Andreas Laeuchli

Ludwig-Maximilian-University of Munich, München, Bavaria, Germany

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Publications (107)344.13 Total impact

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    Hitesh J. Changlani, Andreas M. Läuchli
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    ABSTRACT: We study the phase diagram of the spin-1 quantum antiferromagnet on the kagome lattice with nearest neighbor bilinear and biquadratic interactions using exact diagonalization (ED) and the density matrix renormalization group (DMRG) algorithm. Our results indicate that at the Heisenberg point, the ground state is trimerized, in contrast to previous proposals.
    06/2014;
  • Lars Bonnes, Daniel Charrier, Andreas M. Läuchli
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    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.
    05/2014;
  • Lars Bonnes, Fabian H. L. Essler, Andreas M. Läuchli
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    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.
    04/2014;
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    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.
    12/2013;
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    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.
    Physical Review Letters 10/2013; 111(17):173004. · 7.73 Impact Factor
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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 large-scale Exact Diagonalization on lattices up to 63 sites.
    Physical Review B 10/2013; 88(14):144416. · 3.66 Impact Factor
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    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.
    Physical Review Letters 09/2013; 111(12):126802. · 7.73 Impact Factor
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    Vincenzo Alba, Masudul Haque, Andreas M Läuchli
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    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.
    Physical Review Letters 06/2013; 110(26):260403. · 7.73 Impact Factor
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    Chia-Min Chung, Lars Bonnes, Pochung Chen, Andreas M. Läuchli
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    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.
    05/2013;
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    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.
    Physical Review Letters 05/2013; 110(18):185302. · 7.73 Impact Factor
  • Lars Bonnes, Hannes Pichler, Andreas M. Läuchli
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    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.
    Physical review. B, Condensed matter 04/2013; 88(15). · 3.77 Impact Factor
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    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). · 3.04 Impact Factor
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    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.
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    Andreas M. Läuchli
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    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.
    03/2013;
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    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.
    Physical review. B, Condensed matter 02/2013; 87(19). · 3.77 Impact Factor
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    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.
    02/2013;
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    Fabian H. L. Essler, Andreas M. Läuchli, Pasquale Calabrese
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    ABSTRACT: We consider the von Neumann and R\'enyi entropies of the one dimensional quarter-filled Hubbard model. We observe that for periodic boundary conditions the entropies exhibit an unexpected dependence on system size: for L=4 mod 8 the results are in agreement with expectations based on conformal field theory, while for L=0 mod 8 additional contributions arise. We explain this observation in terms of a shell-filling effect, and develop a conformal field theory approach to calculate the extra term in the entropies. Similar shell filling effects in entanglement entropies are expected to be present in higher dimensions and for other multicomponent systems.
    Physical Review Letters 11/2012; 110(11). · 7.73 Impact Factor
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    Zhao Liu, Emil J Bergholtz, Heng Fan, Andreas M Läuchli
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    ABSTRACT: Lattice models forming bands with higher Chern number offer an intriguing possibility for new phases of matter with no analogue in continuum Landau levels. Here, we establish the existence of a number of new bulk insulating states at fractional filling in flat bands with a Chern number C=N>1, forming in a recently proposed pyrochlore model with strong spin-orbit coupling. In particular, we find compelling evidence for a series of stable states at ν=1/(2N+1) for fermions as well as bosonic states at ν=1/(N+1). By examining the topological ground state degeneracies and the excitation structure as well as the entanglement spectrum, we conclude that these states are Abelian. We also explicitly demonstrate that these states are nevertheless qualitatively different from conventional quantum Hall (multilayer) states due to the novel properties of the underlying band structure.
    Physical Review Letters 11/2012; 109(18):186805. · 7.73 Impact Factor
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    ABSTRACT: To understand the role of local sublattice imbalance in low-energy spectra of s=1/2 quantum antiferromagnets, we study the s=1/2 quantum nearest neighbor Heisenberg antiferromagnet on the coordination 3 Cayley tree. We perform many-body calculations using an implementation of the density matrix renormalization group (DMRG) technique for generic tree graphs. We discover that the bond-centered Cayley tree has a quasidegenerate set of a low-lying tower of states and an "anomalous" singlet-triplet finite-size gap scaling. For understanding the construction of the first excited state from the many-body ground state, we consider a wave function ansatz given by the single-mode approximation, which yields a high overlap with the DMRG wave function. Observing the ground-state entanglement spectrum leads us to a picture of the low-energy degrees of freedom being "giant spins" arising out of sublattice imbalance, which helps us analytically understand the scaling of the finite-size spin gap. The Schwinger-boson mean-field theory has been generalized to nonuniform lattices, and ground states have been found which are spatially inhomogeneous in the mean-field parameters.
    Physical review. B, Condensed matter 08/2012; · 3.77 Impact Factor
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    P. Corboz, M. Lajkó, A. M. Läuchli, K. Penc, F. Mila
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    ABSTRACT: In addition to low-energy spin fluctuations, which distinguish them from band insulators, Mott insulators often possess orbital degrees of freedom when crystal-field levels are partially filled. While in most situations spins and orbitals develop long-range order, the possibility for the ground state to be a quantum liquid opens new perspectives. In this paper, we provide clear evidence that the SU(4) symmetric Kugel-Khomskii model on the honeycomb lattice is a quantum spin-orbital liquid. The absence of any form of symmetry breaking - lattice or SU(N) - is supported by a combination of semiclassical and numerical approaches: flavor-wave theory, tensor network algorithm, and exact diagonalizations. In addition, all properties revealed by these methods are very accurately accounted for by a projected variational wave-function based on the \pi-flux state of fermions on the honeycomb lattice at 1/4-filling. In that state, correlations are algebraic because of the presence of a Dirac point at the Fermi level, suggesting that the symmetric Kugel-Khomskii model on the honeycomb lattice is an algebraic quantum spin-orbital liquid. This model provides a good starting point to understand the recently discovered spin-orbital liquid behavior of Ba_3CuSb_2O_9. The present results also suggest to choose optical lattices with honeycomb geometry in the search for quantum liquids in ultra-cold four-color fermionic atoms.
    Physical Review X. 07/2012; 2(4).

Publication Stats

1k Citations
344.13 Total Impact Points

Institutions

  • 2013
    • Ludwig-Maximilian-University of Munich
      • Department of Physics
      München, Bavaria, Germany
  • 2011–2013
    • University of Innsbruck
      • Department of Theoretical Physics
      Innsbruck, Tyrol, Austria
  • 2012
    • French National Centre for Scientific Research
      Lutetia Parisorum, Île-de-France, France
    • Beijing Computational Science Research Center
      Peping, Beijing, China
  • 2010–2011
    • École Polytechnique Fédérale de Lausanne
      • Institut de théorie des phénomènes physiques
      Lausanne, VD, Switzerland
    • Max Planck Institute for the Physics of Complex Systems
      Dresden, Saxony, Germany
  • 2008–2011
    • Max Planck Institute of Physics
      München, Bavaria, Germany
  • 2002–2011
    • ETH Zurich
      • Institute for Theoretical Physics
      Zürich, ZH, Switzerland
  • 2009
    • Rutgers, The State University of New Jersey
      • Department Physics and Astronomy
      New Brunswick, NJ, United States
  • 2008–2009
    • Paul Scherrer Institut
      • Laboratory for Neutron Scattering (LNS)
      Villigen, AG, Switzerland