arXiv subjects

Philipp Hauke

Publications and source records attributed to Philipp Hauke.

126 records · Page 7Linked to original sources

arXiv2014

Tomography of band insulators from quench dynamics

We propose a simple scheme for tomography of band-insulating states in one- and two-dimensional optical lattices with two sublattice states. In particular, the scheme maps out the Berry curvature in the entire Brillouin zone and extracts topological invariants such as the Chern number. The measurement relies on observing---via time-of-flight imaging---the time evolution of the momentum distribution following a sudden quench in the band structure. We consider two examples of experimental relevance: the Harper model with $π$-flux and the Haldane model on a honeycomb lattice. Moreover, we illustrate the performance of the scheme in the presence of a parabolic trap, noise, and finite measurement resolution.

cond-mat.quant-gas↗

arXiv2013

Quantum simulation of a lattice Schwinger model in a chain of trapped ions

We discuss how a lattice Schwinger model can be realized in a linear ion trap, allowing a detailed study of the physics of Abelian lattice gauge theories related to one-dimensional quantum electrodynamics. Relying on the rich quantum-simulation toolbox available in state-of-the-art trapped-ion experiments, we show how one can engineer an effectively gauge-invariant dynamics by imposing energetic constraints, provided by strong Ising-like interactions. Applying exact diagonalization to ground-state and time-dependent properties, we study the underlying microscopic model, and discuss undesired interaction terms and other imperfections. As our analysis shows, the proposed scheme allows for the observation in realistic setups of spontaneous parity- and charge-symmetry breaking, as well as false-vacuum decay. Besides an implementation aimed at larger ion chains, we also discuss a minimal setting, consisting of only four ions in a simpler experimental setup, which enables to probe basic physical phenomena related to the full many-body problem. The proposal opens a new route for analog quantum simulation of high-energy and condensed-matter models where gauge symmetries play a prominent role.

cond-mat.quant-gas↗

arXiv2013

Spread of correlations in long-range interacting quantum systems

The non-equilibrium response of a quantum many-body system defines its fundamental transport properties and how initially localized quantum information spreads. However, for long-range-interacting quantum systems little is known. We address this issue by analyzing a local quantum quench in the long-range Ising model in a transverse field, where interactions decay as a variable power-law with distance $\propto r^{-α}$, $α>0$. Using complementary numerical and analytical techniques, we identify three dynamical regimes: short-range-like with an emerging light cone for $α>2$; weakly long-range for $1<α<2$ without a clear light cone but with a finite propagation speed of almost all excitations; and fully non-local for $α<1$ with instantaneous transmission of correlations. This last regime breaks generalized Lieb--Robinson bounds and thus locality. Numerical calculation of the entanglement spectrum demonstrates that the usual picture of propagating quasi-particles remains valid, allowing an intuitive interpretation of our findings via divergences of quasi-particle velocities. Our results may be tested in state-of-the-art trapped-ion experiments.

quant-ph↗

arXiv2013

Density dependent tunneling in the extended Bose-Hubbard model

Recently, it has become apparent that, when the interactions between polar molecules in optical lattices becomes strong, the conventional description using the extended Hubbard model has to be modified by additional terms, in particular a density-dependent tunneling term. We investigate here the influence of this term on the ground-state phase diagrams of the two dimensional extended Bose-Hubbard model. Using Quantum Monte Carlo simulations, we investigate the changes of the superfluid, supersolid, and phase-separated parameter regions in the phase diagram of the system. By studying the interplay of the density-dependent hopping with the usual on-site interaction U and nearest-neighbor repulsion V, we show that the ground-state phase diagrams differ significantly from the ones that are expected from the standard extended Bose-Hubbard model. However we find no indication of pair-superfluid behavior in this two dimensional square lattice study in contrast to the one-dimensional case.

cond-mat.quant-gas↗

arXiv2013

Engineering Ising-XY spin models in a triangular lattice via tunable artificial gauge fields

Emulation of gauge fields for ultracold atoms provides access to a class of exotic states arising in strong magnetic fields. Here we report on the experimental realisation of tunable staggered gauge fields in a periodically driven triangular lattice. For maximal staggered magnetic fluxes, the doubly degenerate superfluid ground state breaks both a discrete Z2 (Ising) symmetry and a continuous U(1) symmetry. By measuring an Ising order parameter, we observe a thermally driven phase transition from an ordered antiferromagnetic to an unordered paramagnetic state and textbook-like magnetisation curves. Both the experimental and theoretical analysis of the coherence properties of the ultracold gas demonstrate the strong influence of the Z2 symmetry onto the condensed phase.

cond-mat.quant-gas↗

arXiv2013

Quantum disorder in the spatially completely anisotropic triangular lattice I: Heisenberg $S=1/2$ antiferromagnet

Spin liquids occuring in 2D frustrated spin systems were initially assumed to appear at strongest frustration, but evidence grows that they more likely intervene at transitions between two different types of order. To identify if this is more general, we here analyze a generalization of the spatially anisotropic triangular lattice (SATL) with antiferromagnetic Heisenberg interactions, the spatially \emph{completely} anisotropic triangular lattice (SCATL). Using Takahashi's modified spin-wave theory, complemented by exact diagonalizations, we find indications that indeed different kinds of order are always separated by disordered phases. Our results further suggest that two gapped non-magnetic phases, identified as distinct in the SATL, are actually continuously connected via the additional anisotropy of the SCATL. Finally, measurements on several materials found magnetic long-range order where calculations on the SATL predict disordered behavior. Our results suggest a simple explanation through the additional anisotropy of the SCATL, which locates the corresponding parameter values in ordered phases. The studied model might therefore not only yield fundamental insight into quantum disordered phases, but should also be relevant for experiments on the quest for spin liquids.

cond-mat.str-el↗

arXiv2012

Quantum spin models with long-range interactions and tunnelings: A quantum Monte Carlo study

We use a quantum Monte Carlo method to investigate various classes of 2D spin models with long-range interactions at low temperatures. In particular, we study a dipolar XXZ model with U(1) symmetry that appears as a hard-core boson limit of an extended Hubbard model describing polarized dipolar atoms or molecules in an optical lattice. Tunneling, in such a model, is short-range, whereas density-density couplings decay with distance following a cubic power law. We investigate also an XXZ model with long-range couplings of all three spin components - such a model describes a system of ultracold ions in a lattice of microtraps. We describe an approximate phase diagram for such systems at zero and at finite temperature, and compare their properties. In particular, we compare the extent of crystalline, super?uid, and supersolid phases. Our predictions apply directly to current experiments with mesoscopic numbers of polar molecules and trapped ions.

cond-mat.quant-gas↗

arXiv2012

Non-Abelian gauge fields and topological insulators in shaken optical lattices

Time-periodic driving like lattice shaking offers a low-demanding method to generate artificial gauge fields in optical lattices. We identify the relevant symmetries that have to be broken by the driving function for that purpose and demonstrate the power of this method by making concrete proposals for its application to two-dimensional lattice systems: We show how to tune frustration and how to create and control band touching points like Dirac cones in the shaken kagomé lattice. We propose the realization of a topological and a quantum spin Hall insulator in a shaken spin-dependent hexagonal lattice. We describe how strong artificial magnetic fields can be achieved for example in a square lattice by employing superlattice modulation. Finally, exemplified on a shaken spin-dependent square lattice, we develop a method to create strong non-Abelian gauge fields.

cond-mat.quant-gas↗

arXiv2012

Can One Trust Quantum Simulators?

Various fundamental phenomena of strongly-correlated quantum systems such as high-$T_c$ superconductivity, the fractional quantum-Hall effect, and quark confinement are still awaiting a universally accepted explanation. The main obstacle is the computational complexity of solving even the most simplified theoretical models that are designed to capture the relevant quantum correlations of the many-body system of interest. In his seminal 1982 paper [Int. J. Theor. Phys. 21, 467], Richard Feynman suggested that such models might be solved by "simulation" with a new type of computer whose constituent parts are effectively governed by a desired quantum many-body dynamics. Measurements on this engineered machine, now known as a "quantum simulator," would reveal some unknown or difficult to compute properties of a model of interest. We argue that a useful quantum simulator must satisfy four conditions: relevance, controllability, reliability, and efficiency. We review the current state of the art of digital and analog quantum simulators. Whereas so far the majority of the focus, both theoretically and experimentally, has been on controllability of relevant models, we emphasize here the need for a careful analysis of reliability and efficiency in the presence of imperfections. We discuss how disorder and noise can impact these conditions, and illustrate our concerns with novel numerical simulations of a paradigmatic example: a disordered quantum spin chain governed by the Ising model in a transverse magnetic field. We find that disorder can decrease the reliability of an analog quantum simulator of this model, although large errors in local observables are introduced only for strong levels of disorder. We conclude that the answer to the question "Can we trust quantum simulators?" is... to some extent.

quant-ph↗

arXiv2012

Dipolar Molecules in Optical Lattices

We study the extended Bose--Hubbard model describing an ultracold gas of dipolar molecules in an optical lattice, taking into account all on-site and nearest-neighbor interactions, including occupation-dependent tunneling and pair tunneling terms. Using exact diagonalization and the multiscale entanglement renormalization ansatz, we show that these terms can destroy insulating phases and lead to novel quantum phases. These considerable changes of the phase diagram have to be taken into account in upcoming experiments with dipolar molecules.

cond-mat.quant-gas↗

arXiv2012

Tunable gauge potential for neutral and spinless particles in driven lattices

We present a universal method to create a tunable, artificial vector gauge potential for neutral particles trapped in an optical lattice. The necessary Peierls phase of the hopping parameters between neighboring lattice sites is generated by applying a suitable periodic inertial force such that the method does not rely on any internal structure of the particles. We experimentally demonstrate the realization of such artificial potentials, which generate ground state superfluids at arbitrary non-zero quasi-momentum. We furthermore investigate possible implementations of this scheme to create tuneable magnetic fluxes, going towards model systems for strong-field physics.

cond-mat.quant-gas↗

arXiv2011

Orbital order of spinless fermions near an optical Feshbach resonance

We study the quantum phases of a three-color Hubbard model that arises in the dynamics of the p-band orbitals of spinless fermions in an optical lattice. Strong, color-dependent interactions are induced by an optical Feshbach resonance. Starting from the microscopic scattering properties of ultracold atoms, we derive the orbital exchange constants at 1/3 filling on the cubic optical lattice. Using this, we compute the phase diagram in a Gutzwiller ansatz. We find novel phases with 'axial orbital order' in which pz and px + ipy (or px - ipy) orbitals alternate.

cond-mat.quant-gas↗

arXiv2010

Modified spin-wave theory with ordering vector optimization II: Spatially anisotropic triangular lattice and $J_1J_2J_3$ model with Heisenberg interactions

We study the ground state phases of the $S=1/2$ Heisenberg quantum antiferromagnet on the spatially anisotropic triangular lattice and on the square lattice with up to next-next-nearest neighbor coupling (the $J_1J_2J_3$ model), making use of Takahashi's modified spin-wave (MSW) theory supplemented by ordering vector optimization. We compare the MSW results with exact diagonalization and projected-entangled-pair-states calculations, demonstrating their qualitative and quantitative reliability. We find that MSW theory correctly accounts for strong quantum effects on the ordering vector of the magnetic phases of the models under investigation: in particular collinear magnetic order is promoted at the expenses of non-collinear (spiral) order, and several spiral states which are stable at the classical level, disappear from the quantum phase diagram. Moreover, collinear states and non-collinear ones are never connected continuously, but they are separated by parameter regions in which MSW breaks down, signaling the possible appearance of a non-magnetic ground state. In the case of the spatially anisotropic triangular lattice, a large breakdown region appears also for weak couplings between the chains composing the lattice, suggesting the possible occurrence of a large non-magnetic region continuously connected with the spin-liquid state of the uncoupled chains.

cond-mat.str-el↗

arXiv2010

Bose-Hubbard model with occupation dependent parameters

We study the ground-state properties of ultracold bosons in an optical lattice in the regime of strong interactions. The system is described by a non-standard Bose-Hubbard model with both occupation-dependent tunneling and on-site interaction. We find that for sufficiently strong coupling the system features a phase-transition from a Mott insulator with one particle per site to a superfluid of spatially extended particle pairs living on top of the Mott background -- instead of the usual transition to a superfluid of single particles/holes. Increasing the interaction further, a superfluid of particle pairs localized on a single site (rather than being extended) on top of the Mott background appears. This happens at the same interaction strength where the Mott-insulator phase with 2 particles per site is destroyed completely by particle-hole fluctuations for arbitrarily small tunneling. In another regime, characterized by weak interaction, but high occupation numbers, we observe a dynamical instability in the superfluid excitation spectrum. The new ground state is a superfluid, forming a 2D slab, localized along one spatial direction that is spontaneously chosen.

cond-mat.quant-gas↗

arXiv2010

Complete devil's staircase and crystal--superfluid transitions in a dipolar XXZ spin chain: A trapped ion quantum simulation

Systems with long-range interactions show a variety of intriguing properties: they typically accommodate many meta-stable states, they can give rise to spontaneous formation of supersolids, and they can lead to counterintuitive thermodynamic behavior. However, the increased complexity that comes with long-range interactions strongly hinders theoretical studies. This makes a quantum simulator for long-range models highly desirable. Here, we show that a chain of trapped ions can be used to quantum simulate a one-dimensional model of hard-core bosons with dipolar off-site interaction and tunneling, equivalent to a dipolar XXZ spin-1/2 chain. We explore the rich phase diagram of this model in detail, employing perturbative mean-field theory, exact diagonalization, and quasiexact numerical techniques (density-matrix renormalization group and infinite time evolving block decimation). We find that the complete devil's staircase -- an infinite sequence of crystal states existing at vanishing tunneling -- spreads to a succession of lobes similar to the Mott-lobes found in Bose--Hubbard models. Investigating the melting of these crystal states at increased tunneling, we do not find (contrary to similar two-dimensional models) clear indications of supersolid behavior in the region around the melting transition. However, we find that inside the insulating lobes there are quasi-long range (algebraic) correlations, opposed to models with nearest-neighbor tunneling which show exponential decay of correlations.

cond-mat.quant-gas↗

arXiv2010

Multi-Component Quantum Gases in Spin-Dependent Hexagonal Lattices

Periodicity is one of the most fundamental structural characteristics of systems occurring in nature. The properties of these systems depend strongly on the symmetry of the underlying periodic structure. In solid state materials - for example - the static and transport properties as well as the magnetic and electronic characteristics are crucially influenced by the crystal symmetry. In this context, hexagonal structures play an extremely important role and lead to novel physics like that of carbon nanotubes or graphene. Here we report on the first realization of ultracold atoms in a spin-dependent optical lattice with hexagonal symmetry. We show how combined effects of the lattice and interactions between atoms lead to a forced antiferromagnetic Néel order when two spin-components localize at different lattice sites. We also demonstrate that the coexistence of two components - one Mott-insulating and the other one superfluid - leads to the formation of a forced supersolid. Our observations are consistent with theoretical predictions using Gutzwiller mean-field theory.

cond-mat.quant-gas↗

arXiv2010

Frustrated quantum antiferromagnetism with ultracold bosons in a triangular lattice

We propose to realize the anisotropic triangular-lattice Bose-Hubbard model with positive tunneling matrix elements by using ultracold atoms in an optical lattice dressed by a fast lattice oscillation. This model exhibits frustrated antiferromagnetism at experimentally feasible temperatures; it interpolates between a classical rotor model for weak interaction, and a quantum spin-1/2 $XY$-model in the limit of hard-core bosons. This allows to explore experimentally gapped spin liquid phases predicted recently [Schmied et al., New J. Phys. {\bf 10}, 045017 (2008)].

cond-mat.quant-gas↗

arXiv2009

Modified spin-wave theory with ordering vector optimization I: frustrated bosons on the spatially anisotropic triangular lattice

We investigate a system of frustrated hardcore bosons, modeled by an XY antiferromagnet on the spatially anisotropic triangular lattice, using Takahashi's modified spin-wave (MSW) theory. In particular we implement ordering vector optimization on the ordered reference state of MSW theory, which leads to significant improvement of the theory and accounts for quantum corrections to the classically ordered state. The MSW results at zero temperature compare favorably to exact diagonalization (ED) and projected entangled-pair state (PEPS) calculations. The resulting zero-temperature phase diagram includes a 1D quasi-ordered phase, a 2D Neel ordered phase, and a 2D spiraling ordered phase. We have strong indications that the various ordered or quasi-ordered phases are separated by spin-liquid phases with short-range correlations, in analogy to what has been predicted for the Heisenberg model on the same lattice. Within MSW theory we also explore the finite-temperature phase diagram. We find that the zero-temperature long-range-ordered phases turn into quasi-ordered phases (up to a Berezinskii-Kosterlitz-Thouless temperature), while zero-temperature quasi-ordered phases become short-range correlated at finite temperature. These results show that modified spin-wave theory is very well suited for describing ordered and quasi-ordered phases of frustrated XY spins (or, equivalently, of frustrated lattice bosons) both at zero and finite temperatures. While MSW theory, just as other theoretical methods, cannot describe spin-liquid phases, its breakdown provides a fast method for singling out Hamiltonians which may feature these intriguing quantum phases. We thus suggest a tool for guiding our search for interesting systems whose properties are necessarily studied with a physical quantum simulator.

cond-mat.quant-gas↗