Quantum emulsion: a glassy phase of bosonic mixtures in optical lattices

We numerically investigate mixtures of two interacting bosonic species with unequal parameters in one-dimensional optical lattices. In large parameter regions full phase segregation is seen to minimize the energy of the system, but the true ground state is masked by an exponentially large number of metastable states characterized by microscopic phase separation. The ensemble of these quantum emulsion states, reminiscent of emulsions of immiscible fluids, has macroscopic properties analogous to those of a Bose glass, namely a finite compressibility in absence of superfluidity. Their metastability is probed by extensive quantum Monte Carlo simulations generating a rich correlated stochastic dynamics. The tuning of the repulsion of one of the two species via a Feshbach resonance drives the system through a quantum phase transition to the superfluid state.Comment: 4 pages, 3 figure

Time-dependent study of disordered models with infinite projected entangled pair states

Infinite projected entangled pair states (iPEPS), the tensor network ansatz for two-dimensional systems in the thermodynamic limit, already provide excellent results on ground-state quantities using either imaginary-time evolution or variational optimisation. Here, we show (i) the feasibility of real-time evolution in iPEPS to simulate the dynamics of an infinite system after a global quench and (ii) the application of disorder-averaging to obtain translationally invariant systems in the presence of disorder. To illustrate the approach, we study the short-time dynamics of the square lattice Heisenberg model in the presence of a bi-valued disorder field

Continuous Tensor Network States for Quantum Fields

We introduce a new class of states for bosonic quantum fields which extend tensor network states to the continuum and generalize continuous matrix product states (cMPS) to spatial dimensions $d\geq 2$. By construction, they are Euclidean invariant, and are genuine continuum limits of discrete tensor network states. Admitting both a functional integral and an operator representation, they share the important properties of their discrete counterparts: expressiveness, invariance under gauge transformations, simple rescaling flow, and compact expressions for the $N$-point functions of local observables. While we discuss mostly the continuous tensor network states extending Projected Entangled Pair States (PEPS), we propose a generalization bearing similarities with the continuum Multi-scale Entanglement Renormalization Ansatz (cMERA).Comment: 16 pages, 5 figures, close to published versio

Combining Tensor Networks with Monte Carlo Methods for Lattice Gauge Theories

Gauged gaussian Projected Entangled Pair States are particular tensor network constructions that describe lattice states of fermionic matter interacting with dynamical gauge fields. We show how one can efficiently compute, using Monte-Carlo techniques, expectation values of physical observables in that class of states. This opens up the possibility of using tensor network techniques to investigate lattice gauge theories in two and three spatial dimensions

Discrete entanglement distribution with squeezed light

We show how one can entangle distant atoms by using squeezed light. Entanglement is obtained in steady state, and can be increased by manipulating the atoms locally. We study the effects of imperfections, and show how to scale up the scheme to build a quantum network.Comment: 5 pages, 4 figure

Ultrafast molecular dynamics in terahertz-STM experiments: Theoretical analysis using Anderson-Holstein model

We analyze ultrafast tunneling experiments in which electron transport through a localized orbital is induced by a single cycle THz pulse. We include both electron-electron and electron-phonon interactions on the localized orbital using the Anderson-Holstein model and consider two possible filling factors, the singly occupied Kondo regime and the doubly occupied regime relevant to recent experiments with a pentacene molecule. Our analysis is based on variational non-Gaussian states and provides the accurate description of the degrees of freedom at very different energies, from the high microscopic energy scales to the Kondo temperature $T_K$. To establish the validity of the new method we apply this formalism to study the Anderson model in the Kondo regime in the absence of coupling to phonons. We demonstrate that it correctly reproduces key properties of the model, including the screening of the impurity spin, formation of the resonance at the Fermi energy, and a linear conductance of $2e^2/h$. We discuss the suppression of the Kondo resonance by the electron-phonon interaction on the impurity site. When analyzing THz STM experiments we compute the time dependence of the key physical quantities, including current, the number of electrons on the localized orbital, and the number of excited phonons. We find long-lived oscillations of the phonon that persist long after the end of the pulse. We compare the results for the interacting system to the non-interacting resonant level model.Comment: 24 pages, 12 figure

Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices

Can high energy physics be simulated by low-energy, non-relativistic, many-body systems, such as ultracold atoms? Such ultracold atomic systems lack the type of symmetries and dynamical properties of high energy physics models: in particular, they manifest neither local gauge invariance nor Lorentz invariance, which are crucial properties of the quantum field theories which are the building blocks of the standard model of elementary particles. However, it turns out, surprisingly, that there are ways to configure atomic system to manifest both local gauge invariance and Lorentz invariance. In particular, local gauge invariance can arise either as an effective, low energy, symmetry, or as an "exact" symmetry, following from the conservation laws in atomic interactions. Hence, one could hope that such quantum simulators may lead to new type of (table-top) experiments, that shall be used to study various QCD phenomena, as the confinement of dynamical quarks, phase transitions, and other effects, which are inaccessible using the currently known computational methods. In this report, we review the Hamiltonian formulation of lattice gauge theories, and then describe our recent progress in constructing quantum simulation of Abelian and non-Abelian lattice gauge theories in 1+1 and 2+1 dimensions using ultracold atoms in optical lattices.Comment: A review; 55 pages, 14 figure

Chiral topological spin liquids with projected entangled pair states

Topological chiral phases are ubiquitous in the physics of the Fractional Quantum Hall Effect. Non-chiral topological spin liquids are also well known. Here, using the framework of projected entangled pair states (PEPS), we construct a family of chiral spin liquids on the square lattice which are generalized spin-1/2 Resonating Valence Bond (RVB) states obtained from deformed local tensors with $d+i\, d$ symmetry. On a cylinder, we construct four topological sectors with even or odd number of spinons on the boundary and even or odd number of ($\mathbb{Z}_2$) fluxes penetrating the cylinder which, we argue, remain orthogonal in the limit of infinite perimeter. The analysis of the transfer matrix provides evidence of short-range (long-range) triplet (singlet) correlations as for the critical (non-chiral) RVB state. The Entanglement Spectrum exhibits chiral edge modes, which we confront to predictions of Conformal Field Theory, and the corresponding Entanglement Hamiltonian is shown to be long ranged.Comment: 7 pages, 6 figures, Final version (small changes