Publications (136)463.7 Total impact

Article: SU(6) Heisenberg model on the honeycomb lattice: competition between plaquette and chiral order
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ABSTRACT: We revisit the SU(6) Heisenberg model on the honeycomb lattice, which has been predicted to be a chiral spin liquid by meanfield theory [G. Szirmai et al., Phys. Rev. A 84, 011611 (2011)]. Using exact diagonalizations of finite clusters, infinite projected entangled pair states simulations, and variational Monte Carlo simulations based on Gutzwiller projected wave functions, we provide strong evidence in favour of the competing plaquette state, which was reported to be higher but close by in energy according to meanfield theory. This is further confirmed by the investigation of the model with a ring exchange term, which shows that there is a transition between the plaquette state and the chiral state at a finite value of the ring exchange term.  [Show abstract] [Hide abstract]
ABSTRACT: We show that, in the presence of a $\pi/2$ artificial gauge field per plaquette, Mott insulating phases of ultracold fermions with $SU(N)$ symmetry and one particle per site generically possess an extended chiral phase with intrinsic topological order characterized by a multiplet of $N$ lowlying singlet excitations for periodic boundary conditions, and by chiral edge states described by the $SU(N)_1$ WessZuminoNovikovWitten conformal field theory for open boundary conditions. This has been achieved by extensive exact diagonalizations for $N$ between $3$ and $9$, and by a parton construction based on a set of $N$ Gutzwiller projected fermionic wavefunctions with flux $\pi/N$ per triangular plaquette. Experimental implications are briefly discussed.  [Show abstract] [Hide abstract]
ABSTRACT: We investigate the phase diagram of spinless fermions with nearest and nextnearest neighbour densitydensity interactions on the honeycomb lattice at halffilling. Using Exact Diagonalization techniques of the full Hamiltonian and constrained subspaces, combined with a careful choice of finitesize clusters, we determine the different charge orderings that occur for large interactions. In this regime we find a twosublattice N\'eellike state, a charge modulated state with a tripling of the unit cell, a zigzag 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 orderbydisorder mechanism will lift the degeneracy. For intermediate repulsion we find evidence for a Kekul\'e or plaquette bondorder wave phase. We also investigate the possibility of a spontaneous Chern insulator phase (dubbed topological Mott insulator), as previously put forward by several meanfield studies. Although we are unable to detect convincing evidence for this phase based on energy spectra and order parameters, we find an enhancement of currentcurrent correlations with the expected spatial structure compared to the noninteracting 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.  [Show abstract] [Hide abstract]
ABSTRACT: We investigate the stability and the nature of the chiral spin liquids which were recently uncovered in extended Heisenberg models on the kagome lattice. Using a Gutzwiller projected wave function approach  i.e. a parton construction  we obtain large overlaps with ground states of these extended Heisenberg models. We further suggest that the appearance of the chiral spin liquid in the timereversal invariant case is linked to a classical transition line between two magnetically ordered phases.  [Show abstract] [Hide abstract]
ABSTRACT: We investigate the quantum phases of hardcore bosonic atoms in an extended Hubbard model where particles interact via softshoulder potentials in one dimension. Using a combination of fieldtheoretical methods and strongcoupling perturbation theory, we demonstrate that the lowenergy 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 densitymatrixrenormalizationgroup methods, we demonstrate that the CLL phase, first predicted in [Phys. Rev. Lett. 111, 165302 (2013)], is separated from a conventional TomonagaLuttinger 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 weaklydressed Rydberg atoms confined to optical lattices. Using quantum MonteCarlo 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.  [Show abstract] [Hide abstract]
ABSTRACT: Quantum trajectories and superoperator algorithms implemented within the matrix product state (MPS) framework are powerful tools to simulate the realtime dynamics of open dissipative quantum systems. As for the unitary case, the reachable timescales as well as system sizes are limited by the (possible) buildup of entanglement entropy. The aforementioned methods constitute complementary approaches how Lindblad master equations can be integrated relying either on a quasiexact 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 BoseHubbard chain in the presence of local as well as global dephasing. The buildup as well as systemsize 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 spin1 quantum bilinearbiquadratic 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.  [Show abstract] [Hide abstract]
ABSTRACT: We study a dissipative BoseHubbard 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 nontrivial 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.  [Show abstract] [Hide abstract]
ABSTRACT: We study the momentum space entanglement spectra of bosonic and fermionic formulations of the spin1/2 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 manyparticle quantum systems, the spin1/2 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 hardcore 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 BoseHubbard model in the superfluid phase. Remarkably, the finitesize effects are smaller and QMC data are already in impressive agreement with CFT at moderate large sizes.  [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 pairhopping interactions in cold atom gases confined in optical lattices. 
Article: Numerical study of magnetization plateaux in the spin1/2 kagome Heisenberg antiferromagnet
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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 largescale Exact Diagonalization on lattices up to 63 sites.  [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 twoparticle problem. Important distinctions to standard fractional quantum Hall physics are striking: in the absence of particlehole symmetry in a single band, an interactioninduced singlehole 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 BoseHubbard model on the twodimensional 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 boundarylocal (perturbative) structure, the ES exhibits substructures arising from onedimensional 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 lowlying 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 matrixproductstate 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 BoseHubbard model in one dimension where we are able to resolve the quasidegeneracy of the entanglement spectrum in the HaldaneInsulator 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.  [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 twodimensional array of driven, dipolarinteracting 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 nearterm capabilities. Prospects for the realization of such phases in solidstate 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 socalled dynamical transition near the satisfiability threshold. Taken together, these results allow us to elucidate the phase diagram of random $k$QSAT in a twodimensional energydensityclausedensity space.  [Show abstract] [Hide abstract]
ABSTRACT: We show how to measure the ordertwo Renyi entropy of manybody states of spinful fermionic atoms in an optical lattice in equilibrium and nonequilibrium 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 siteand spinresolved 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 FermiHubbard model at finite temperature, and its possible measurement in an experiment using the present scheme.
Publication Stats
3k  Citations  
463.70  Total Impact Points  
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Institutions

20112015

University of Innsbruck
 Department of Theoretical Physics
Innsbruck, Tyrol, Austria


20102012

French National Centre for Scientific Research
Lutetia Parisorum, ÎledeFrance, France 
Max Planck Institute for the Physics of Complex Systems
Dresden, Saxony, Germany


20082011

Max Planck Institute of Physics
München, Bavaria, Germany 
Paul Scherrer Institut
Aargau, Switzerland


2009

Max Planck Institute for Dynamics of Complex Technical Systems
Magdeburg, SaxonyAnhalt, Germany


2007

Ecole polytechnique fédérale de Lausanne
Lausanne, Vaud, Switzerland


20032004

Paul Sabatier University  Toulouse III
 Laboratoire de Physique Théorique  UMR 5152  LPT
Tolosa de Llenguadoc, MidiPyrénées, France
