boundary-local (perturbative) structure, the ES exhibits substructures arising from one-dimensional dispersions along the boundary. In the superfluid phase, the structure of the ES is qualitatively different, and reflects the spontaneously broken U(1) symmetry of the phase. We attribute the basic low-lying structure to the "tower of states" Hamiltonian of the model. We then discuss how these characteristic structures evolve across the superfluid to Mott insulator transition and their influence on the behavior of the entanglement entropies. We briefly outline the implications of the ES structure on the efficiency of matrix-product-state based algorithms in two dimensions.
[Show abstract][Hide abstract] ABSTRACT: We present a numerical scheme to reconstruct a subset of the entanglement
spectrum of quantum many body systems using quantum Monte Carlo. The approach
builds on the replica trick to evaluate particle number resolved traces of the
first n of powers of a reduced density matrix. From this information we
reconstruct n entanglement spectrum levels using a polynomial root solver. We
illustrate the power and limitations of the method by an application to the
extended Bose-Hubbard model in one dimension where we are able to resolve the
quasi-degeneracy of the entanglement spectrum in the Haldane-Insulator phase.
In general the method is able to reconstruct the largest few eigenvalues in
each symmetry sector and typically performs better when the eigenvalues are not
too different.
Physical Review B 05/2013; 89(19). DOI:10.1103/PhysRevB.89.195147 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Strongly correlated quantum systems can exhibit exotic behavior controlled by topology. We predict that the ν=1/2 fractional Chern insulator arises naturally in a two-dimensional array of driven, dipolar-interacting spins. As a specific implementation, we analyze how to prepare and detect synthetic gauge potentials for the rotational excitations of ultracold polar molecules trapped in a deep optical lattice. With the motion of the molecules pinned, under certain conditions, these rotational excitations form a fractional Chern insulating state. We present a detailed experimental blueprint for its realization and demonstrate that the implementation is consistent with near-term capabilities. Prospects for the realization of such phases in solid-state dipolar systems are discussed as are their possible applications.
[Show abstract][Hide abstract] ABSTRACT: We study the Renyi entropy in the finite temperature crossover regime of a
Hubbard chain using quantum Monte Carlo. The ground state entropy has
characteristic features such as a logarithmic divergence with block size and
$2\kF$ oscillations that are a hallmark of its Luttinger liquid nature. The
interplay between the (extensive) thermal entropy and the ground state features
is studied and we analyze the temperature induced decay of the amplitude of the
oscillations as well as the scaling of the purity. Furthermore, we show how the
spin and charge velocities can be extracted from the temperature dependence of
the Renyi entropy, bridging our findings to recent experimental proposals on
how to implement the measurement of Renyi entropies in cold atom system.
Studying the Renyi mutual information, we also demonstrate how constraints such
as particle number conservation can induce persistent correlations visible in
the mutual information even at high temperature.
[Show abstract][Hide abstract] ABSTRACT: We report a cluster of results regarding the difficulty of finding
approximate ground states to typical instances of the quantum satisfiability
problem $k$-QSAT on large random graphs. As an approximation strategy, we
optimize the solution space over `classical' product states, which in turn
introduces a novel autonomous classical optimization problem, PSAT, over a
space of continuous degrees of freedom rather than discrete bits. Our central
results are: (i) The derivation of a set of bounds and approximations in
various limits of the problem, several of which we believe may be amenable to a
rigorous treatment. (ii) A demonstration that an approximation based on a
greedy algorithm borrowed from the study of frustrated magnetism performs well
over a wide range in parameter space, and its performance reflects structure of
the solution space of random $k$-QSAT. Simulated annealing exhibits
metastability in similar `hard' regions of parameter space. (iii) A
generalization of belief propagation algorithms introduced for classical
problems to the case of continuous spins. This yields both approximate
solutions, as well as insights into the free energy `landscape' of the
approximation problem, including a so-called dynamical transition near the
satisfiability threshold. Taken together, these results allow us to elucidate
the phase diagram of random $k$-QSAT in a two-dimensional
energy-density--clause-density space.
Physical Review A 04/2013; 87(6). DOI:10.1103/PhysRevA.87.062334 · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We show how to measure the order-two Renyi entropy of many-body states of spinful fermionic atoms in an optical lattice in equilibrium and non-equilibrium situations. The proposed scheme relies on the possibility to produce and couple two copies of the state under investigation, and to measure the occupation number in a site-and spin-resolved manner, e.g. with a quantum gas microscope. Such a protocol opens the possibility to measure entanglement and test a number of theoretical predictions, such as area laws and their corrections. As an illustration we discuss the interplay between thermal and entanglement entropy for a one dimensional Fermi-Hubbard model at finite temperature, and its possible measurement in an experiment using the present scheme.
[Show abstract][Hide abstract] ABSTRACT: We provide numerical evidence that the low-lying part of the entanglement
spectrum of a real-space block (i.e. a single interval) of a one-dimensional
quantum many body system at a conformal critical point corresponds to the
energy spectrum of a boundary conformal field theory (CFT). This correspondence
allows to uncover a subset of the operator content of a conformal field theory
by inspection of the entanglement spectrum of a single wave function, thus
providing important information on a CFT beyond its central charge. As a
practical application we show that for many systems described by a compactified
boson CFT, one can infer the compactification radius (governing e.g. the power
law decay of correlation functions) of the theory in a simple way based on the
entanglement spectrum.
[Show abstract][Hide abstract] ABSTRACT: Conflicting predictions have been made for the ground state of the SU(3)
Heisenberg model on the honeycomb lattice: Tensor network simulations found a
plaquette order [Zhao et al, Phys. Rev. B 85, 134416 (2012)], where singlets
are formed on hexagons, while linear flavor-wave theory (LFWT) suggested a
dimerized, color ordered state [Lee and Yang, Phys. Rev. B 85, 100402 (2012)].
In this work we show that the former state is the true ground state by a
systematic study with infinite projected-entangled pair states (iPEPS), for
which the accuracy can be systematically controlled by the so-called bond
dimension $D$. Both competing states can be reproduced with iPEPS by using
different unit cell sizes. For small $D$ the dimer state has a lower
variational energy than the plaquette state, however, for large $D$ it is the
latter which becomes energetically favorable. The plaquette formation is also
confirmed by exact diagonalizations and variational Monte Carlo studies,
according to which both the dimerized and plaquette states are non-chiral flux
states.
[Show abstract][Hide abstract] ABSTRACT: We show how to measure the order-two Renyi entropy of many-body states of
spinful fermionic atoms in an optical lattice in equilibrium and
non-equilibrium situations. The proposed scheme relies on the possibility to
produce and couple two copies of the state under investigation, and to measure
the occupation number in a site- and spin-resolved manner, e.g. with a quantum
gas microscope. Such a protocol opens the possibility to measure entanglement
and test a number of theoretical predictions, such as area laws and their
corrections. As an illustration we discuss the interplay between thermal and
entanglement entropy for a one dimensional Fermi-Hubbard model at finite
temperature, and its possible measurement in an experiment using the present
scheme.
New Journal of Physics 02/2013; 15(6). DOI:10.1088/1367-2630/15/6/063003 · 3.56 Impact Factor